Electrical generation of surface plasmon polaritons in plasmonic heterostructures

Abstract

Surface plasmon polaritons (SPPs) can be understood as two-dimensional light confined to a conductor-dielectric interface via plasmonic excitations. While low-energy SPPs behave similarly to photons, higher-frequency SPPs resemble surface plasmons. Electrically generating mid-range SPPs is particularly challenging because it requires compensating for momentum mismatch, a process conventionally achieved through inelastic electron transport in nanostructures. Here, we theoretically demonstrate that electrical SPP generation is possible by directly coupling electron-hole dipoles to the quantized SPP field across an insulating spacer without accompanying electron transport. This approach can be realized in plasmonic van der Waals heterostructures composed of strongly-biased monolayer graphene as the emitter, few-layer hexagonal boron nitride as the spacer, and silver (or gold) as the plasmonic material. In this configuration, graphene's remarkable ability to support a strongly non-equilibrium steady-state electron-hole population results in non-thermal, bias-tunable SPP emission that is uniform along the hBN/Ag interface, achieving a power conversion efficiency of up to 1% and a Purcell factor of up to 100. These findings pave the way for integrating photonic and electronic functionalities within a single two-dimensional heterostructure.

Figures (8)

• Figure 1: SPP generation by biased electrons in an hBN/graphene/hBN/Ag heterostructure. (a) Schematic of the proposed device, where highly mobile graphene electrons, driven out of equilibrium by a strong bias field, generate SPPs at the Ag/hBN interface. (b) SPP field penetration lengths in the dielectric ($l_d$) and metal ($l_m$), compared to the separation $z_0$ between the Ag/hBN interface and the graphene layer. (c) Dispersion relations for graphene electrons, photons in hBN, SPPs, and surface plasmons, illustrating a momentum mismatch in the near-infrared excitation range. (d) SPP emission via electron-hole recombination in strongly biased graphene, where the bias induces carrier population inversion in both energy and momentum, as indicated by the shaded electron bands. Due to the inequality $q\ll |\mathbf{k}'-\mathbf{k}|$, SPPs are emitted nearly normal to the electron motion under bias. (e) Angle-resolved non-equilibrium SPP distribution function at $T_e\sim 2800$K and nearly equal drift and band velocities, showing a preferred propagation direction perpendicular to the bias field, with a peak in the near-infrared region ($\sim$1.5 eV). (f) The Purcell factor, defined as the ratio of SPP to photon emission rates, demonstrates enhancement of 2D light emission at $T_e>1500$K and $z_0<2$nm.
• Figure 2: Extrinsic SPP attenuation due to electrons in graphene. (a) SPP decay rate in graphene due to SPP absorption by hot electrons at $T_e=2800$K. The dashed curve corresponds to the approximate model with the SPP decay rate given by Eq. (\ref{['tauq']}). (b) Extrinsic SPP decay rate rapidly approaches the intrinsic (interfacial) values of the order of $10^{13}$ s$^{-1}$ at the resonance $vq=\omega$ due to a nesting effect in the SPP absorption.
• Figure 3: Non-equilibrium SPP distribution function compared to the thermal SPP bath distribution (gray shaded area). Solid curves represent the full solution, while dashed curves correspond to the approximate model, where the SPP emission is due to non-thermalized electrons only and the generation rate is given by Eq. (\ref{['Gq']}). (a) The peak of the propagating SPP distribution shifts away from the thermally excited background as the electron drift velocity approaches the graphene band velocity under increasing bias. (b) At strong bias fields, the non-equilibrium SPP distribution becomes more pronounced with rising electron temperature relative to the SPP bath. The maximum emission occurs at the energy estimated by Eq. (\ref{['spp-max']}). Note the different scale of the ordinate axis in panels (a,b).
• Figure 4: SPP generation efficiency in the high-bias regime ($\mu {\cal E}_x/v = 0.9$). (a) SPP emission power (red curve) compared with photon emission (orange curve) and electrical (Joule) power (black curve). Note the exponential increase in SPP emission between 1500 and 2000 K, surpassing photon emission at around 1800 K. (b) SPP power conversion efficiency computed for different separations between the hBN/Ag interface and graphene is comparable or higher than the typical literature values zhang2021electricalpommier2023nanoscalewang2023engineering.
• Figure S1: SPP dispersion contrasted to the photon and surface plasmon dispersions for the Ag/hBN interface.