Collision-dominated conductance in clean two-dimensional metals

Abstract

We study the temperature-dependent corrections to the conductance due to electron-electron (ee) interactions in clean two-dimensional conductors, such as lightly doped graphene or other Dirac matter. We use semiclassical Boltzmann kinetic theory to solve the problem of collision-dominated transport between reflection-free contacts. Time-reversal symmetry and the kinematic constraints of scattering in two dimensions (2D) ensure that inversion-odd and inversion-even distortions of the quasiparticle distribution relax with parametrically different rates at low temperature. This entails the surprising result that at lowest temperatures the conductance of very long samples tends to the noninteracting, ballistic conductance, despite the relaxation of the quasiparticle distribution to a drifting equilibrium. The relative correction to the conductance depends on the ratio of relaxation rates of even and odd modes and scales as δG/G ballistic ∼ (T /εF ) log ε F T , in stark contrast to the behavior in other dimensionalities. This holds generally in 2D systems with simply connected and convex but otherwise arbitrary Fermi surfaces, as long as e-e scattering processes are dominant and umklapp scattering is negligible. These results are especially relevant to the bulk of wide and long suspended high-mobility graphene sheets.

Two‐Particle Scattering and Resistivity of Rashba Electron Gas

“…The corresponding current density is given by Eq. (12) with v µ , p ±µ , and Φ ±µ taken (20) and has the temperature dependence T 4 ln |E F /T |. A similar temperature dependence was recently obtained for the relaxation rate of higher-order odd angular harmonics of electron distribution in 2D systems with parabolic spectrum due to electron-electron collisions.…”

“…The T 4 dependence was predicted by Gurzhi et al 19 , and the additional logarithmic factor was recently found in Ref. 20 . The j(E F /E SO ) dependence is shown in Fig.…”

Hydrodynamics with triangular point group

“…However, in reality, whenever the Fermi surface is a convex polygon, this assumption is likely to break down. The problem is most studied on circular (isotropic) Fermi surfaces [49][50][51][52],…”