We present a theoretical study of the local optical conductivity, plasmon spectra, and thermoelectric properties of twisted bilayer graphene (TBG) at different filling factors and twist angles $θ$. Our calculations are based on the electronic band structures obtained from a continuum model that has two tunable parameters, $u_0$ and $u_1$, which parametrize the intra-sublattice inter-layer and inter-sublattice inter-layer tunneling rate, respectively. In this Article we focus on two key aspects: i) we study the dependence of our results on the value of $u_0$, exploring the whole range $0\leq u_0\leq u_1$; ii) we take into account effects arising from the intrinsic charge density inhomogeneity present in TBG, by calculating the band structures within the self-consistent Hartree approximation. At zero filling factor, i.e. at the charge neutrality point, the optical conductivity is quite sensitive to the value of $u_0$ and twist angle, whereas the charge inhomogeneity brings about only modest corrections. On the other hand, away from zero filling, static screening dominates and the optical conductivity is appreciably affected by the charge inhomogeneity, the largest effects being seen on the intra-band contribution to it. These findings are also reflected by the plasmonic spectra. We compare our results with existing ones in the literature, where effects i) and ii) above have not been studied systematically. As natural byproducts of our calculations, we obtain the Drude weight and Seebeck coefficient. The former displays an enhanced particle-hole asymmetry stemming from the inhomogeneous ground-state charge distribution. The latter is shown to display a broad sign-changing feature even at low temperatures ($\approx 5~{\rm K}$) due to the reduced slope of the bands, as compared to those of single-layer graphene.
Interlayer excitons in van der Waals heterostructures of two-dimensional transition metal dichalcogenides have recently emerged as a fascinating platform for quantum many-body effects, long-range interactions, and opto-valleytronic applications. The practical implementation of such phenomena and applications requires further development of the long-lived character of interlayer excitons. Whereas material developments have successfully enhanced the nonradiative lifetime, the out-of-plane polarization nature of the interlayer excitons has made it challenging to improve the radiative lifetime wit…
We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At sub-nanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nano-imaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tu…
We explore the temperature-dependent plasmonic modes of an n-doped double-layer silicene system which is composed of two spatially separated single layers of silicene with a distance large enough to prevent the interlayer electron tunneling. By applying an externally applied electric field, we numerically obtain the poles of the loss function within the so-called random phase approximation, to investigate the effects of temperature and geometry on the plasmon branches in three different regimes: topological insulator, valley-spin polarized metal, and band insulator. Also, we present the finite…
We theoretically examine the role of Kerr nonlinearities for graphene plasmonics in nanostructures, specifically in nanoribbons. The nonlinear Kerr interaction is included semiclassically in the intraband approximation. The resulting electromagnetic problem is solved numerically by self-consistent iteration with linear steps using a real-space discretization. We derive a simple approximation for the resonance shifts in general graphene nanostructures, and obtain excellent agreement with numerics for moderately high field strengths. Near plasmonic resonances the nonlinearities are strongly enha…
Moiré superlattices can induce correlated-electronic phases in twisted van-der-Waals materials. Strongly correlated quantum phenomena emerge, such as superconductivity and the Mott-insulating state. However, moiré superlattices produced through artificial stacking can be quite inhomogeneous, which hampers the development of a clear correlation between the moiré period and the emerging electrical and optical properties. Here we demonstrate in twisted-bilayer transition-metal dichalcogenides that low-frequency Raman scattering can be utilized not only to detect atomic reconstruction, but also to…
Work function-mediated charge transfer in graphene/$α$-RuCl$_3$ heterostructures has been proposed as a strategy for generating highly-doped 2D interfaces. In this geometry, graphene should become sufficiently doped to host surface and edge plasmon-polaritons (SPPs and EPPs, respectively). Characterization of the SPP and EPP behavior as a function of frequency and temperature can be used to simultaneously probe the magnitude of interlayer charge transfer while extracting the optical response of the interfacial doped $α$-RuCl$_3$. We accomplish this using scanning near-field optical microscopy …
We discuss the non-radiative heat transfer in non-equilibrium double layer graphene system. We show that at the neutrality point the heat exchange is dominated by the inter-layer plasmon modes and derive analytic expressions for the heat current as a function of temperature and the interlayer separation. These results show that for a range of low temperatures the two graphene layers are much more efficient heat exchanger than conventional metals. The physical reason behind this phenomenon is the presence of inter-band excitations with a large energy, and a small momentum in graphene spectrum. …
Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local ac conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic stand…
We study optical coefficients that characterize wave propagation through layered structures called plasmonic crystals. These consist of a finite number of stacked metallic sheets embedded in dielectric hosts with a subwavelength spacing. By adjustment of the frequency, spacing, number as well as geometry of the layers, these structures may exhibit appealing transmission properties in a range of frequencies from the terahertz to the mid-infrared regime. Our approach uses a blend of analytical and numerical methods for the distinct geometries with infinite, translation invariant, flat sheets and…
Plasmons in van der Waals heterostructures comprised of graphene and related layered materials demonstrate deep subwavelength confinement and large propagation length. In this letter, we show that graphene-insulator-graphene tunnel structures can serve as plasmonic gain media. The gain stems from the stimulated electron tunneling accompanied by the emission of coherent plasmons under interlayer population inversion. The probability of tunneling with plasmon emission appears to be resonantly large at certain values of frequency and interlayer voltage corresponding to the transitions between ele…
Van der Waals (vdW) heterostructures, which are produced by the precise assemblies of varieties of two-dimensional (2D) materials, have demonstrated many novel properties and functionalities. Here we report a nano-plasmonic study of vdW heterostructures that were produced by depositing ordered molecular layers of pentacene on top of graphene. We find through nano-infrared (IR) imaging that surface plasmons formed due to the collective oscillations of Dirac fermions in graphene are highly sensitive to the adjacent pentacene layers. In particular, the plasmon wavelength declines systematically b…
We discuss the conditions under which the predicted (but not yet observed) zero-field interlayer excitonic condensation in double layer graphene has a critical temperature high enough to allow detection. Crucially, disorder arising from charged impurities and corrugation in the lattice structure --- invariably present in all real samples --- affects the formation of the condensate via the induced charge inhomogeneity. In the former case, we use a numerical Thomas-Fermi-Dirac theory to describe the local fluctuations in the electronic density in double layer graphene devices and estimate the ef…
We study Dirac plasmons and their damping in spatially separated $N$-layer graphene structures at finite doping and temperatures. The plasmon spectrum consists of one optical excitation with a square-root dispersion and $N-1$ acoustical excitations with linear dispersions, which are undamped at zero temperature within a triangular energy region outside the electron-hole continuum. For any finite number of graphene layers we have found that the energy and weight of the optical plasmon increase in the long wavelength limit, respectively, as square-root and linear functions of $N$. This is in agr…
Inspired by recent advances in atomic homo and heterostructures, we consider the vertical stacking of plasmonic lattices as a new degree of freedom to create a coupled system showing a modified optical response concerning the monolayer. The precise design of the stacking and the geometrical parameters of two honeycomb plasmonic lattices tailors the interaction among their metallic nanoparticles. Based on the similarity of the lattice symmetry, analogies can be drawn with stacked atomic crystals, such as graphene. We use the multipolar spectral representation to study the plasmonic vertical sta…
We analytically describe the plasmonic edge modes for an interface that involves the twisted bilayer graphene (TBG) or other similar Moire van der Waals heterostructure. For this purpose, we employ a spatially homogeneous, isotropic and frequency-dependent tensor conductivity which in principle accounts for electronic and electrostatic interlayer couplings. We predict that the edge mode dispersion relation explicitly depends on the chiral response even in the nonretarded limit, in contrast to the collective bulk plasmonic excitations in the TBG. We obtain a universal function for the dispersio…
We study localized plasmonic excitations in bilayer graphene (BLG) nanodisks, comparing AA-stacked and AB-stacked BLG and contrasting the results to the case of two monolayers without electronic hybridization. The electrodynamic response of the BLG electron gas is described in terms of a spatially homogeneous surface conductivity, and an efficient alternative two-dimensional electrostatic approach is employed to carry out all the numerical calculations of plasmon resonances. Due to a unique electronic band structures, the resonance frequency of the traditional dipolar plasmonic mode in the AA-…
Recent results have shown unprecedented control over separation distances between two metallic elements hundreds of nanometers in size, underlying the effects of free-electron nonlocal response also at mid-infrared wavelengths. Most of metallic systems however, still suffer from some degree of inhomogeneity due to fabrication-induced surface roughness. Nanoscale roughness in such systems might hinder the understanding of the role of microscopic interactions. Here we investigate the effect of surface roughness in coaxial nanoapertures resonating at mid-infrared frequencies. We show that althoug…
We investigate the dispersion relation and damping of plasmon modes in a bilayer-monolayer graphene heterostructure with carrier densities and at zero temperature within the random-phase-approximation taking into account the nonhomogeneity of the dielectric background of the system. We derive analytical expressions for plasmon frequencies by using long wavelength expansion of response and bare Coulomb interaction functions. We show that optical plasmon dispersion curve of the bilayer-monolayer system lies slightly below that of double-layer graphene (DLG) and the acoustic one lies much lower t…
We report a systematic plasmonic study of twisted bilayer graphene (TBLG) - two graphene layers stacked with a twist angle. Through real-space nanoimaging of TBLG single crystals with a wide distribution of twist angles, we find that TBLG supports confined infrared plasmons that are sensitively dependent on the twist angle. At small twist angles, TBLG has a plasmon wavelength comparable to that of single-layer graphene. At larger twist angles, the plasmon wavelength of TBLG increases significantly with apparently lower damping. Further analysis and modeling indicate that the observed twist-ang…
Graphene is an atomically thin plasmonic medium that supports highly confined plasmon polaritons, or nano-light, with very low loss. Electronic properties of graphene can be drastically altered when it is laid upon another graphene layer, resulting in a moiré superlattice. The relative twist angle between the two layers is a key tuning parameter of the interlayer coupling in thus obtained twisted bilayer graphene (TBG). We studied propagation of plasmon polaritons in TBG by infrared nano-imaging. We discovered that the atomic reconstruction occurring at small twist angles transforms the TBG in…
We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features previously reported by us [T. Stauber et al. Phys. Rev. Lett. 120, 046801 (2018)] for the Drude matrix in the continuum model are also present in the tight-binding calculation, with increasing quantitative agreement for decreasing twist angle. These features include the chiral longitudinal magnetic moment associated with plasmonic modes, and the anomalous co…
We study plasmon modes in doped AA-stacked bilayer graphene (BLG) within the nearest-neighbor tight-binding and the random phase approximation. We obtain closed analytical expressions for the polarizability function which are used to obtain the low-energy dispersion relations of and the numerical results for both acoustic and optical plasmon modes. Our result reveal the potential of AA-stacked BLG to be used as a tunable plasmonic device. In particular we find that the long-wavelength acoustic plasmon disperse as $ω_{+}\approx\sqrt{max(|μ|,t_{1})q}$ with a phase space which shrinks and vanishe…
Recent experimental and theoretical investigations demonstrate that twisted trilayer graphene (tTLG) is a highly tunable platform to study the correlated insulating states, ferromagnetism, and superconducting properties. Here we explore the possibility of tuning electronic correlations of the tTLG via a vertical pressure. A full tight-binding model is used to accurately describe the pressure-dependent interlayer interactions. Our results show that pressure can push a relatively larger twist angle (for instance, $1.89^{\circ}$) tTLG to reach the flat-band regime. Next, we obtain the relationshi…
Twisted van der Waals bilayers provide an ideal platform to study the electron correlation in solids. Of particular interest is the 30 degree twisted bilayer honeycomb lattice system, which possesses an incommensurate Moire pattern and uncommon electronic behaviors may appear due to the absence of phase coherence. Such system is extremely sensitive to further twist and many intriguing phenomena will occur. In this work, we show that due to the twist induced spatial inhomogeneity of interlayer coupling, there emerges an U(1) gauge field in magnetic transition-metal dichalcogenides (TMD) bilayer…
