Plasmons in tunnel-coupled graphene layers: Backward waves with quantum cascade gain

Abstract

We predict a new mechanism of surface plasmon amplification in graphene-insulator-graphene van der Waals heterostructures. The amplification occurs upon the stimulated interlayer electron tunneling accompanied by the emission of a coherent plasmon. The quantum-mechanical calculations of the non-local high-frequency tunnel conductivity show that a relative smallness of the tunneling exponent can be compensated by a strong resonance due to the enhanced tunneling between electron states with collinear momenta in the neighboring graphene layers. With the optimal selection of the barrier layer, the surface plasmon gain due to the inelastic tunneling can compensate or even exceed the loss due to both Drude and interband absorption. The tunneling emission of the surface plasmons is robust against a slight twist of the graphene layers and might explain the electroluminescence from the tunnel-coupled graphene layers observed in the recent experiments.The ultrarelativistic nature of electrons in graphene gives rise to the uncommon properties of their collective excitations -surface plasmons [1][2][3]. The deep subwavelength confinement [3], the unconventional density dependence of frequency [4,5], and the absence of Landau damping [4] are probably the most well-known features of plasmons in graphene-based heterostructures. Among more sophisticated predictions there stand the existence of weakly damped transverse electric plasmons [6] and quasi-neutral electron-hole sound waves near the neutrality point [7,8]. Some peculiar types of plasmons can be excited in the graphene p − n junctions [9], field-effect transistors [10,11], optoelectronic modulators [12], and nanomechanical resonators [13] engaging for the improved device performance at the terahertz frequencies.Unfortunately, the experimental studies of graphene plasmons are yet unable to confirm or refute many of these predictions. To achieve an extreme plasmon confinement, one has to sacrifice their propagation length. The latter is of the order of several micrometers at the infrared frequencies [14,15] and is limited by the interband absorption in intrinsic samples and somewhat lower Drude absorption in the doped ones [16]. The experimentally reported quality factors of graphene plasmons reach only five for graphene on SiO 2 [14, 15], and 25 for graphene encapsulated in hexagonal boron nitride [17] at room temperature. In the latter case, the damping is due to the scattering by the intrinsic acoustic phonons [16] and can be suppressed only by lowering the temperature.Instead of reducing the plasmon loss, it is possible to overcome the damping by introducing the gain medium which can replenish the energy being dissipated upon scattering. This idea has stimulated the re-examination of various 'classical' plasma instabilities in graphene, including the beam and resistive instabilities [18], Dyakonov-Shur self-excitation [10,11], and generation due to the negative differential conductance [19]. On the other hand, the plasmon gain can be provided by the photogenerated ele...

Optical antennas driven by quantum tunneling: a key issues review

“…Promising platforms for the realization of such strategies are molecular tunnel junctions [148,149] and van der Waals heterostructures [132,150,151]. Several theoretical works have predicted the efficient excitation of graphene plasmons by IET in graphene-based tunneling devices, promising an excitation source for the farinfrared and Terahertz regime [152][153][154].…”

Plasmon Modes in Bilayer–Monolayer Graphene Heterostructures

“…The dispersion relations for the longitudinal collective excitations are given by the zeroes of dynamical dielectric function where is the plasmon frequency at a given wave‐vector and is the damping rate of plasma oscillations. In case of weak damping (), the plasmon dispersion and decay rate are determined from the following equations: and …”

“…The dispersion relations for the longitudinal collective excitations are given by the zeroes of dynamical dielectric function [11][12][13][14][15][16][17][18][19][20][21] e q; ω p À iγ…”

“…Due to chirality of graphene carriers, the plasmons in MLG and BLG exhibit significantly different from those of ordinary two‐dimensional electron gas (2DEG) . Plasmon dispersion in double‐layer systems was revealed to be considerably different from the single layer ones . It was shown recently that plasmon modes in MLG–2DEG and BLG–2DEG heterostructures even have more interesting properties due to linear electron energy dispersion and chiral character of graphene carriers.…”

“…[11,12,13] Plasmon dispersion in double-layer systems was revealed to be considerably different from the single layer ones. [14][15][16][17][18][19][20][21] It was shown recently that plasmon modes in MLG-2DEG [22][23] and BLG-2DEG [24] heterostructures even have more interesting properties due to linear electron energy dispersion and chiral character of graphene carriers. Ground state [25] and Coulomb drag [26] in a BLG-MLG heterostructure, which is chiral system, have been investigated recently.…”