Quantization of graphene plasmons

Abstract

In this article we perform the quantization of graphene plasmons using both a macroscopic approach based on the classical average electromagnetic energy and a quantum hydrodynamic model, in which graphene charge carriers are modeled as a charged fluid. Both models allow to take into account the dispersion of graphenes optical response, with the hydrodynamic model also allowing for the inclusion of non-local effects. Using both methods, the electromagnetic field mode-functions, and the respective frequencies, are determined for two different graphene structures. we show how to quantize graphene plasmons, considering that graphene is a dispersive medium, and taking into account both local and nonlocal descriptions. It is found that the dispersion of graphene's optical response leads to a non-trivial normalization condition for the mode-functions. The obtained mode-functions are then used to calculate the decay of an emitter, represented by a dipole, via the excitation of graphene surface plasmon-polaritons. The obtained results are compared with the total spontaneous decay rate of the emitter and a near perfect match is found in the relevant spectral range. It is found that non-local effects in graphene's conductivity, become relevant for the emission rate for small Fermi energies and small distances between the dipole and the graphene sheet. :1905.11521v1 [cond-mat.mes-hall] arXiv

Far-field excitation of single graphene plasmon cavities with ultracompressed mode volumes

“…Although we can experimentally thin down the hBN spacer until the monolayer case (16), we note that below thicknesses of 1 to 2 nm, strong nonlocal effects in the graphene should be introduced (16,34), given that we estimated the relative correction due to nonlocal effects to be~23% in our experiment (21). In addition, we estimated the nonlocal response of the metal (17,35,36) and found it to be negligible above 1 nm (21).…”

Hydrodynamic collective modes in graphene

“…The above dispersion can be illustrated numerically as follows. Using the same typical values τ −1 dis = 1 THz, ν = 0.2 m 2 /s (the kinematic viscosity varies only weakly with the carrier density 46 ), and T = 300 K, as well as the typical value of the coupling constant 12,63 α g = 0.23 and the parameters characterizing the external gate in a typical graphene-on-boron nitride structure 3 , the dielectric constant of the hexagonal boron nitride = 4.4 and the graphene to gate distance d = 80 nm, we plot the two dispersions (40) and (42) in Figs. 8-10.…”

“…In particular, the underlying gradient expansion is valid at length scales much larger than the typical length scale ee describing the energy-and momentum-conserving interaction (responsible for equilibration of the system). At smaller length scales, one can study more traditional collective excitations in interacting many-electron systems, including plasmons 15,21,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] , which behavior is well established both theoretically and experimentally.…”

Photonic Chern insulators from two-dimensional atomic lattices interacting with a single surface plasmon polariton

“…Thus the lossless SPP model is a good approximation as long as the SPP propagation length is larger than few lattice periods. In the Coulomb gauge, the SPP vector potential operator A(r, z) in the upper half space (z > 0) is given by [16][17][18][19]:…”