Testing the tomographic Fermi liquid hypothesis with high-order cyclotron resonance

TL;DR

This paper proposes a method to test the 'tomographic Fermi liquid' hypothesis by analyzing high-order cyclotron resonance in graphene, revealing different relaxation times for angular harmonics of electron distribution.

Contribution

It introduces a novel approach to directly measure angular harmonic lifetimes using high-order cyclotron resonance, providing experimental validation for the theoretical 'tomographic Fermi liquid' model.

Findings

Third-order resonance is narrower than second-order, supporting the hypothesis.

Method allows direct determination of all harmonic lifetimes from linear equations.

Experimental results align with theoretical predictions of the model.

Abstract

Recent theoretical studies of carrier-carrier scattering in degenerate two-dimensional systems have revealed radically different relaxation times for odd and even angular harmonics of distribution function. This theoretical concept, dubbed as 'tomographic Fermi liquid', is yet challenging to test with dc electrical measurements as electron scattering weakly affects the electrical resistivity. Here, we show that linewidth and amplitude of electromagnetic absorption at the multiple harmonics of the cyclotron resonance carries all necessary information to test the tomographic Fermi liquid hypothesis. Namely, the height and inverse width of $m$-th order cyclotron resonance ($m \ge 2$) is proportional to the lifetime of $m$-th angular harmonic of electron distribution function $\tau_m$, if probed at wavelengths exceeding the cyclotron radius $R_c$. Measurements of high-order cyclotron resonance at short wavelengths order of $R_c$ also enable a direct determination of all lifetimes $\tau_m$ from a simple linear system of equations that we hereby derive. Extraction of cyclotron resonance lifetimes from an experiment on terahertz photoconductivity in graphene shows that third-order resonance is systematically narrower than second-order one, supporting the prediction of tomographic Fermi liquid hypothesis.