Monitoring many aspects of patient care is based on assessments of sequences of data. Clinical de... more Monitoring many aspects of patient care is based on assessments of sequences of data. Clinical decision-making relies to a considerable extent on an understanding of the correspondence between the pattern of the observations, conveyed most effectively by presentations as graphs, and of the underlying biological events. Changes in established patterns are of particular interest, as these can indicate the occurrence of biological events which need additional diagnostic effort or therapeutic intervention. Interpretation of sequences of data can be difficult even when physicians, from their experience of similar patients, or because of an understanding of the physiology and pathology that influence the variable being studied, can anticipate the forms of the pattern that might arise and of the changes in pattern that are most likely. Important changes in observed sequences may not be obvious, because either the underlying pattern, a change in the pattern, or both, are masked by "noise," resulting from biological variability and from errors in the collection, measurement and processing of the data. It is clearly desirable to be able
Starting from the strong-coupling limit of an extended Hubbard model, we develop a spin-fermion t... more Starting from the strong-coupling limit of an extended Hubbard model, we develop a spin-fermion theory to study the insulating phase and pairing symmetry of the superconducting phase in twisted bilayer graphene. Assuming that the insulating phase is an anti-ferromagnetic insulator, we show that fluctuations of the anti-ferromagnetic order in the conducting phase can mediate superconducting pairing. Using a self-consistent mean-field analysis, we find that the pairing wave function has a chiral d-wave symmetry. Consistent with this observation, we show explicitly the existence of chiral Majorana edge modes by diagonalizing our proposed Hamiltonian on a finite-sized system. These results establish twisted bilayer graphene as a promising platform to realize topological superconductivity. 1(b). This loss of monolayer valley quantum number explains why the experimentally observed Landau level degeneracy close to half filling is half that at charge neutrality. This breaking of valley symmetry (as opposed to spin symmetry) is supported by Hartree-Fock calculations [10], and because experiments suggests spin-singlet
Remote control of excitons in a two-dimensional semiconductor is achieved by tuning electron dens... more Remote control of excitons in a two-dimensional semiconductor is achieved by tuning electron density in adjacent graphene.
Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relat... more Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime because although they couple to current, they do not induce charge and are therefore unscreened by the large density of states close to magic angle. We show that the resistivity has a strong monotonically decreasing carrier density dependence at low temperature due to charged impurity scattering, and weak density dependence at high temperature due to gauge phonons. Away from charge neutrality, the resistivity increases with temperature, while it does the opposite close to the Dirac point. A non-monotonic temperature dependence observed only at low temperature and carrier density is a signature of our theory that can be tested in experimentally available samples.
Using the continuum model for low energy non-interacting electronic structure of moiré van der Wa... more Using the continuum model for low energy non-interacting electronic structure of moiré van der Waals heterostructures developed by Bistritzer and MacDonald [1] , we study the competition between spin, charge, and superconducting order in twisted bilayer graphene. Surprisingly, we find that for a range of small angles inclusive of the so-called magic angle, this model features robust Fermi pockets that preclude any Mott insulating phase at weak coupling. However, a Fermi surface reconstruction at θ 1.2 • gives emergent van Hove singularities without any Fermi pockets. Using a hot-spot model for Fermi surface patches around these emergent saddle points, we develop a random-phase approximation from which we obtain a phase diagram very similar to that obtained recently by Isobe, Yuan, and Fu using the parquet renormalization group [2] but with additional insights. For example, our model shows strong nesting around time-reversal symmetric points at a moderate doping of ∼ 2 × 10 11 cm −2 away from the van Hove singularity. When this nesting dominates, we predict that charge-order enhances singlet superconductivity, while spin-order suppresses superconductivity. Our theory also provides additional possibilities for the case of unnested Fermi surfaces.
Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the va... more Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene-black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene-black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of devel...
There is a huge demand for magnetoresistance (MR) sensors with high sensitivity, low energy consu... more There is a huge demand for magnetoresistance (MR) sensors with high sensitivity, low energy consumption, and room temperature operation. It is well-known that spatial charge inhomogeneity due to impurities or defects introduces mobility fluctuations in monolayer graphene and gives rise to MR in the presence of an externally applied magnetic field. However, to realize a MR sensor based on this effect is hampered by the difficulty in controlling the spatial distribution of impurities and the weak magnetoresistance effect at the monolayer regime. Here, we fabricate a highly stable monolayer graphene-on-black phosphorus (G/BP) heterostructure device that exhibits a giant MR of 775% at 9 T magnetic field and 300 K, exceeding by far the MR effects from devices made from either monolayer graphene or few-layer BP alone. The positive MR of the G/BP device decreases when the temperature is lowered, indicating a phonon-mediated process in addition to scattering by charge impurities. Moreover, ...
Heterostructures can be assembled from atomically thin materials by combining a wide range of ava... more Heterostructures can be assembled from atomically thin materials by combining a wide range of available van der Waals crystals, providing exciting possibilities for designer electronics . In many cases, beyond simply realizing new material combinations, interlayer interactions lead to emergent electronic properties that are fundamentally distinct from those of the constituent layers . A critical parameter in these structures is the interlayer coupling strength, but this is often not easy to determine and is typically considered to be a fixed property of the system. Here we demonstrate that we can controllably tune the interlayer separation in van der Waals heterostructures using hydrostatic pressure, providing a dynamic way to modify their electronic properties. In devices in which graphene is encapsulated in boron nitride and aligned with one of the encapsulating layers, we observe that increasing pressure produces a superlinear increase in the moiré-superlattice-induced bandgap-ne...
Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Ha... more Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moiré pattern pseudospin fields. Here, we present the moiré-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moiré patterns, leading to primary Dirac point gaps when the moiré strains give rise to a finite average mass, and to secondary gaps when the moiré pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to ∼ 40 Tesla near symmetry points in the moiré cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moiré strains.
Monitoring many aspects of patient care is based on assessments of sequences of data. Clinical de... more Monitoring many aspects of patient care is based on assessments of sequences of data. Clinical decision-making relies to a considerable extent on an understanding of the correspondence between the pattern of the observations, conveyed most effectively by presentations as graphs, and of the underlying biological events. Changes in established patterns are of particular interest, as these can indicate the occurrence of biological events which need additional diagnostic effort or therapeutic intervention. Interpretation of sequences of data can be difficult even when physicians, from their experience of similar patients, or because of an understanding of the physiology and pathology that influence the variable being studied, can anticipate the forms of the pattern that might arise and of the changes in pattern that are most likely. Important changes in observed sequences may not be obvious, because either the underlying pattern, a change in the pattern, or both, are masked by "noise," resulting from biological variability and from errors in the collection, measurement and processing of the data. It is clearly desirable to be able
Starting from the strong-coupling limit of an extended Hubbard model, we develop a spin-fermion t... more Starting from the strong-coupling limit of an extended Hubbard model, we develop a spin-fermion theory to study the insulating phase and pairing symmetry of the superconducting phase in twisted bilayer graphene. Assuming that the insulating phase is an anti-ferromagnetic insulator, we show that fluctuations of the anti-ferromagnetic order in the conducting phase can mediate superconducting pairing. Using a self-consistent mean-field analysis, we find that the pairing wave function has a chiral d-wave symmetry. Consistent with this observation, we show explicitly the existence of chiral Majorana edge modes by diagonalizing our proposed Hamiltonian on a finite-sized system. These results establish twisted bilayer graphene as a promising platform to realize topological superconductivity. 1(b). This loss of monolayer valley quantum number explains why the experimentally observed Landau level degeneracy close to half filling is half that at charge neutrality. This breaking of valley symmetry (as opposed to spin symmetry) is supported by Hartree-Fock calculations [10], and because experiments suggests spin-singlet
Remote control of excitons in a two-dimensional semiconductor is achieved by tuning electron dens... more Remote control of excitons in a two-dimensional semiconductor is achieved by tuning electron density in adjacent graphene.
Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relat... more Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime because although they couple to current, they do not induce charge and are therefore unscreened by the large density of states close to magic angle. We show that the resistivity has a strong monotonically decreasing carrier density dependence at low temperature due to charged impurity scattering, and weak density dependence at high temperature due to gauge phonons. Away from charge neutrality, the resistivity increases with temperature, while it does the opposite close to the Dirac point. A non-monotonic temperature dependence observed only at low temperature and carrier density is a signature of our theory that can be tested in experimentally available samples.
Using the continuum model for low energy non-interacting electronic structure of moiré van der Wa... more Using the continuum model for low energy non-interacting electronic structure of moiré van der Waals heterostructures developed by Bistritzer and MacDonald [1] , we study the competition between spin, charge, and superconducting order in twisted bilayer graphene. Surprisingly, we find that for a range of small angles inclusive of the so-called magic angle, this model features robust Fermi pockets that preclude any Mott insulating phase at weak coupling. However, a Fermi surface reconstruction at θ 1.2 • gives emergent van Hove singularities without any Fermi pockets. Using a hot-spot model for Fermi surface patches around these emergent saddle points, we develop a random-phase approximation from which we obtain a phase diagram very similar to that obtained recently by Isobe, Yuan, and Fu using the parquet renormalization group [2] but with additional insights. For example, our model shows strong nesting around time-reversal symmetric points at a moderate doping of ∼ 2 × 10 11 cm −2 away from the van Hove singularity. When this nesting dominates, we predict that charge-order enhances singlet superconductivity, while spin-order suppresses superconductivity. Our theory also provides additional possibilities for the case of unnested Fermi surfaces.
Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the va... more Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene-black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene-black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of devel...
There is a huge demand for magnetoresistance (MR) sensors with high sensitivity, low energy consu... more There is a huge demand for magnetoresistance (MR) sensors with high sensitivity, low energy consumption, and room temperature operation. It is well-known that spatial charge inhomogeneity due to impurities or defects introduces mobility fluctuations in monolayer graphene and gives rise to MR in the presence of an externally applied magnetic field. However, to realize a MR sensor based on this effect is hampered by the difficulty in controlling the spatial distribution of impurities and the weak magnetoresistance effect at the monolayer regime. Here, we fabricate a highly stable monolayer graphene-on-black phosphorus (G/BP) heterostructure device that exhibits a giant MR of 775% at 9 T magnetic field and 300 K, exceeding by far the MR effects from devices made from either monolayer graphene or few-layer BP alone. The positive MR of the G/BP device decreases when the temperature is lowered, indicating a phonon-mediated process in addition to scattering by charge impurities. Moreover, ...
Heterostructures can be assembled from atomically thin materials by combining a wide range of ava... more Heterostructures can be assembled from atomically thin materials by combining a wide range of available van der Waals crystals, providing exciting possibilities for designer electronics . In many cases, beyond simply realizing new material combinations, interlayer interactions lead to emergent electronic properties that are fundamentally distinct from those of the constituent layers . A critical parameter in these structures is the interlayer coupling strength, but this is often not easy to determine and is typically considered to be a fixed property of the system. Here we demonstrate that we can controllably tune the interlayer separation in van der Waals heterostructures using hydrostatic pressure, providing a dynamic way to modify their electronic properties. In devices in which graphene is encapsulated in boron nitride and aligned with one of the encapsulating layers, we observe that increasing pressure produces a superlinear increase in the moiré-superlattice-induced bandgap-ne...
Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Ha... more Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moiré pattern pseudospin fields. Here, we present the moiré-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moiré patterns, leading to primary Dirac point gaps when the moiré strains give rise to a finite average mass, and to secondary gaps when the moiré pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to ∼ 40 Tesla near symmetry points in the moiré cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moiré strains.
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Papers by Evan Laksono