Tomographic collective modes in a magnetic field

TL;DR

This paper investigates how magnetic fields influence the collective modes in two-dimensional Fermi liquids, revealing a transition from a unique tomographic transport regime to conventional regimes as the magnetic field strength increases.

Contribution

It provides a numerically exact analysis of the transition of collective modes in Fermi liquids under magnetic fields, highlighting the disappearance of certain modes and the role of Landau parameters.

Findings

One of the two tomographic modes disappears at a critical magnetic field.

The remaining mode becomes more hydrodynamic at high magnetic fields.

The transition depends on Landau parameters and can be observed via current response damping.

Abstract

Two-dimensional Fermi liquids at low temperatures have been theoretically established to exhibit an odd-even effect in the collective quasiparticle relaxation rates where even-parity deformations of the Fermi surface decay at a much faster rate than odd-parity ones. A predicted consequence of this effect is a new tomographic transport regime that mixes hydrodynamic and collisionless transport. In the presence of a magnetic field, however, the tomographic regime is expected to evolve towards conventional transport regimes as soon as the cyclotron radius becomes smaller than the dominant odd-parity mean free path. In this work, we examine this transition from the point of view of collective modes, using a numerically exact solution of the linearized Boltzmann equation within a generalized relaxation time approximation for the odd-parity and even-parity modes. In the absence of a magnetic field, the transverse conductivity exhibits two diffusive tomographic collective modes, and we find that at a critical magnetic field one of these two tomographic modes disappears. Which tomographic mode persists depends on the Landau parameters, with the remaining mode becoming increasingly dominated by hydrodynamic modes at high fields. We corroborate our analysis using a variational approach for the Fermi surface deformation that captures the angular structure of the deformation and the critical magnetic field strength. The collective modes discussed here can in principle be observed by examining the damping of longitudinal and transverse current responses in finite magnetic fields.