Hydrodynamic and ballistic AC transport in two-dimensional Fermi liquids

Abstract

Electronic transport in Fermi liquids is usually Ohmic, because of momentum-relaxing scattering due to defects and phonons. These processes can become sufficiently weak in two-dimensional materials, giving rise to either ballistic or hydrodynamic transport, depending on the strength of electron-electron scattering. We show that the ballistic regime is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a free conformal field theory (CFT) with a dynamical scaling exponent z = 1. Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has vortices at all spatial scales. We image the fluctuations in high-definition and animate their emergence as experimental parameters are tuned to the QCP a . The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics b . The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. Our findings provide a theoretical framework for both interaction-free and interaction-dominated non-Ohmic transport in two-dimensional materials, as seen in several contemporary experiments. a Spatial fluctuations: https://vimeo.com/365020115 , Fermi surface fluctuations: https://vimeo.com/ 364982637 b Vortex dynamics and frequency crossover: https://vimeo.com/366725650Quantum critical points (QCP) mediate second-order quantum phase transitions (QPT), produced by tuning non-thermal parameters such as doping, magnetic field or pressure. Systems at QCPs obey universal scaling, and are dominated by quantum fluctuations [1]. A prototypical QPT occurs in the 1D quantum Ising model in a transverse magnetic field, realized in CoNb 2 O 6 [2]. As the external field is increased, the ground state changes from an ordered phase set by exchange interaction to a field-aligned quantum paramagnet. The transition occurs through a QCP with a dynamical scaling exponent z = 1, which connects the correlation length ξ and time τ via τ ∝ ξ z . Remarkably, the ubiquitous Fermi liquid hosts exactly such a QCP in the form of free fermions; a Fermi gas. Absent all interactions, gapless quasiparticles on the Fermi surface obey a relativistic free-field conformal field theory (CFT), with the speed of light set by the Fermi velocity v F [3]. This simple CFT exhibits critical scaling with z = 1. Microscopic interactions are indeed irrelevant, as expected at criticality, because there are none.Although a Fermi gas obeys critical scaling [4], it is never pictured as a QCP. The singleparticle Green's function has a simple pole, not a branch cut characteristic of interacting QCPs [5]; it is unclear how and where critical fluctuatio...

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

“…In real two-dimensional materials (e.g., graphene), it is very hard to distinguish the ballistic and hydrodynamic phonon transport clearly by the heat vortexes at steady state. Therefore, more work is needed to be done to distinguish the ballistic and hydrodynamic phonon transport clearly by the vortexes in the future, which may be inspired by recent studies of unsteady viscous electron flow [50].…”

“…In addition, as normal scattering dominates the heat conduction, the corresponding macroscopic Guyer-Krumhansl (G-K) equation [14,22,30,[45][46][47] is similar to the Navier-Stokes equation in fluid dynamics [36,38]. Hence, will phonon transport like the vortexes in fluid dynamics [36][37][38] or viscous electron flow in hall bar geometries [48][49][50][51]?…”

“…In this work, motivated by the viscous fluid dynamics [36][37][38] or viscous electron flow [48][49][50][51], the heat vortexes in two different structures (porous (Fig. 2) and ribbon ( Fig.…”

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

“…We simulate magnetotransport in the actual experimental device geometry using BOLT, a high-resolution solver for kinetic theories 9 , 11 , 37 , which solves the Boltzmann transport equation: where f ( x , p , t ) is the probability distribution of electrons along the spatial coordinates x ≡ ( x , y ) and momentum coordinates , where θ denotes the angle on the Fermi surface, t denotes time, and v F denotes the Fermi velocity. The Lorentz force due to B appears in the third term on the left, which for a circular Fermi surface simplifies to the form shown.…”

“…A collective phenomenon such as vortices being observed in a TMF setting, which is widely regarded as a purely ballistic experiment, is counterintuitive. Yet, at B = 0 it has been shown both theoretically and experimentally that even ballistic dynamics can lead to collective phenomena 9 – 11 . Here we show additional evidence in the presence of B .…”