The hierarchy of excitation lifetimes in two-dimensional Fermi gases

Abstract

Momentum-conserving quasiparticle collisions in two-dimensional Fermi gases give rise to a large family of exceptionally long-lived excitation modes. The lifetimes of these modes exceed by a factor (TF /T ) 2 1 the conventional Landau Fermi-liquid lifetimes τ ∼ TF /T 2 . The long-lived modes have a distinct angular structure, taking the form of cos mθ and sin mθ with odd m values for a circular Fermi surface, with relaxation rate dependence on m of the form m 4 log m, valid at not-too-large m. In contrast, the even-m harmonics feature conventional lifetimes with a weak m dependence. The long-time dynamics, governed by the long-lived modes, takes the form of angular (super)diffusion over the Fermi surface. Altogether, this leads to unusual long-time memory effects, defining an intriguing transport regime that lies between the conventional ballistic and hydrodynamic regimes. CONTENTS

Lévy Flights and Hydrodynamic Superdiffusion on the Dirac Cone of Graphene

“…There are some profound implications that this fractional Fokker-Planck formulation immediately reveals. For example, we consider a scenario where we inject a highly directed excitation [22]. To this end we consider a source term in the Boltzmann equation that causes this excitation:…”

“…The occurrence of Lévy flights to describe scattering processes in momentum space is a more general phenomenon and not restricted to graphene at the neutrality point. In two-dimensional Fermi liquids with char- [18,22]. T F is the Fermi temperature.…”

“…To generate Figs. 1 a) and b) of the main text we created a sequence of random angles ∆θ i using the distribution (22). The position of the particle after N steps, i.e.…”

“…Candidate systems are itinerant electrons near magnetic or nematic quantum phase transitions [5][6][7][8][9][10][11][12][13][14], the superconductorinsulator phase transition [15], or graphene near the Dirac point [16]. Anomalous diffusion was even shown to be present in two-dimensional Fermi liquids [17][18][19][20][21][22].…”

Four regimes of transport in a two-dimensional Fermi fluid

“…In two dimensions, where the Fermi surface is a circle, these fluctuations can be expressed in terms of angular harmonics, with angular momentum m. Simple phase space arguments suggest that the relaxation rate of these fluctuations should be given by a relaxation time with a temperature dependence τ −1 m ∝ m 2 (k B T ) 2 /E F , up to logarithmic corrections. Reference [7] presents a very complete analysis of the collision integral of the two dimensional electron gas, and uses it to estimate the relaxation rate of excitations as function of angular momentum. The work makes use of the fact that α = (k B T )/E F 1, and uses the value of α as an expansion parameter [8].…”