Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry

Abstract

Ultra-pure conductors may exhibit hydrodynamic transport where the collective motion of charge carriers resembles the flow of a viscous fluid. In a confined geometry (e.g., in ultra-high quality nanostructures) the electronic fluid assumes a Poiseuille-like flow. Applying an external magnetic field tends to diminish viscous effects leading to large negative magnetoresistance. In two-component systems near charge neutrality the hydrodynamic flow of charge carriers is strongly affected by the mutual friction between the two constituents. At low fields, the magnetoresistance is negative, however at high fields the interplay between electron-hole scattering, recombination, and viscosity results in a dramatic change of the flow profile: the magnetoresistance changes its sign and eventually becomes linear in very high fields. This novel non-monotonic magnetoresistance can be used as a fingerprint to detect viscous flow in two-component conducting systems.The independent particle approximation 1,2 has dominated the solid state physics for nearly a century. While clearly successful in describing most of the basic transport phenomena in metals and semiconductors, this approach completely neglects Coulomb interaction between charge carriers (the latter is frequently said to be justified by the "weakness" of electron-electron interaction due to, e.g., screening or statistical effects). To be more specific, in many conventional conductors the typical interaction length scale, ee , is too long in comparison to other relevant scales in the system. In particular, at low temperatures the dominant scattering process is due to potential disorder and hence the shortest length scale is the mean free path, dis ee , which determines the residual Drude resistivity at T = 0. At high temperatures, the electron-phonon interaction dominates, ph ee . If these two temperature regimes overlap, then indeed (at least, away from any phase transitions) the role of electron-electron interaction is reduced to small corrections. However, if there exists a temperature window where ee dis , ph , then in that case the independent particle approximation is violated: the motion of charge carriers becomes collective (or hydrodynamic) and hence transport properties of the system are determined by interaction 3 .Signatures of the hydrodynamic behavior have been observed in recent experiments in graphene 4-6 and palladium cobaltate 7 . The effect of external magnetic field on electronic transport in systems with ee dis , ph was studied in magnetotransport measurements in ultra-highmobility GaAs quantum wells 8-10 and more recently in the Weyl semimetal WP 2 11 reporting, in both cases, large negative magnetoresistance. A detailed account of the history of magnetotransport measurements is beyond the scope of this paper. Here we only stress the following well known facts: at the single-particle level, there is no classical magnetoresistance (MR) in single-band (or one-component) systems; taking into account more than one band of carriers (e.g., in semiconduct...

Dissipative and Hall Viscosity of a Disordered 2D Electron Gas

“…It was understood that beyond the Hall conductivity and viscosity there are additional non-dissipative electro-magnetic and geometrical response functions in gapped quantum systems [32][33][34][35][36][37][38][39][40][41][42][43][44]. Within the hydrodynamic description of electron transport, non-zero η H influences significantly the structure of the electron flow [45][46][47][48][49][50], which allows one to access η H experimentally [51]. Also, it was argued that the dissipative and Hall viscosity affect the spectrum of edge magnetoplasmons [52][53][54].For noninteracting electrons in the absence of disorder each filled Landau level (LL) gives a contribution to the Hall viscosity equal (2n + 1)/(8πl 2 B ) [25], where n denotes the LL index and l B = c/(eB) stands for the magnetic length.…”

Anti-Poiseuille flow in neutral graphene

“…Since the latter cannot leave the sample, this flow has to vanish at both edges and (nontrivial) homogeneous solutions are no longer allowed. In the two-fluid model of compensated semimetals [28,[72][73][74] the nontrivial inhomogeneous solution becomes possible due to quasiparticle recombination.…”

“…[51] in the context of thermoelectric phenomena. Recently, recombination effects were shown to lead to linear magnetoresistance in compensated semimetals [28,72,73,81], giant magnetodrag [67,82], and giant nonlocality [74,83].…”

“…The possibility for an electronic system to exhibit the Poiseuille flow in a narrow wire was first pointed out by Gurzhi [19][20][21]. Recently, similar behavior has been a subject of intense theoretical [22][23][24][25][26][27][28][29][30][31][32][33] and experimental [10][11][12][13]22,[34][35][36][37][38][39][40][41][42][43][44] research in the context of electronic transport in high-mobility 2D materials. In contrast to conventional fluids, the electronic flow is affected not only by viscous effects, but also by weak disorder scattering and is characterized by a typical length scale known as the Gurzhi length [26][27][28][29]33]…”

Hydrodynamic Approach to Electronic Transport in Graphene: Energy Relaxation

“…This was first established in [6] in the context of thermoelectric phenomena (for the most recent discussion see [23]). Later, quasiparticle recombination was shown to lead to linear magnetoresistance in compensated semimetals [24][25][26][27] as well as to giant magnetodrag [28,29].…”