Deformations in graphene are central elements in the novel field of "straintronics". Various stra... more Deformations in graphene are central elements in the novel field of "straintronics". Various strain geometries have been to produce specific properties but their experimental realization has been limited. Because folds occur naturally in graphene samples, or could be engineered with appropriate substrates, we study their effects on graphene transport properties [1]. We show the existence of an enhanced local density of states (LDOS) along the fold that originates from localization of higher energy states, and provides extra conductance channels at lower energies. In addition to exhibit sublattice symmetry breaking, these states are valley polarized, with quasi-ballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making folds viable electronic waveguides. These findings could be tested in currently available experimental settings.
One of the fundamental properties of spin 1/2 particles is their interaction with magnetic fields... more One of the fundamental properties of spin 1/2 particles is their interaction with magnetic fields. The exploration of this coupling can be quite elusive, for example in the case of neutrinos. Graphene has been shown to be a condensed matter platform for the study of such ultrarelativistic particles, with its neutrino-like charge carriers having a spin-like degree of freedom called pseudospin. Here we show that in analogy to the spin alignment of a fermion in a magnetic field, the pseudo-spin of graphene can be oriented by a strain induced pseudo-magnetic field through the Zeeman term. We reveal this pseudo-spin polarization as a sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunnelling microscope. The observed pseudo-spin polarization scales with the lifting height of the strained deformation and therefore with the pseudo-magnetic field strength. Its magnitude is quantitatively reproduced by analytic and tight-binding models. This adds a key i...
We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter appro... more We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cutoff plane wave. We show that the probability density is governed by an interplay between diffraction in time and Zitterbewegung phenomena, typical of relativistic quantum shutter systems with nonzero mass. The time-diffraction appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. 88, 625] for Schrödinger free matter-waves. The Zitterbewegung manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, ky, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the Zitterbewegung appears as a series of quantum beats in the probability density, with a beating frequency 2kyvF , where vF is the Fermi velocity.
Graphene's electronic structure can be fundamentally altered when a substrate-or adatom-induced K... more Graphene's electronic structure can be fundamentally altered when a substrate-or adatom-induced Kekulé superlattice couples the valley and isospin degrees of freedom. Here, we show that the band structure of Kekulétextured graphene can be re-engineered through layer stacking. We predict a family of Kekulé graphene bilayers that exhibit band structures with up to six valleys, and room-temperature Dirac quasiparticles whose masses can be tuned electrostatically. Fermi velocities half as large as in pristine graphene put this system in the strongly coupled regime, where correlated ground states can be expected.
We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kek... more We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity κ xy at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of κ xy as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, κ xy can be easily tuned with external parameters such as the magnetic field and temperature.
physica status solidi (RRL) - Rapid Research Letters, 2018
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic prope... more The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The deformation is taken into account by introducing its corresponding pseudo-vector and pseudo-scalar potentials in the Dirac equation. By using a transformation to the time-cone of the strain wave, the Dirac equation is reduced to an ordinary second-order differential Matthieu equation, i.e., to a parametric pendulum, giving a spectrum of bands and gaps determined by resonance conditions between the electron and ripple wave-vector (G), and their incidence angles. The location of the nth gap is thus determined by E ≈ nvF G, where vF is the Fermi velocity. Physically, gaps are produced by diffraction of electrons in phase with the wave. The propagation is mainly in the direction of the ripple. In the case of a pure pseudoelectric field and for energies lower than a certain threshold, we found a different kind of equation. Its analytical solutions are in excellent agreement with the numerical solutions. The wavefunctions can be expressed in terms of the Matthieu cosine and sine functions, and for the case of a pure pseudo-electric potential, as a combination of Bessel functions.
A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin... more A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekulé-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the dispersion relation and present analytical expressions for the low-energy limit. Our results indicate the emergence of a Zeeman-like term due to the coupling of the pseudospin with the pseudomagnetic strain potential which separates the valleys by moving them in opposite directions away from the center of the Brillouin zone. For the Kek-O phase, this results in a competition between the Kekulé parameter that opens a gap and the magnitude of strain which closes it. While for the Kek-Y phase, in a superposition of two shifted Dirac cones. As the Dirac cones are much closer in the supperlattice reciprocal space that in pristine graphene, we propose strain as a control parameter for intervalley scattering.
We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya int... more We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magnon insulator. We find four topological phases in terms of the KC parameter and the DMI strength. We present the bulk-edge correspondence for the magnons in a honeycomb lattice with an armchair or a zigzag boundary. Furthermore, we find Tamm-like edge states due to the intrinsic on-site interactions along the boundary sites. Our results may have significant implications to magnon transport properties in the 2D magnets at low temperatures.
We study the electron scattering produced by local out-of-plane strain deformations in the form o... more We study the electron scattering produced by local out-of-plane strain deformations in the form of Gaussian bumps in graphene. Of special interest is to take into account the scalar field associated with the redistribution of charge due to deformations, and in the same footing as the pseudomagnetic field. Working with the Born approximation approach we show analytically that even when a relatively small scalar field is considered, a strong backscattering and enhancement of the valley splitting effect could arise as a function of the energy and angle of incidence. In addition, we find that the valley polarization can reverse its sign as the incident energy is increased. These behaviors are totally absent if the scalar field is neglected or screened. Interestingly, we find that there is a further possibility of controlling the valley scattering polarization purely by electrical means through the presence of external scalar fields in combination with strain fields. These results are supported by quantum dynamical simulations of electron wave packets. Results for the average trajectories of wave packets in locally strained graphene clearly show focusing and beam splitting effects enhanced by the presence of the scalar field that can be of interest in the implementation of valleytronic devices.
Deformations in graphene systems are central elements in the novel field of straintronics. Variou... more Deformations in graphene systems are central elements in the novel field of straintronics. Various strain geometries have been proposed to produce specific properties but their experimental realization has been limited. Because strained folds can be engineered on graphene samples on appropriate substrates, we study their effects on graphene transport properties. We show the existence of an enhanced local density of states (LDOS) along the direction of the strained fold that originates from localization of higher energy states, and provides extra conductance channels at lower energies. In addition to exhibit sublattice symmetry breaking, these states are valley polarized, with quasi-ballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making these geometries viable electronic waveguides. These findings could be tested in properly engineered experimental settings.
We study transport properties of hexagonal zigzag graphene quantum rings connected to semiinfinit... more We study transport properties of hexagonal zigzag graphene quantum rings connected to semiinfinite nanoribbons. Open twofold symmetric structures support localized states that can be traced back to those existing in the isolated six-fold symmetric rings. Using a tight-binding Hamiltonian within the Green's function formalism, we show that an external magnetic field promotes these localized states to Fano resonances with robust signatures in transport. Local density of states and current distributions of the resonant states are calculated as a function of the magnetic flux intensity. For structures on corrugated substrates we analyze the effect of strain by including an outof-plane centro-symmetric deformation in the model. We show that small strains shift the resonance positions without further modifications, while high strains introduce new ones.
The coupling of geometrical and electronic properties is a promising avenue to engineer conductio... more The coupling of geometrical and electronic properties is a promising avenue to engineer conduction properties in graphene. Confinement added to strain allows for interplay of different transport mechanisms with potential device applications. In particular, strain-predicted to produce localized states similar to those in an external magnetic field-can be tailored for desired transport properties. To investigate specific strain signatures on transport in confined geometries, we focus on graphene nanoribbons with different edge terminations and circularly symmetric deformations. In particular, we study nanoribbons with an inhomogeneous, out of plane Gaussian bump deformation, connected to reservoirs, with and without external magnetic field. We use the tight-binding approximation with the deformation described by elasticity theory. Using the recursive Green function algorithm, we calculate the local density of states and obtain the Landauer conductance. An enhancement of the density of states in the deformed region, similar to the one appearing with constant fields in confined regions is observed. We show how these confined states give rise to peculiar features in the emerging Landau levels and discuss their effect on the overall conductance.
The coupling of geometrical and electronic properties is a promising venue to engineer conduction... more The coupling of geometrical and electronic properties is a promising venue to engineer conduction properties in graphene. Confinement added to strain allows for interplay of different transport mechanisms with potential device applications. To investigate strain signatures on transport in confined geometries, we focus on graphene nanoribbons (GNR) with circularly symmetric deformations. In particular, we study GNR with an inhomogeneous, out of plane Gaussian deformation, connected to reservoirs. We observe an enhancement of the density of states in the deformed region, accompanied with a decrease in the conductance, signaling the presence of confined states. The local density of states exhibits a six-fold symmetric structure with an oscillating sub-lattice occupation asymmetry, that persist for a wide range of energy and model parameters.
The formation of a superlattice in graphene can serve as a way to modify its electronic bandstruc... more The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered ν = ±1 Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekulé parameter in graphene nanoribbons.
We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya int... more We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magnon insulator. We find four topological phases in terms of the KC parameter and the DMI strength. We present the bulk-edge correspondence for the magnons in a honeycomb lattice with an armchair or a zigzag boundary. Furthermore, we find Tamm-like edge states due to the intrinsic on-site interactions along the boundary sites. Our results may have significant implications to magnon transport properties in the 2D magnets at low temperatures.
We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kek... more We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity κ xy at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of κ xy as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, κ xy can be easily tuned with external parameters such as the magnetic field and temperature.
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic prope... more The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The deformation is taken into account by introducing its corresponding pseudo-vector and pseudo-scalar potentials in the Dirac equation. By using a transformation to the time-cone of the strain wave, the Dirac equation is reduced to an ordinary second-order differential Matthieu equation, i.e., to a parametric pendulum, giving a spectrum of bands and gaps determined by resonance conditions between the electron and ripple wave-vector (G), and their incidence angles. The location of the nth gap is thus determined by E ≈ nvF G, where vF is the Fermi velocity. Physically, gaps are produced by diffraction of electrons in phase with the wave. The propagation is mainly in the direction of the ripple. In the case of a pure pseudoelectric field and for energies lower than a certain threshold, we found a different kind of equation. Its analytical solutions are in excellent agreement with the numerical solutions. The wavefunctions can be expressed in terms of the Matthieu cosine and sine functions, and for the case of a pure pseudo-electric potential, as a combination of Bessel functions.
The formation of a superlattice in graphene can serve as a way to modify its electronic bandstruc... more The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered ν = ±1 Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekulé parameter in graphene nanoribbons.
We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter appro... more We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cutoff plane wave. We show that the probability density is governed by an interplay between diffraction in time and Zitterbewegung phenomena , typical of relativistic quantum shutter systems with nonzero mass. The time-diffraction appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshin-sky in 1952 [Phys. Rev. 88, 625] for Schrödinger free matter-waves. The Zitterbewegung manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, ky, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the Zitter-bewegung appears as a series of quantum beats in the probability density, with a beating frequency 2kyvF , where vF is the Fermi velocity. Since the experimental discovery of graphene 1 , the study of two-dimensional (2D) Dirac fermions in condensed matter physics has become of great interest both at the fundamental and applied levels 2. Graphene exhibits a dispersion relation with two bands touching at two singular points at the corners of the Bril-louin zone. Near these Dirac points the spectrum is linear in momentum, and the electronic excitations are described by a Dirac-like equation for massless particles 3,4. Nevertheless, graphene is not the only condensed matter system that exhibits an effective Dirac Hamiltonian 5 , other examples include silicene 6 , germanene 7 , Pmmn borophene 8 , cold atoms systems 9 , and topological insulators 10. These materials constitute the so call Dirac matter, and due to its relativis-tic Hamiltonian they have allowed probing several phenomena originally predicted by quantum electrodynam-ics, such as Klein tunneling 11,12 and the Zitterbewegung (ZBW) effect 13-16 , which have now become available to experimentalists 17,18. While the Klein tunneling occurs at equilibrium, the ZBW being an oscillation is an out of equilibrium effect, and in fact it appears as a transient phenomenon in two-dimensional Dirac systems 14,15. In general, transient effects 19-21 arise from the properties of quantum waves involving either relativistic or non-relativistic equations subject to sudden changes as initial condition. The most representative transient effect is the diffraction in time (DIT) of free matter-waves, predicted by Moshinsky 22 (1952) using a non-relativistic plane wave quantum-shutter model. A quantum-shutter setup involves a cutoff plane wave representing a matter-wave beam initially confined in a region of space (x < 0), stopped by an absorbing shutter at x = 0. After opening the shutter at t = 0, the free Schrödinger probability density exhibits a distinctive DIT 22,23 oscillatory pattern, similar to the intensity profile of a light beam diffracted by a straight edge. The DIT effect was later verified by multiple condensed matter experiments involving ultracold atoms 24 , cold-neutrons 25 , and atomic Bose-Einstein condensates 26. Also, the understanding and control of the features of DIT are of relevance, for example, in the field of atom lasers 27-29 , which operate by extracting matter-waves from Bose-Einstein conden-sates. After Moshinsky's seminal paper, several theoretical works have addressed the study of transients using various initial quantum states as well as generalizations of the shutter model to explore time-dependent phenomena 20. However, most of these works were developed in the non-relativistic context. The first studies regarding relativistic transients involved solutions to the Klein-Gordon 22 and Dirac 30 equations for a free massive three-dimensional particle moving in one-dimension within a plane wave quantum-shutter model. Some later works explored issues such as non-locality, forerunners, and time scales, using different types of relativistic initial conditions 31-38. A nice feature of these approaches is that they can describe electronic dynamics based on exact analytical solutions, which may provide a useful tool for exploring time-dependent features of 2D Dirac-matter. Moreover, although the transport effects in these 2D systems have been studied 14,15 and the importance of transient phenomena has been stressed, until now (and up to our knowledge) the DIT for two-dimensional mass-less Dirac particles have not been explored. In this work we present a new approach based on a quantum shutter model to study transient effects in 2D massless Dirac matter. By considering the Hamiltonian for graphene as typical example, we derive an exact analytical solution to explore the systems dynamics, that can be generalize to other 2D Dirac massless materials. We find that the probability density of massless Dirac-fermions exhibit two transient effects previously observed (DIT) or overlooked (ZBW) in quantum shutter approaches involving relativistic systems with non-zero arXiv:1912.08800v1 [cond-mat.mes-hall]
Deformations in graphene are central elements in the novel field of "straintronics". Various stra... more Deformations in graphene are central elements in the novel field of "straintronics". Various strain geometries have been to produce specific properties but their experimental realization has been limited. Because folds occur naturally in graphene samples, or could be engineered with appropriate substrates, we study their effects on graphene transport properties [1]. We show the existence of an enhanced local density of states (LDOS) along the fold that originates from localization of higher energy states, and provides extra conductance channels at lower energies. In addition to exhibit sublattice symmetry breaking, these states are valley polarized, with quasi-ballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making folds viable electronic waveguides. These findings could be tested in currently available experimental settings.
One of the fundamental properties of spin 1/2 particles is their interaction with magnetic fields... more One of the fundamental properties of spin 1/2 particles is their interaction with magnetic fields. The exploration of this coupling can be quite elusive, for example in the case of neutrinos. Graphene has been shown to be a condensed matter platform for the study of such ultrarelativistic particles, with its neutrino-like charge carriers having a spin-like degree of freedom called pseudospin. Here we show that in analogy to the spin alignment of a fermion in a magnetic field, the pseudo-spin of graphene can be oriented by a strain induced pseudo-magnetic field through the Zeeman term. We reveal this pseudo-spin polarization as a sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunnelling microscope. The observed pseudo-spin polarization scales with the lifting height of the strained deformation and therefore with the pseudo-magnetic field strength. Its magnitude is quantitatively reproduced by analytic and tight-binding models. This adds a key i...
We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter appro... more We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cutoff plane wave. We show that the probability density is governed by an interplay between diffraction in time and Zitterbewegung phenomena, typical of relativistic quantum shutter systems with nonzero mass. The time-diffraction appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. 88, 625] for Schrödinger free matter-waves. The Zitterbewegung manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, ky, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the Zitterbewegung appears as a series of quantum beats in the probability density, with a beating frequency 2kyvF , where vF is the Fermi velocity.
Graphene's electronic structure can be fundamentally altered when a substrate-or adatom-induced K... more Graphene's electronic structure can be fundamentally altered when a substrate-or adatom-induced Kekulé superlattice couples the valley and isospin degrees of freedom. Here, we show that the band structure of Kekulétextured graphene can be re-engineered through layer stacking. We predict a family of Kekulé graphene bilayers that exhibit band structures with up to six valleys, and room-temperature Dirac quasiparticles whose masses can be tuned electrostatically. Fermi velocities half as large as in pristine graphene put this system in the strongly coupled regime, where correlated ground states can be expected.
We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kek... more We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity κ xy at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of κ xy as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, κ xy can be easily tuned with external parameters such as the magnetic field and temperature.
physica status solidi (RRL) - Rapid Research Letters, 2018
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic prope... more The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The deformation is taken into account by introducing its corresponding pseudo-vector and pseudo-scalar potentials in the Dirac equation. By using a transformation to the time-cone of the strain wave, the Dirac equation is reduced to an ordinary second-order differential Matthieu equation, i.e., to a parametric pendulum, giving a spectrum of bands and gaps determined by resonance conditions between the electron and ripple wave-vector (G), and their incidence angles. The location of the nth gap is thus determined by E ≈ nvF G, where vF is the Fermi velocity. Physically, gaps are produced by diffraction of electrons in phase with the wave. The propagation is mainly in the direction of the ripple. In the case of a pure pseudoelectric field and for energies lower than a certain threshold, we found a different kind of equation. Its analytical solutions are in excellent agreement with the numerical solutions. The wavefunctions can be expressed in terms of the Matthieu cosine and sine functions, and for the case of a pure pseudo-electric potential, as a combination of Bessel functions.
A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin... more A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekulé-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the dispersion relation and present analytical expressions for the low-energy limit. Our results indicate the emergence of a Zeeman-like term due to the coupling of the pseudospin with the pseudomagnetic strain potential which separates the valleys by moving them in opposite directions away from the center of the Brillouin zone. For the Kek-O phase, this results in a competition between the Kekulé parameter that opens a gap and the magnitude of strain which closes it. While for the Kek-Y phase, in a superposition of two shifted Dirac cones. As the Dirac cones are much closer in the supperlattice reciprocal space that in pristine graphene, we propose strain as a control parameter for intervalley scattering.
We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya int... more We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magnon insulator. We find four topological phases in terms of the KC parameter and the DMI strength. We present the bulk-edge correspondence for the magnons in a honeycomb lattice with an armchair or a zigzag boundary. Furthermore, we find Tamm-like edge states due to the intrinsic on-site interactions along the boundary sites. Our results may have significant implications to magnon transport properties in the 2D magnets at low temperatures.
We study the electron scattering produced by local out-of-plane strain deformations in the form o... more We study the electron scattering produced by local out-of-plane strain deformations in the form of Gaussian bumps in graphene. Of special interest is to take into account the scalar field associated with the redistribution of charge due to deformations, and in the same footing as the pseudomagnetic field. Working with the Born approximation approach we show analytically that even when a relatively small scalar field is considered, a strong backscattering and enhancement of the valley splitting effect could arise as a function of the energy and angle of incidence. In addition, we find that the valley polarization can reverse its sign as the incident energy is increased. These behaviors are totally absent if the scalar field is neglected or screened. Interestingly, we find that there is a further possibility of controlling the valley scattering polarization purely by electrical means through the presence of external scalar fields in combination with strain fields. These results are supported by quantum dynamical simulations of electron wave packets. Results for the average trajectories of wave packets in locally strained graphene clearly show focusing and beam splitting effects enhanced by the presence of the scalar field that can be of interest in the implementation of valleytronic devices.
Deformations in graphene systems are central elements in the novel field of straintronics. Variou... more Deformations in graphene systems are central elements in the novel field of straintronics. Various strain geometries have been proposed to produce specific properties but their experimental realization has been limited. Because strained folds can be engineered on graphene samples on appropriate substrates, we study their effects on graphene transport properties. We show the existence of an enhanced local density of states (LDOS) along the direction of the strained fold that originates from localization of higher energy states, and provides extra conductance channels at lower energies. In addition to exhibit sublattice symmetry breaking, these states are valley polarized, with quasi-ballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making these geometries viable electronic waveguides. These findings could be tested in properly engineered experimental settings.
We study transport properties of hexagonal zigzag graphene quantum rings connected to semiinfinit... more We study transport properties of hexagonal zigzag graphene quantum rings connected to semiinfinite nanoribbons. Open twofold symmetric structures support localized states that can be traced back to those existing in the isolated six-fold symmetric rings. Using a tight-binding Hamiltonian within the Green's function formalism, we show that an external magnetic field promotes these localized states to Fano resonances with robust signatures in transport. Local density of states and current distributions of the resonant states are calculated as a function of the magnetic flux intensity. For structures on corrugated substrates we analyze the effect of strain by including an outof-plane centro-symmetric deformation in the model. We show that small strains shift the resonance positions without further modifications, while high strains introduce new ones.
The coupling of geometrical and electronic properties is a promising avenue to engineer conductio... more The coupling of geometrical and electronic properties is a promising avenue to engineer conduction properties in graphene. Confinement added to strain allows for interplay of different transport mechanisms with potential device applications. In particular, strain-predicted to produce localized states similar to those in an external magnetic field-can be tailored for desired transport properties. To investigate specific strain signatures on transport in confined geometries, we focus on graphene nanoribbons with different edge terminations and circularly symmetric deformations. In particular, we study nanoribbons with an inhomogeneous, out of plane Gaussian bump deformation, connected to reservoirs, with and without external magnetic field. We use the tight-binding approximation with the deformation described by elasticity theory. Using the recursive Green function algorithm, we calculate the local density of states and obtain the Landauer conductance. An enhancement of the density of states in the deformed region, similar to the one appearing with constant fields in confined regions is observed. We show how these confined states give rise to peculiar features in the emerging Landau levels and discuss their effect on the overall conductance.
The coupling of geometrical and electronic properties is a promising venue to engineer conduction... more The coupling of geometrical and electronic properties is a promising venue to engineer conduction properties in graphene. Confinement added to strain allows for interplay of different transport mechanisms with potential device applications. To investigate strain signatures on transport in confined geometries, we focus on graphene nanoribbons (GNR) with circularly symmetric deformations. In particular, we study GNR with an inhomogeneous, out of plane Gaussian deformation, connected to reservoirs. We observe an enhancement of the density of states in the deformed region, accompanied with a decrease in the conductance, signaling the presence of confined states. The local density of states exhibits a six-fold symmetric structure with an oscillating sub-lattice occupation asymmetry, that persist for a wide range of energy and model parameters.
The formation of a superlattice in graphene can serve as a way to modify its electronic bandstruc... more The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered ν = ±1 Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekulé parameter in graphene nanoribbons.
We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya int... more We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magnon insulator. We find four topological phases in terms of the KC parameter and the DMI strength. We present the bulk-edge correspondence for the magnons in a honeycomb lattice with an armchair or a zigzag boundary. Furthermore, we find Tamm-like edge states due to the intrinsic on-site interactions along the boundary sites. Our results may have significant implications to magnon transport properties in the 2D magnets at low temperatures.
We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kek... more We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity κ xy at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of κ xy as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, κ xy can be easily tuned with external parameters such as the magnetic field and temperature.
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic prope... more The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The deformation is taken into account by introducing its corresponding pseudo-vector and pseudo-scalar potentials in the Dirac equation. By using a transformation to the time-cone of the strain wave, the Dirac equation is reduced to an ordinary second-order differential Matthieu equation, i.e., to a parametric pendulum, giving a spectrum of bands and gaps determined by resonance conditions between the electron and ripple wave-vector (G), and their incidence angles. The location of the nth gap is thus determined by E ≈ nvF G, where vF is the Fermi velocity. Physically, gaps are produced by diffraction of electrons in phase with the wave. The propagation is mainly in the direction of the ripple. In the case of a pure pseudoelectric field and for energies lower than a certain threshold, we found a different kind of equation. Its analytical solutions are in excellent agreement with the numerical solutions. The wavefunctions can be expressed in terms of the Matthieu cosine and sine functions, and for the case of a pure pseudo-electric potential, as a combination of Bessel functions.
The formation of a superlattice in graphene can serve as a way to modify its electronic bandstruc... more The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekulé distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered ν = ±1 Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekulé parameter in graphene nanoribbons.
We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter appro... more We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cutoff plane wave. We show that the probability density is governed by an interplay between diffraction in time and Zitterbewegung phenomena , typical of relativistic quantum shutter systems with nonzero mass. The time-diffraction appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshin-sky in 1952 [Phys. Rev. 88, 625] for Schrödinger free matter-waves. The Zitterbewegung manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, ky, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the Zitter-bewegung appears as a series of quantum beats in the probability density, with a beating frequency 2kyvF , where vF is the Fermi velocity. Since the experimental discovery of graphene 1 , the study of two-dimensional (2D) Dirac fermions in condensed matter physics has become of great interest both at the fundamental and applied levels 2. Graphene exhibits a dispersion relation with two bands touching at two singular points at the corners of the Bril-louin zone. Near these Dirac points the spectrum is linear in momentum, and the electronic excitations are described by a Dirac-like equation for massless particles 3,4. Nevertheless, graphene is not the only condensed matter system that exhibits an effective Dirac Hamiltonian 5 , other examples include silicene 6 , germanene 7 , Pmmn borophene 8 , cold atoms systems 9 , and topological insulators 10. These materials constitute the so call Dirac matter, and due to its relativis-tic Hamiltonian they have allowed probing several phenomena originally predicted by quantum electrodynam-ics, such as Klein tunneling 11,12 and the Zitterbewegung (ZBW) effect 13-16 , which have now become available to experimentalists 17,18. While the Klein tunneling occurs at equilibrium, the ZBW being an oscillation is an out of equilibrium effect, and in fact it appears as a transient phenomenon in two-dimensional Dirac systems 14,15. In general, transient effects 19-21 arise from the properties of quantum waves involving either relativistic or non-relativistic equations subject to sudden changes as initial condition. The most representative transient effect is the diffraction in time (DIT) of free matter-waves, predicted by Moshinsky 22 (1952) using a non-relativistic plane wave quantum-shutter model. A quantum-shutter setup involves a cutoff plane wave representing a matter-wave beam initially confined in a region of space (x < 0), stopped by an absorbing shutter at x = 0. After opening the shutter at t = 0, the free Schrödinger probability density exhibits a distinctive DIT 22,23 oscillatory pattern, similar to the intensity profile of a light beam diffracted by a straight edge. The DIT effect was later verified by multiple condensed matter experiments involving ultracold atoms 24 , cold-neutrons 25 , and atomic Bose-Einstein condensates 26. Also, the understanding and control of the features of DIT are of relevance, for example, in the field of atom lasers 27-29 , which operate by extracting matter-waves from Bose-Einstein conden-sates. After Moshinsky's seminal paper, several theoretical works have addressed the study of transients using various initial quantum states as well as generalizations of the shutter model to explore time-dependent phenomena 20. However, most of these works were developed in the non-relativistic context. The first studies regarding relativistic transients involved solutions to the Klein-Gordon 22 and Dirac 30 equations for a free massive three-dimensional particle moving in one-dimension within a plane wave quantum-shutter model. Some later works explored issues such as non-locality, forerunners, and time scales, using different types of relativistic initial conditions 31-38. A nice feature of these approaches is that they can describe electronic dynamics based on exact analytical solutions, which may provide a useful tool for exploring time-dependent features of 2D Dirac-matter. Moreover, although the transport effects in these 2D systems have been studied 14,15 and the importance of transient phenomena has been stressed, until now (and up to our knowledge) the DIT for two-dimensional mass-less Dirac particles have not been explored. In this work we present a new approach based on a quantum shutter model to study transient effects in 2D massless Dirac matter. By considering the Hamiltonian for graphene as typical example, we derive an exact analytical solution to explore the systems dynamics, that can be generalize to other 2D Dirac massless materials. We find that the probability density of massless Dirac-fermions exhibit two transient effects previously observed (DIT) or overlooked (ZBW) in quantum shutter approaches involving relativistic systems with non-zero arXiv:1912.08800v1 [cond-mat.mes-hall]
A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin... more A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekulé-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the dispersion relation and present analytical expressions for the low-energy limit. Our results indicate the emergence of a Zeeman-like term due to the coupling of the pseudospin with the pseudomagnetic strain potential which separates the valleys by moving them in opposite directions away from the center of the Brillouin zone. For the Kek-O phase, this results in a competition between the Kekulé parameter that opens a gap and the magnitude of strain which closes it. While for the Kek-Y phase, in a superposition of two shifted Dirac cones. As the Dirac cones are much closer in the supperlattice reciprocal space that in pristine graphene, we propose strain as a control parameter for intervalley scattering.
Deformations in graphene systems are central elements in the novel field of straintronics. Variou... more Deformations in graphene systems are central elements in the novel field of straintronics. Various strain geometries have been proposed to produce specific properties but their experimental realization has been limited. Because folds occur naturally in graphene samples, or could be engineered with appropriate substrates, we study their effects on graphene transport properties. We show the existence of an enhanced local density of states (LDOS) along the fold that originates from localization of higher energy states, and provides extra conductance channels at lower energies. In addition to exhibit sublattice symmetry breaking, these states are valley polarized, with quasi-ballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making folds viable electronic waveguides. These findings could be tested in currently available experimental settings.
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Papers by Ramon Carrillo