Plasmonic Dirac Cone in Twisted Bilayer Graphene

Abstract

We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states that appear at the AB-BA interfaces. The CEP form a hexagonal network with a unique energy scale ϵ p ¼ ðe 2 Þ=ðϵ 0 ϵt 0 Þ with t 0 the moiré lattice constant and ϵ the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the presence of a plasmonic Dirac cone at ℏω ∼ ϵ p =2 with sound velocity v D ¼ 0.0075c, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4=9 into each of the deflected directions and 1=9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.

Plasmonic Transverse Dipole Moment in Chiral Fermion Nanowires

“…For example, understanding the behavior of nanowire plasmons for other classes of boundary conditions, in particular those for which valley mixing is induced at the single-particle level 46,48 , would likely be important for many types of nanowires. One may also consider the effects of transverse dipole moments on plasmon nanochannel networks, which arise naturally in moiré superlattices, and which have been shown to support their own unique dynamics 29,30,64 . Such systems under some circumstances may become spontaneously valley-polarized, opening another avenue for the broken time-reversal symmetry needed for transverse dipole moments.…”

“…In more recent years, the advent of van der Waals materials, particularly graphene, has greatly enriched the set of interesting physical possibilities for two-dimensional plasmons [11][12][13][14][15][16] . These include a myriad of applications and phenomena, in areas as diverse as terahertz radiation, biosensing, photodetection, quantum computing and more [17][18][19][20][21][22][23][24][25][26][27][28][29][30] .…”

Theory of plasmonic edge states in chiral bilayer systems

“…In addition, for minimal twist angles, the lattice relaxation-induced domain walls between the two equivalent Bernal-stacked configurations may act as a periodic potential for plasmons, opening up the prospect of photonic crystals for nanoscale light [46]. Novel chiral plasmons consisting of topologically protected electronic domain-wall states are also predicted if the chemical potential lies inside the energy gap [47]. Lastly, plasmons in flat bands are extremely long-lived since they are unlikely to couple and decay into the particle-hole continuum [48,49] with nonreciprocal dispersion [50].…”

“…Regarding previous works on the TBG, only bulk plasmonic excitations have been considered so far; see, e.g., [44,47,53,[55][56][57][58][59]. On the other hand, it is well known that at an interface collective plasmonic modes may arise with an electromagnetic field that is localized near edges.…”

Atomic-Scale Confinement and Negative Refraction of Plasmons by Twisted Bilayer Graphene

“…The dynamical conductivities of the AB, BA, and AA regions are sequentially computed by the Kubo formula, , as illustrated in Figure c,d. In domain walls, topological protected Dirac edge states dominate the optical properties . At low energy, the electronic structure of the domain walls is described by the Dirac equation H = normalℏ v D ( σ z k x + σ x k y ) + E D , where σ x and σ z are Pauli matrices and v D = 0.0075 c , c is the speed of light.…”