Tomographic Dynamics and Scale-Dependent Viscosity in 2D Electron Systems

Fermi gases in two dimensions display collective dynamics originating from head-on collisions, a collinear carrier scattering process that dominates angular relaxation at not-too-high temperatures $T\ll T_F$. In this regime, a large family of excitations emerges, with an odd-parity angular structure of momentum distribution and 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 timescales and scale-dependent transport coefficients with nontrivial fractional scaling dimensions, leading to fractional-power current flow profiles and unusual conductance scaling versus sample width.

Figure 1

Types of two-body collisions $1,2\to 1^{\prime },2^{\prime }$ at a thermally broadened 2D Fermi surface (red rings), which are allowed by momentum and energy conservation and not inhibited by fermion exclusion. Head-on collisions (a) occur at a rate $\gamma \sim T^2/T_F$, with typical recoil $\mathrm{\Delta }\theta \sim 1$. Such processes, however, affect only the even-parity part of momentum distribution. The odd-parity part relaxes much slower, at a rate ${\gamma }^{\prime }\sim T^4/T_F^3\ll \gamma$ [33] due to processes illustrated in (b) and other non-head-on processes.

Figure 2

Current density in a long strip of width $w$ induced by a uniform dc electric field, Eq. (26). Inset: Flow schematic. The flow profile is different for the conventional viscous and tomographic regimes, showing signatures that depend on the angular relaxation dynamics type, parametrized by $p=4$ and 2. A semicircle is shown as a guide to the eye.