The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental... more The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental basis of the topological properties in solids. This phase can be tuned by modulating the band structure of a material, providing a way to drive a topological phase transition. However, despite significant efforts in designing and understanding topological materials, it remains still challenging to tune a given material across different topological phases while tracing the impact of the Berry phase on its quantum transport properties. Here, we report these two effects in a magnetotransport study of ZrTe5. By tuning the band structure with uniaxial strain, we use quantum oscillations to directly map a weak-to-strong topological insulator phase transition through a gapless Dirac semimetal phase. Moreover, we demonstrate the impact of the strain-tunable spin-dependent Berry phase on the Zeeman effect through the amplitude of the quantum oscillations. We show that such a spin-dependent Berry...
Two-dimensional atomic crystals (2DACs) can be mechanically assembled with precision for the fabr... more Two-dimensional atomic crystals (2DACs) can be mechanically assembled with precision for the fabrication of heterostructures, allowing for the combination of material building blocks with great flexibility. In addition, while conventional nanolithography can be detrimental to most of the 2DACs which are not sufficiently inert, mechanical assembly potentially minimizes the nanofabrication processing and preserves the intrinsic physical properties of the 2DACs. In this work we study the interfacial charge transport between various 2DACs and electrical contacts, by fabricating and characterizing 2DAC-superconductor junctions through mechanical transfer. Compared to devices fabricated with conventional nanolithography, mechanically assembled devices show comparable or better interface transparency. Surface roughness at the electrical contacts is identified to be a major limitation to the interface quality.
The ability to localize and manipulate individual quasiparticles in mesoscopic structures is crit... more The ability to localize and manipulate individual quasiparticles in mesoscopic structures is critical in experimental studies of quantum mechanics and thermodynamics, and in potential quantum information devices, e.g., for topological schemes of quantum computation. In strong magnetic field, the quantum Hall edge modes can be confined around the circumference of a small antidot, forming discrete energy levels that have a unique ability to localize fractionally charged quasiparticles. Here, we demonstrate a Dirac fermion quantum Hall antidot in a graphene, where charge transport characteristics can be adjusted through the coupling strength between the contacts and the antidot, from Coulomb blockade dominated tunneling under weak coupling to the effectively non-interacting resonant tunneling under strong coupling. Both regimes are characterized by single-flux and-charge oscillations in conductance persisting up to temperatures over 2 orders of magnitude higher than previous reports in other material systems. Such graphene quantum Hall antidots may serve as a promising platform for building and studying novel quantum circuits for quantum simulation and computation.
In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles ... more In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion gas system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional “pseudo-diffusive” charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to the presence of strong disorder in graphene devices which limits the accessibility of the low carrier density regime close enough to the Dirac point. Here we report transport measurements on ballistic suspended graphene-Niobium Josephson weak links that demonstrate a transition from ballistic to pseudo-diffusive like evanescent transport below a carrier density of ~1010 cm−2. Approaching th...
The Dirac Fermion nature of the quasiparticles in graphene has led to many predictions for novel ... more The Dirac Fermion nature of the quasiparticles in graphene has led to many predictions for novel phenomena such as specular Andreev reflections at graphenesuperconductor interfaces and a negative index of refraction for transmission of charge across graphene p-n junctions. These predictions presuppose ballistic transport, which requires long mean free paths compared to the distance between leads. However, within current fabrication techniques, the mean free paths of charge carriers in graphene devices are often too short for ballistic transport. The reduced mean free path is primarily due to excess scattering introduced by extrinsic factors such as material imperfections, substrate contamination, e-beam resist residue, chemical doping, contact potential and contact geometry. We will discuss the results of systematic studies of extrinsic factors, highlighting the case of graphene SNS weak links, and will propose strategies to increase the mean free path.
Graphene is a fascinating material for exploring fundamental science questions as well as a poten... more Graphene is a fascinating material for exploring fundamental science questions as well as a potential building block for novel electronic applications. In order to realize the full potential of this material the fabrication techniques of graphene devices, still in their infancy, need to be refined to better isolate the graphene layer from the environment. We present results from a study on the influence of extrinsic factors on the quality of graphene devices including material defects, lithography, doping by metallic leads and the substrate. The main finding is that trapped Coulomb scatterers associated with the substrate are the primary factor reducing the quality of graphene devices. A fabrication scheme is proposed to produce high quality graphene devices dependably and reproducibly. In these devices, the transport properties approach theoretical predictions of ballistic transport.
This review covers recent experimental progress in probing the electronic properties of graphene ... more This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magneto-transport techniques. A.
For studying surface properties of nanocrystals, we present an approach based on a combination of... more For studying surface properties of nanocrystals, we present an approach based on a combination of the grazing incidence small angle x-ray scattering ͑GISAXS͒ technique and tomographic methods. In this approach, GISAXS data from a micro-or nanometer sized object are collected successively at different azimuthal angular positions, which makes it possible to measure the whole three-dimensional ͑3D͒ intensity distribution in reciprocal space. As an example, the full 3D reciprocal space intensity originating from the truncated epitaxially grown ͕111͖ facetted SiGe pyramids with a square base on ͑001͒ Si substrate was measured. This technique enables us to observe and explain crystal truncation planes which originate from scattering on the edges of the nanocrystals.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010
Recently, fractional quantization of two-terminal conductance was reported in suspended graphene.... more Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p–n–p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained ...
Many systems in nature-glasses 1-11 , interfaces 12 and fractures 13 being some examples-cannot e... more Many systems in nature-glasses 1-11 , interfaces 12 and fractures 13 being some examples-cannot equilibrate with their environment, which gives rise to novel and surprising behaviour such as memory effects, ageing and nonlinear dynamics. Unlike their equilibrated counterparts, the dynamics of out-ofequilibrium systems is generally too complex to be captured by simple macroscopic laws 1. Here we investigate a system that straddles the boundary between glass and crystal: a Bragg glass 14,15 , formed by vortices in a superconductor. We find that the response to an applied force evolves according to a stretched exponential, with the exponent reflecting the deviation from equilibrium. After the force is removed, the system ages with time and its subsequent response time scales linearly with its 'age' (simple ageing), meaning that older systems are slower than younger ones. We show that simple ageing can occur naturally in the presence of sufficient quenched disorder. Moreover, the hierarchical distribution of timescales, arising when chunks of loose vortices cannot move before trapped ones become dislodged, leads to a stretched-exponential response. Glassy states of matter abound with seeming contradictions: macroscopically they are rigid like crystals, but microscopically their structure is closer to that of liquids. At the same time, their response to external drives is unlike that of either crystals or liquids, showing metastability, hysteresis and nonlinear dynamics 1. In recent years the glass family has expanded to include systems that can be modelled by elastic manifolds in random potentials, such as vortices in superconductors 14-21 , domain walls 12 or twodimensional electron layers 5,6. When the random potential is weak these systems are expected to form a marginal glassy state, a 'Bragg glass' , which is topologically ordered like a perfect crystal, but unlike crystals has no long-range spatial order 14,15. An intriguing and enduring puzzle associated with this phase is the dynamics at the onset of motion: does it move as a rigid object or break up into pieces; does it crystallize at high velocities or retain its glassy nature 22-25 ? To probe the dynamics, we focused on vortex states in single crystals of 2H-NbSe 2 because in this material quenched disorder can be sufficiently weak to allow the formation of a Bragg glass. The vortex states were prepared by field cooling the sample below the superconducting transition in a field of 0.2 T and temperatures down to 4.2 K (see the Supplementary Information). The results reported here were obtained on a sample of size 4.4 × 0.8 × 0.006 mm 3 and transition temperature 7.2 K (see the Supplementary Information). At low temperatures (T < 5.7 K),
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties... more In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers' two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field 1,2. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is qualitatively different from its semiconductor analogue 3. As a third distinguishing feature of graphene, it has been conjectured that interactions and correlations should be important in this material, but surprisingly, evidence of collective behaviour in graphene is lacking. In particular, the quintessential collective quantum behaviour in two dimensions, the fractional quantum Hall effect (FQHE), has so far resisted observation in graphene despite intense efforts and theoretical predictions of its existence 4-9. Here we report the observation of the FQHE in graphene. Our observations are made possible by using suspended graphene devices probed by two-terminal charge transport measurements 10. This allows us to isolate the sample from substrate-induced perturbations that usually obscure the effects of interactions in this system and to avoid effects of finite geometry. At low carrier density, we find a field-induced transition to an insulator that competes with the FQHE, allowing its observation only in the highest quality samples. We believe that these results will open the door to the physics of FQHE and other collective behaviour in graphene.
Using time resolved transport measurements, we observed clear evidence of glassy dynamics in the ... more Using time resolved transport measurements, we observed clear evidence of glassy dynamics in the current driven vortex system in clean, weak pinning 2H-NbSe2 single crystals prepared by field cooling through the superconducting transition. Simple aging was observed by means of scaling over the waiting times between two consecutive current pulses. A memory function was defined to describe how the previous pulse is ``memorized'' when the system is probed by a second pulse. The complex behavior of the driven vortex system in the glassy state is well characterized by a simple picture of the time evolution of the glassy states in configuration space. Preliminary results on direct imaging of the current driven vortices using Hall probe microscopy will be discussed.
We study the onset of motion of a vortex lattice in response to a driving current that is turned ... more We study the onset of motion of a vortex lattice in response to a driving current that is turned on suddenly. For sufficiently high currents we find that the average vortex velocity (obtained from the longitudinal voltage drop) grows smoothly with time and obeys a stretched exponential with an exponent ∼ 0.7. The response is governed by two time scales: a delay time (t 0) before the appearance of a measurable voltage drop, and a rise time () characterizing the evolution of voltage response. Both time scales increase with decreasing saturation voltage V 0 : decreases exponentially, while t 0 as a power law. When the saturation velocity is too low the response slows down significantly and shows a step structure indicating plastic response.
... I am dearly thankful to current and former members of our group (Josh Kelly, Jeremy Nesbitt, ... more ... I am dearly thankful to current and former members of our group (Josh Kelly, Jeremy Nesbitt, Partha Mitra, Ryan Rairigh, Sinan Selcuk, Guneeta Singh, Kevin ... his students (Tara Dhakal, Jacob Tosado, and Sung-Hee Yun), who provided me great help in using their facilities. ...
The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental... more The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental basis of the topological properties in solids. This phase can be tuned by modulating the band structure of a material, providing a way to drive a topological phase transition. However, despite significant efforts in designing and understanding topological materials, it remains still challenging to tune a given material across different topological phases while tracing the impact of the Berry phase on its quantum transport properties. Here, we report these two effects in a magnetotransport study of ZrTe5. By tuning the band structure with uniaxial strain, we use quantum oscillations to directly map a weak-to-strong topological insulator phase transition through a gapless Dirac semimetal phase. Moreover, we demonstrate the impact of the strain-tunable spin-dependent Berry phase on the Zeeman effect through the amplitude of the quantum oscillations. We show that such a spin-dependent Berry...
Two-dimensional atomic crystals (2DACs) can be mechanically assembled with precision for the fabr... more Two-dimensional atomic crystals (2DACs) can be mechanically assembled with precision for the fabrication of heterostructures, allowing for the combination of material building blocks with great flexibility. In addition, while conventional nanolithography can be detrimental to most of the 2DACs which are not sufficiently inert, mechanical assembly potentially minimizes the nanofabrication processing and preserves the intrinsic physical properties of the 2DACs. In this work we study the interfacial charge transport between various 2DACs and electrical contacts, by fabricating and characterizing 2DAC-superconductor junctions through mechanical transfer. Compared to devices fabricated with conventional nanolithography, mechanically assembled devices show comparable or better interface transparency. Surface roughness at the electrical contacts is identified to be a major limitation to the interface quality.
The ability to localize and manipulate individual quasiparticles in mesoscopic structures is crit... more The ability to localize and manipulate individual quasiparticles in mesoscopic structures is critical in experimental studies of quantum mechanics and thermodynamics, and in potential quantum information devices, e.g., for topological schemes of quantum computation. In strong magnetic field, the quantum Hall edge modes can be confined around the circumference of a small antidot, forming discrete energy levels that have a unique ability to localize fractionally charged quasiparticles. Here, we demonstrate a Dirac fermion quantum Hall antidot in a graphene, where charge transport characteristics can be adjusted through the coupling strength between the contacts and the antidot, from Coulomb blockade dominated tunneling under weak coupling to the effectively non-interacting resonant tunneling under strong coupling. Both regimes are characterized by single-flux and-charge oscillations in conductance persisting up to temperatures over 2 orders of magnitude higher than previous reports in other material systems. Such graphene quantum Hall antidots may serve as a promising platform for building and studying novel quantum circuits for quantum simulation and computation.
In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles ... more In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion gas system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional “pseudo-diffusive” charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to the presence of strong disorder in graphene devices which limits the accessibility of the low carrier density regime close enough to the Dirac point. Here we report transport measurements on ballistic suspended graphene-Niobium Josephson weak links that demonstrate a transition from ballistic to pseudo-diffusive like evanescent transport below a carrier density of ~1010 cm−2. Approaching th...
The Dirac Fermion nature of the quasiparticles in graphene has led to many predictions for novel ... more The Dirac Fermion nature of the quasiparticles in graphene has led to many predictions for novel phenomena such as specular Andreev reflections at graphenesuperconductor interfaces and a negative index of refraction for transmission of charge across graphene p-n junctions. These predictions presuppose ballistic transport, which requires long mean free paths compared to the distance between leads. However, within current fabrication techniques, the mean free paths of charge carriers in graphene devices are often too short for ballistic transport. The reduced mean free path is primarily due to excess scattering introduced by extrinsic factors such as material imperfections, substrate contamination, e-beam resist residue, chemical doping, contact potential and contact geometry. We will discuss the results of systematic studies of extrinsic factors, highlighting the case of graphene SNS weak links, and will propose strategies to increase the mean free path.
Graphene is a fascinating material for exploring fundamental science questions as well as a poten... more Graphene is a fascinating material for exploring fundamental science questions as well as a potential building block for novel electronic applications. In order to realize the full potential of this material the fabrication techniques of graphene devices, still in their infancy, need to be refined to better isolate the graphene layer from the environment. We present results from a study on the influence of extrinsic factors on the quality of graphene devices including material defects, lithography, doping by metallic leads and the substrate. The main finding is that trapped Coulomb scatterers associated with the substrate are the primary factor reducing the quality of graphene devices. A fabrication scheme is proposed to produce high quality graphene devices dependably and reproducibly. In these devices, the transport properties approach theoretical predictions of ballistic transport.
This review covers recent experimental progress in probing the electronic properties of graphene ... more This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magneto-transport techniques. A.
For studying surface properties of nanocrystals, we present an approach based on a combination of... more For studying surface properties of nanocrystals, we present an approach based on a combination of the grazing incidence small angle x-ray scattering ͑GISAXS͒ technique and tomographic methods. In this approach, GISAXS data from a micro-or nanometer sized object are collected successively at different azimuthal angular positions, which makes it possible to measure the whole three-dimensional ͑3D͒ intensity distribution in reciprocal space. As an example, the full 3D reciprocal space intensity originating from the truncated epitaxially grown ͕111͖ facetted SiGe pyramids with a square base on ͑001͒ Si substrate was measured. This technique enables us to observe and explain crystal truncation planes which originate from scattering on the edges of the nanocrystals.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010
Recently, fractional quantization of two-terminal conductance was reported in suspended graphene.... more Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p–n–p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained ...
Many systems in nature-glasses 1-11 , interfaces 12 and fractures 13 being some examples-cannot e... more Many systems in nature-glasses 1-11 , interfaces 12 and fractures 13 being some examples-cannot equilibrate with their environment, which gives rise to novel and surprising behaviour such as memory effects, ageing and nonlinear dynamics. Unlike their equilibrated counterparts, the dynamics of out-ofequilibrium systems is generally too complex to be captured by simple macroscopic laws 1. Here we investigate a system that straddles the boundary between glass and crystal: a Bragg glass 14,15 , formed by vortices in a superconductor. We find that the response to an applied force evolves according to a stretched exponential, with the exponent reflecting the deviation from equilibrium. After the force is removed, the system ages with time and its subsequent response time scales linearly with its 'age' (simple ageing), meaning that older systems are slower than younger ones. We show that simple ageing can occur naturally in the presence of sufficient quenched disorder. Moreover, the hierarchical distribution of timescales, arising when chunks of loose vortices cannot move before trapped ones become dislodged, leads to a stretched-exponential response. Glassy states of matter abound with seeming contradictions: macroscopically they are rigid like crystals, but microscopically their structure is closer to that of liquids. At the same time, their response to external drives is unlike that of either crystals or liquids, showing metastability, hysteresis and nonlinear dynamics 1. In recent years the glass family has expanded to include systems that can be modelled by elastic manifolds in random potentials, such as vortices in superconductors 14-21 , domain walls 12 or twodimensional electron layers 5,6. When the random potential is weak these systems are expected to form a marginal glassy state, a 'Bragg glass' , which is topologically ordered like a perfect crystal, but unlike crystals has no long-range spatial order 14,15. An intriguing and enduring puzzle associated with this phase is the dynamics at the onset of motion: does it move as a rigid object or break up into pieces; does it crystallize at high velocities or retain its glassy nature 22-25 ? To probe the dynamics, we focused on vortex states in single crystals of 2H-NbSe 2 because in this material quenched disorder can be sufficiently weak to allow the formation of a Bragg glass. The vortex states were prepared by field cooling the sample below the superconducting transition in a field of 0.2 T and temperatures down to 4.2 K (see the Supplementary Information). The results reported here were obtained on a sample of size 4.4 × 0.8 × 0.006 mm 3 and transition temperature 7.2 K (see the Supplementary Information). At low temperatures (T < 5.7 K),
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties... more In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers' two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field 1,2. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is qualitatively different from its semiconductor analogue 3. As a third distinguishing feature of graphene, it has been conjectured that interactions and correlations should be important in this material, but surprisingly, evidence of collective behaviour in graphene is lacking. In particular, the quintessential collective quantum behaviour in two dimensions, the fractional quantum Hall effect (FQHE), has so far resisted observation in graphene despite intense efforts and theoretical predictions of its existence 4-9. Here we report the observation of the FQHE in graphene. Our observations are made possible by using suspended graphene devices probed by two-terminal charge transport measurements 10. This allows us to isolate the sample from substrate-induced perturbations that usually obscure the effects of interactions in this system and to avoid effects of finite geometry. At low carrier density, we find a field-induced transition to an insulator that competes with the FQHE, allowing its observation only in the highest quality samples. We believe that these results will open the door to the physics of FQHE and other collective behaviour in graphene.
Using time resolved transport measurements, we observed clear evidence of glassy dynamics in the ... more Using time resolved transport measurements, we observed clear evidence of glassy dynamics in the current driven vortex system in clean, weak pinning 2H-NbSe2 single crystals prepared by field cooling through the superconducting transition. Simple aging was observed by means of scaling over the waiting times between two consecutive current pulses. A memory function was defined to describe how the previous pulse is ``memorized'' when the system is probed by a second pulse. The complex behavior of the driven vortex system in the glassy state is well characterized by a simple picture of the time evolution of the glassy states in configuration space. Preliminary results on direct imaging of the current driven vortices using Hall probe microscopy will be discussed.
We study the onset of motion of a vortex lattice in response to a driving current that is turned ... more We study the onset of motion of a vortex lattice in response to a driving current that is turned on suddenly. For sufficiently high currents we find that the average vortex velocity (obtained from the longitudinal voltage drop) grows smoothly with time and obeys a stretched exponential with an exponent ∼ 0.7. The response is governed by two time scales: a delay time (t 0) before the appearance of a measurable voltage drop, and a rise time () characterizing the evolution of voltage response. Both time scales increase with decreasing saturation voltage V 0 : decreases exponentially, while t 0 as a power law. When the saturation velocity is too low the response slows down significantly and shows a step structure indicating plastic response.
... I am dearly thankful to current and former members of our group (Josh Kelly, Jeremy Nesbitt, ... more ... I am dearly thankful to current and former members of our group (Josh Kelly, Jeremy Nesbitt, Partha Mitra, Ryan Rairigh, Sinan Selcuk, Guneeta Singh, Kevin ... his students (Tara Dhakal, Jacob Tosado, and Sung-Hee Yun), who provided me great help in using their facilities. ...
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