Scaling approach to tight-binding transport in realistic graphene devices: The case of transverse magnetic focusing

Beconcini, Michael; Valentini, Stefano; Kumar, Roshan Krishna; Auton, Gregory; Geǐm, A. K.; Пономаренко, Л. А.; Polini, Marco; Taddei, F.

doi:10.1103/physrevb.94.115441

Cited by 17 publications

(15 citation statements)

References 30 publications

(88 reference statements)

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“…In the hydrodynamic regime, negative R v arises as a result of viscous entrainment by the injected current of the fluid in adjacent regions 16 , 20 , 28 . In the free-particle regime, positive R v is expected from single-particle ballistic transport due to reflection of injected carriers from the opposite boundaries 30 , 31 . Therefore, the sign of R v must change from negative to positive upon lowering T , as indeed seen in the data shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Fluidity onset in graphene

et al. 2018

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Viscous electron fluids have emerged recently as a new paradigm of strongly-correlated electron transport in solids. Here we report on a direct observation of the transition to this long-sought-for state of matter in a high-mobility electron system in graphene. Unexpectedly, the electron flow is found to be interaction-dominated but non-hydrodynamic (quasiballistic) in a wide temperature range, showing signatures of viscous flows only at relatively high temperatures. The transition between the two regimes is characterized by a sharp maximum of negative resistance, probed in proximity to the current injector. The resistance decreases as the system goes deeper into the hydrodynamic regime. In a perfect darkness-before-daybreak manner, the interaction-dominated negative response is strongest at the transition to the quasiballistic regime. Our work provides the first demonstration of how the viscous fluid behavior emerges in an interacting electron system.

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Section: Resultsmentioning

confidence: 99%

Fluidity onset in graphene

et al. 2018

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“…While TMF has seen extensive numerical study 41 – 46 , current vortices have not been reported till this work. A probable reason lies in the observation that current computation may be dominated by shot noise in TMF simulations performed using particle schemes 44 , 45 , a limitation not suffered by the present high-resolution kinetic scheme. It would be interesting to check if vortices persist in the coherent transport regime 43 , 46 .…”

Section: Discussionmentioning

confidence: 99%

Precision measurement of electron-electron scattering in GaAs/AlGaAs using transverse magnetic focusing

et al. 2021

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Electron-electron (e-e) interactions assume a cardinal role in solid-state physics. Quantifying the e-e scattering length is hence critical. In this paper we show that the mesoscopic phenomenon of transverse magnetic focusing (TMF) in two-dimensional electron systems forms a precise and sensitive technique to measure this length scale. Conversely we quantitatively demonstrate that e-e scattering is the predominant effect limiting TMF amplitudes in high-mobility materials. Using high-resolution kinetic simulations, we show that the TMF amplitude at a maximum decays exponentially as a function of the e-e scattering length, which leads to a ready approach to extract this length from the measured TMF amplitudes. The approach is applied to measure the temperature-dependent e-e scattering length in high-mobility GaAs/AlGaAs heterostructures. The simulations further reveal current vortices that accompany the cyclotron orbits - a collective phenomenon counterintuitive to the ballistic transport underlying a TMF setting.

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“…The method can be immediately applied to take into account, for example, complex local gating or multi-probe transport, in order to make further analysis for transport experiments or even reliable predictions. We note some recent studies working on developing numerical techniques that allow large-scale efficient transport simulations [47][48][49], but scaling the graphene lattices with an appropriately chosen scaling factor depending on the superlattice periodicity seems to be of least technical complexity and is readily applicable to anyone who is familiar with quantum transport using, for example, real-space Green's function method [32] or the popular open-source python package KWANT [50].…”

Section: Discussionmentioning

confidence: 99%

Electrostatic superlattices on scaled graphene lattices

et al. 2020

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A scalable tight-binding model is applied for large-scale quantum transport calculations in clean graphene subject to electrostatic superlattice potentials, including two types of graphene superlattices: moiré patterns due to the stacking of graphene and hexagonal boron nitride (hBN) lattices, and gate-controllable superlattices using a spatially modulated gate capacitance. In the case of graphene/hBN moiré superlattices, consistency between our transport simulation and experiment is satisfactory at zero and low magnetic field, but breaks down at high magnetic field due to the adopted simple model Hamiltonian that does not comprise higher-order terms of effective vector potential and Dirac mass terms. In the case of gate-controllable superlattices, no higher-order terms are involved, and the simulations are expected to be numerically exact. Revisiting a recent experiment on graphene subject to a gated square superlattice with periodicity of 35 nm, our simulations show excellent agreement, revealing the emergence of multiple extra Dirac cones at stronger superlattice modulation. arXiv:1907.03288v1 [cond-mat.mes-hall]

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Scaling approach to tight-binding transport in realistic graphene devices: The case of transverse magnetic focusing

Cited by 17 publications

References 30 publications

Fluidity onset in graphene

Fluidity onset in graphene

Precision measurement of electron-electron scattering in GaAs/AlGaAs using transverse magnetic focusing

Electrostatic superlattices on scaled graphene lattices

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