Strongly nonlinear Bernstein modes in graphene reveal plasmon-enhanced near-field magnetoabsorption

TL;DR

This work demonstrates strongly nonlinear THz photoresponse from Bernstein magnetoplasmons in graphene, enabled by near-field enhancement from embedded contacts that couple to short-wavelength BM modes. The BM resonances at $B_c/2$ and $B_c/3$ saturate at relatively low intensities, while the cyclotron resonance remains comparatively linear, and the nonlinear behavior follows $\Delta R= \dfrac{A(f)I}{1+I/I_s(f)}$, with $A(f)$ decreasing and $I_s(f)$ increasing with frequency. Polarization analysis confirms a near-field origin for the BM signals, as BM resonances are helicity-insensitive but strongly depend on the linear polarization angle $\alpha$. Overall, graphene emerges as a platform for nonlinear magnetoplasmonics, enabling strong-field manipulation of collective electron dynamics, nonlocal electrodynamics, and solid-state analogues of cavity quantum electrodynamics.

Abstract

Bernstein modes -- hybrid magnetoplasmon excitations arising from the coupling between cyclotron motion and collective oscillations in two-dimensional electron systems -- offer direct access to non-local electrodynamics. These modes can exhibit rich nonlinear behavior akin to strong-coupling phenomena in cavity quantum electrodynamics, but reaching nonlinear regime has remained experimentally challenging. Here we report the observation of nonlinear Bernstein modes in graphene using terahertz excitation with near-field enhancement from embedded metallic contacts. Photoresistance spectroscopy reveals sharp resonances at Bc/2 and Bc/3 that saturate at radiation intensities nearly an order of magnitude lower than the cyclotron resonance. We ascribe this to strong local heating of the electron gas due to resonant excitation of high-amplitude Bernstein magnetoplasmons, associated with a combination of the field-concentration effect of the near field and plasmonic amplification that is resonantly enhanced in the region of Bernstein gaps. Polarization-resolved measurements further confirm the near-field origin: Bernstein resonances are insensitive to circular helicity but strongly depend on the angle of linear polarization, in sharp contrast to the cyclotron resonance response. Our results establish graphene as a platform for nonlinear magnetoplasmonics, opening opportunities for strong-field manipulation of collective electron dynamics, out-of-equilibrium electron transport, and solid-state analogues of cavity quantum electrodynamics.

Figures (8)

• Figure 1: (a) Magnetoplasmon dispersion (schematic): due to non-local effects at $1/q$ comparable to the spatial scale of the cyclotron motion, it includes the avoided crossings and spectral gaps at $\omega/\omega_c\simeq N$, $N=2,3,..$, corresponding to $B=B_c/N$, in contrast to the conventional magnetoplasmon in the local approximation, red dashed line, following $\omega^2=\omega_c^2+\omega_p^2$ where $\omega_p$ is the plasma frequency at $B=0$. The arrow at $q=0$ indicates the collective uniform CR mode at $\omega=\omega_c$ ($B=B_c$). (b) Measurement setup: The longitudinal resistance $R_{xx}$ is measured in a single-layer graphene sample with embedded metallic contacts subjected to a magnetic field $B$ and normally incident cw THz radiation (Faraday configuration). (c) Longitudinal resistance $R_{xx}$ as a function of $B$ in the presence (red line) and absence (gray line) of THz irradiation at a frequency of $f =\omega/2\pi= 1.63$ THz, measured at $T=4.2$ K and back-gate voltage corresponding to an electron carrier concentration $n= 2.84\times10^{12}$ cm$^{-2}$. The lower inset shows a zoomed-in view of the peak at $B_{c}/2$. The upper inset represents the photoresistance $\Delta R$ -- the difference in $R_\text{xx}$ in the presence and absence of the THz radiation. The vertical dashed gray lines indicate the positions of the CR, $B_c$, and its main overtone, $B_c/2$. Thin vertical lines illustrate the opposite phase of oscillations in $\Delta R$ with respect to $R_\text{xx}$, corresponding to suppression of the SdH oscillations under THz illumination. (d) Photoresistance $\Delta R$ versus the magnetic field, measured at $T=1.8$ K and $f=1.63$ THz for various carrier densities $n$, extracted from the period of SdH oscillations. The dashed lines indicate the positions of the CR and its main overtone at the corresponding densities. The intensity of the incoming radiation was $I=0.165$ W/cm$^2$.
• Figure 2: (a) Photoresistance $\Delta R$ vs. magnetic field $B$ at varied intensities $I$ of incoming $f=1.63$ THz irradiation, as given under each trace, measured at $T=1.8$ K and fixed $n=2.83\times{10^{12}}$ cm$^{-2}$. Dashed lines and arrows show the positions of the CR, $\pm B_c$, and its 2nd harmonics, $\pm B_c$/2. Individual traces are shifted and scaled for clarity. The scaling factors (on the right of each trace) are chosen such that the amplitude of magnetooscillations near the CR, $\Delta R_\text{CR}$, remains the same. This is illustrated in the inset in (b); the color code here and in (c), (d) corresponds to that in (a). The resulting amplitudes $\Delta R_\text{CR}$ at corresponding $I$ are shown using blue square symbols in (b). As evident from (a), the BM photoresponse near $\pm B_c/2$ features a quite different evolution with intensity $I$. (c) and (d) show three lowest-$I$ and three highest-$I$ curves from (a), respectively; the gray trace is shown in both (c) and (d). Here, the scaling factors are chosen such that the height of the BM resonance, $\Delta R_\text{CR/2}$, remains the same. The magnitudes of the BM signal $\Delta R_\text{CR/2}$ at corresponding $I$ are shown using red pentagon symbols in (b) and demonstrate almost full saturation of the BM photoresponse. Solid lines in (b) are fits using Eq. \ref{['formula']}.
• Figure 3: (a) Photoresistance $\Delta R$ vs. magnetic field $B$ at varied intensities $I$ of incoming $f=2.54$ THz irradiation. Other parameters and notations are the same as in Fig. \ref{['fig2']}. In addition to the primary BM resonance at $B_c/2$, at higher frequency also the next BM resonance at $B_c/3$ can be resolved. The rescaled traces near $B_c/3$ are shown in the inset in (b). The corresponding intensity dependence of the photoresponse at $B_c/3$ is represented by purple pentagons in (b); blue and gray pentagons show the intensity evolution of the resonances at $B_c/2$ and $B_c$. Zoomed-in plots demonstrating saturation of the signals for $B_c/2$ and $B_c/3$ are presented in the Supplemental Materials. (c) Intensity dependence of the photoresistance at the CR, $B_c$, and at the primary BM resonance, $B_c/2$, for a lower frequency of $f=0.69$ THz. Solid lines in (b) and (c) are fits using Eq. \ref{['formula']}. The corresponding fitting parameters $A(f)$ and $I_s(f)$ are presented in (d) using a double-logarithmic scale; here we also include the results $f=1.63$ THz from Fig. \ref{['fig2']}. Dashed lines following the $1/f^2$ behavior for $A(f)$ and $f^2$ for $I_s(f)$ are shown as guide for the eye. (e) Positions of the detected CR and BM resonances for all three frequencies are shown as symbols; dashed lines are the calculated positions of $B_c$, $B_c/2$, and $B_c/3$ using the density $n=2.83\times{10^{12}}$ cm$^{-2}$ determined from the period of the SdH oscillations.
• Figure 4: (a) Photoresistance $\Delta R$ vs. $B$ for left-circularly polarized (LCP, red) and right-circularly polarized (RCP, black) $f=1.63$ THz radiation. Other parameters and notations are the same as in Figs. \ref{['fig2']} and \ref{['fig3']}. (b) Photoresistance $\Delta R$ vs. $B$ for different orientations of the electric field of linearly polarized $f=2.54$ THz radiation. The corresponding azimuthal angle of the THz field $\alpha$ is defined in the inset. (c)-(e) The $\alpha$-dependences of the BM photoresponse at $B=B_c/2$ for all three frequencies (symbols). The solid lines are fits using Eq. \ref{['cos']}.
• Figure A.1: Optical image of the sample. The dashed-line polygon indicates the edge of the graphene flake. A zoomed image in the top right corner show how contacts penetrate the sample area. (b) Carrier density dependence of the $B=0$ longitudinal resistance $R_{xx}$ measured at $T=1.8$ K (black line), combined with the correspondent carrier mobility $\mu$ (blue line). The carrier density was extracted from the Hall measurements of $R_{xy}$ at low $B$ (not shown). (c) Photoresistance $\Delta R$ versus the magnetic field, measured at $T=1.8$ K and $f=1.63$ THz for various carrier densities (an extended version of Fig. 1d in the main text). The densities $n$, as provided below each trace, were extracted from SdH oscillations period. The dashed lines indicate the position $B_c$ of CR and its main overtone $B_c/2$ at the corresponding densities.