Dirac Cone Spectrum Research Articles

Bound states in the continuum and Fano resonances in the Dirac cone spectrum

We consider light scattering by two dimensional arrays of high-index dielectric spheres arranged into the triangular lattice. It is demonstrated that in the case a triple degeneracy of resonant leaky modes in the Gamma-point the scattering spectra exhibit a complicated picture of Fano resonances with extremely narrow line-width. The Fan features are explained through coupled mode theory for a Dirac cone spectrum as a signature of optical bound states in the continuum (BIC). It is found that the standing wave in-Gamma BIC induces a ring of off-Gamma BICs due to different scaling laws for real and imaginary parts of the resonant eigenfrequencies in the Dirac cone spectrum. A quantitative theory of the spectra is proposed.

Manipulating the anisotropy of the Dirac-Cone in graphene by laser fields

One of the most striking properties of graphene is the relativistic-like Dirac-Cone spectrum of charge carriers. By applying high-frequency laser fields, the system can be described with the use of similar spectrum which is based on a concept of electron quasi-energy. There in this spectrum a creation and annihilation of new Dirac points and cones as well as opening a gap may arise. This allows controlling electron motion without applying DC periodic fields which are effectively described by graphene superlattices. Here we demonstrate that coherent electromagnetic fields applied to graphene can generate new Dirac and Weyl points, induce Lifshitz quantum phase transition for slightly doped graphene and produce an anisotropy of the Dirac cones, which can be even infinite.Graphical abstract

Kinked plasmon dispersion in borophene-borophene and borophene-graphene double layers

We investigate the collective plasmon modes in double layer of two dimensional materials where either one or both of the layers have tilted Dirac cone. Consistent with quite generic hydrodynamic treatment, similar to double layer graphene systems we find two branches of plasmons. The in-phase oscillations of the two layers disperses as $\sqrt q$, while the out-of-phase mode disperses as $q$. When even one of the layers hosts tilted Dirac cone spectrum, the plasmonic kink which is a salient feature of a monolayer of tilted Dirac cone is inherited by both of these branches. In double layers composed of graphene (nontilted) and borophene (tilted) where the two layers have two different Fermi velocities, the velocity scale of plasmonic modes is set by the greater of the two. The kink always takes place when each plasmon mode crosses an energy scale $\omega_{\rm kink}$. When the two layers have different chemical potentials, there will be two such scales, and each of in-phase and out-of-phase modes develop two kinks. Moreover we find that an additional linearly dispersing overdamped mode of monolayer tilted Dirac cone system survives in the double layer system.

Tilt-induced kink in the plasmon dispersion of two-dimensional Dirac electrons

The list of two dimensional Dirac systems with a tilt in their Dirac cone spectrum is expanding, and now in addition to organic system $\alpha$(BEDT-TTF)$_2$I$_3$ includes the two dimensional $8Pmmn$-borophene sheet, which allows for controlled doping by the gate voltage. We analytically calculate the polarization function of tilted Dirac cone for arbitrary tilt parameter, $0\le \eta <1$, and arbitrary doping. This enables us to find two interesting plasmonic effects solely caused by the tilt: (i) In addition to the standard plasmon oscillations, strong enough tilt, induces an additional linearly dispersing overdamped branch of plasmons, which is strongly Landau damped due to overlap with a large density of intra-band free particle-hole (PH) excitations. (ii) There appears a kink in the plasmon dispersion for any non-zero tilt parameter. The kink appears when the plasmon branch enters the inter-band continuum of PH excitations. This kink becomes most manifest for wave vectors perpendicular to the tilt direction and fades away by approaching the tilt direction. Experimental measurement of the wave vector and energy of the plasmonic kink, when combined with our analytic formula for the kink energy scale, allows for a direct experimental measurement of the tilt parameter.

Ternary wurtzite CaAgBi materials family: A playground for essential and accidental, type-I and type-II Dirac fermions

Based on their formation mechanisms, Dirac points in three-dimensional systems can be classified as accidental or essential. The former can be further distinguished into type-I and type-II, depending on whether the Dirac cone spectrum is completely tipped over along certain direction. Here, we predict the coexistence of all three kinds of Dirac points in the low-energy band structure of CaAgBi-family materials with a stuffed Wurtzite structure. Two pairs of accidental Dirac points reside on the rotational axis, with one pair being type-I and the other pair type-II; while another essential Dirac point is pinned at the high symmetry point on the Brillouin zone boundary. Due to broken inversion symmetry, the band degeneracy around accidental Dirac points is completely lifted except along the rotational axis, which may enable the splitting of chiral carriers at a ballistic p-n junction with a double negative refraction effect. We clarify their symmetry protections, and find both the Dirac-cone and Fermi arc topological surface states.

Topologically distinct critical theories emerging from the bulk entanglement spectrum of integer quantum Hall states on a lattice

The critical theories for the topological phase transitions of integer quantum Hall states to a trivial insulating state with the same symmetry can be obtained by calculating the ground state entanglement spectrum under a symmetric checkerboard bipartition. In contrast to the gapless edge excitations under the left-right bipartition, a quantum network with bulk gapless excitations naturally emerges at the Brillouin zone center without fine tuning. On a large finite lattice, the resulting critical theory for the $\nu =1$ state is the (2+1) dimensional relativistic quantum field theory characterized by a \textit{single} Dirac cone spectrum and a pair of \textit{fractionalized} zero-energy states, while for the $\nu =2$ state the critical theory exhibits a parabolic spectrum and no sign of fractionalization in the zero-energy states. A triangular correspondence is established among the bulk topological theory, gapless edge theory, and the critical theory via the ground state entanglement spectrum.

The design of d-character Dirac cones based on graphene

We introduce a new framework for designing a transition metal (TM) d-electrons dominant Dirac cone spectrum based on the hybridization between graphene and a modulated TM d impurity band. The obtained Dirac cone behaves like a ‘copy’ from graphene, insensitive to the TM coverage and order. First-principles calculations reveal such a system of Mn intercalated epitaxial graphene on SiC(0 0 0 1), dubbed manganosine. The robustness of the Dirac cone is discussed in terms of the possible imperfection of Mn atoms. The mechanism at work is expected to be rather general and may open the door to designing new d- or f-character Dirac systems.

Gapless spin-1 neutral collective mode branch for graphite.

Using the standard tight binding model of 2D graphite with short range electron repulsion, we predict a gapless spin-1, neutral collective mode branch below the particle-hole continuum with energy vanishing linearly with momenta at the Gamma and K points in the Brillouin zone. This spin-1 mode has a wide energy dispersion, 0 to approximately 2 eV, and is not Landau damped. The "Dirac cone spectrum" of electrons at the chemical potential of graphite generates our collective mode, so we call this "spin-1 zero sound" of the "Dirac sea." Epithermal neutron scattering experiments and spin polarized electron energy loss spectroscopy can be used to confirm and study our collective mode.