Signatures of merging Dirac points in optics and transport

Abstract

We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter ∆, there are two distinct Dirac points with linear dispersion, these are connected by a saddle point at higher energy. As ∆ goes to zero, the two Dirac points merge and the resulting dispersion exhibits semi-Dirac behaviour which is quadratic in the x-direction ("nonrelativistic") and linear the y-direction ("relativistic"). In the clean limit for each direction (x, y) the contribution of the intraband and interband optical transitions are both given by universal functions of photon energy Ω and chemical potential µ normalized to the energy gap. We provide analytic formulas for both small and large Ω/2∆ and µ/∆ limits. These define, respectively, Dirac and semi-Dirac-like regions.For Ω/2∆ and µ/∆ of order one, there are deviations from these asymptotic behaviors. Considering optics and also transport, such as dc conductivity, thermal conductivity and the Lorenz number, such deviations provide signatures of the evolution from the Dirac to the semi-Dirac regime as the gap ∆ is varied.

Anisotropic and tunable optical conductivity of a two-dimensional semi-Dirac system in the presence of elliptically polarized radiation

“…1(a-c), the longitudinal optical conductivity σ yy (ω) is larger than σ xx (ω) in the whole spectrum regime. At high radiation frequencies, the optical absorption in the y direction is significant stronger than that in the x direction, which is in line with the results obtained previously [15][16][17]. In the low-frequency regime, both σ xx (ω) and σ yy (ω) decrease monotonously with increasing ω, a typical feature of the Drude-like optical conductivity for free carriers [39].…”

“…It should be noted that in Refs. [16,17], Carbotte et al had also calculated the longitudinal optical conductivity of 2D semi-Dirac system in xx and yy directions with/without a gap within a Kubo formalism. Carbotte et al provided separate analytic formulas of optical conductivity for intraband and interband transitions for certain limitation cases and considered the transport properties such as dc conductivity, thermal conductivity, and the Lorenz number.…”

“…Several investigations of the electronic and optical properties of 2D SD systems have been carried out recently. In particular, the electronic, optoelectronic, and transport properties such as Floquet band structure [13,14], optical conductivity [15][16][17][18], dielectric function and plasmons [11], nonlinear response [19], and ballistic transport modulated by magnetic and electrical barriers [20] have been studied. It has been shown that the 2D SD system can transform from normal insulator to the Chern insulating phase under light irradiation with relatively high frequencies [21,22].…”

Nodal Semimetals: A Survey on Optical Conductivity

“…1). More details for specific cases can be found in vast available literature, especially in the works of J. P. Carbotte and coauthors [39][40][41][42][43][44][45][46][47][48].…”

Anisotropic Andreev reflection in semi-Dirac materials

“…Unlike most Dirac materials that possess liner dispersions in all momentum-space directions [3][4][5], in SDMs the low-energy excitations disperse quadratically in one direction but linearly along the orthogonal direction [6][7][8][9][10]. The unique band structures of SDMs are responsible for a series of novel phenomena [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], including the consequences of anisotropic aspect in the superconducting order parameter correlations [25][26][27]. Recent theoretical efforts have demonstrated that the superconductivity in SDMs can be induced by arbitrarily weak attractions in the present of random chemical potential [25].…”