Inter-harmonic ratio structure and saturation of Bernstein modes in graphene

TL;DR

This paper derives the absorption characteristics of Bernstein modes in graphene, revealing how harmonic ratios are affected by launch spectra, screening, linewidth, and saturation effects, with implications for experimental measurements.

Contribution

It provides a theoretical framework for understanding inter-harmonic ratios and saturation in graphene Bernstein modes, including the effects of launch and screening factors.

Findings

Inter-harmonic peak ratios approximate m/n, with corrections from linewidth and residual response.

Moderate launcher/dielectric misspecification shifts ratios by about 1-2%, linewidth assumptions cause 10-30% shifts.

Saturation curves for Bernstein modes and cyclotron resonance differ in linewidth scaling, affecting power dependence.

Abstract

Bernstein modes (BM) in graphene are finite-wavevector magnetoplasmons excited by contact near fields, whereas ordinary cyclotron resonance (CR) probes $q\approx0$. We derive the BM peak absorption in the quasiclassical ballistic regime and show that it factorizes into a launch spectrum, Bernstein-mode splitting, turning-point enhancement, and residual dielectric-response factor. At fixed excitation frequency, BM overtones ($n\ge2$) are sampled, to leading order, at the same momentum $q\simeq\omega/v_F$. Smooth launch and screening factors therefore cancel in inter-harmonic peak ratios, yielding $I_n/I_m\simeq m/n$, modified by linewidth corrections and one residual response ratio for each harmonic pair. In smooth-launcher synthetic tests, noisy full-$q$ spectra recover the residual ratio within errors: moderate launcher/dielectric misspecification within this benchmark family shifts it by only $\sim\!1$--$2\%$, whereas linewidth assumptions shift it by $\sim\!10$--$30\%$. The same factorization connects low-power amplitudes to nonlinear saturation. If BM harmonics share the same cooling region and bolometric readout, the low-power slope times onset intensity is harmonic independent, while BM and CR power sweeps obey distinct normalized saturation curves with linewidth scalings $\Gamma^{-1/2}$ and $\Gamma^{-1}$.