Tomographic Dynamics and Scale-Dependent Viscosity in Two-Dimensional Electron Systems

TL;DR

This paper explores the unique 'tomographic' dynamics in two-dimensional Fermi gases, revealing long-lived excitations, scale-dependent transport, and fractional conductance scaling due to dominant head-on collisions.

Contribution

It introduces the concept of tomographic dynamics in 2D electron systems, highlighting the role of head-on collisions in creating scale-dependent viscosity and fractional transport phenomena.

Findings

Long-lived odd-parity excitations emerge from head-on collisions.

Transport coefficients exhibit fractional scaling with system size.

Current flow profiles and conductance show unconventional scaling behaviors.

Abstract

Fermi gases in two dimensions display a surprising collective behavior originating from the head-on carrier collisions. The head-on processes dominate angular relaxation at not-too-high temperatures $T\ll T_F$ owing to the interplay of Pauli blocking and momentum conservation. As a result, a large family of excitations emerges, associated with the odd-parity harmonics of momentum distribution and having exceptionally long lifetimes. This leads to "tomographic" dynamics: fast 1D spatial diffusion along the unchanging velocity direction accompanied by a slow angular dynamics that gradually randomizes velocity orientation. The tomographic regime features an unusual hierarchy of time scales and scale-dependent transport coefficients with nontrivial fractional scaling dimensions, leading to fractional-power current flow profiles and unusual conductance scaling vs. sample width.