Optical properties of a semi-Dirac material

Abstract

Within a Kubo formalism, we calculate the absorptive part of the dynamic longitudinal conductivity σ(Ω) of a 2D semi-Dirac material. In the clean limit, we provide separate analytic formulas for intraband (Drude) and interband contributions for σ(Ω) in both the relativistic and nonrelativistic directions. At finite doping, in the relativistic direction, a sumrule holds between the increase in optical spectral weight in the Drude component and that lost in the interband optical transitions. For the nonrelativistic direction, no such sumrule applies. Results are also presented when an energy gap opens in the energy dispersion. Numerical results due to finite residual scattering are provided and analytic results for the dc limit are derived. Energy dependence and possible anisotropy in the impurity scattering rate is considered. Throughout, we provide comparison of our results for √ σxxσyy with the corresponding results for graphene. A generalization of the 2D Hamiltonian to include powers of higher order than quadratic (nonrelativistic) and linear (relativistic) is considered. We also discuss the modifications introduced when an additional flat band is included via a semi-Dirac version of the α-T3 model, for which an α parameter tunes between the 2D semi-Dirac (graphene-like) limit and the semi-Dirac version of the dice or T3 lattice.

Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmnborophene: Role of frequency, temperature, and scattering limits

“…Notice that apart from ϕ ter yy and ϕ tra yy , the anisotropy in the energy dispersion introduces an additional scaling factor v y /v x to σ yy , in agreement with calculations using the Landauer formalism [38] or in a semi-Dirac material [47].…”

Electronic properties and polaronic dynamics of semi-Dirac system within Ladder approximation

“…It is easy to find that, unlike the result obtained base on anisotropic model as shown above, the DOS obtained in low-density approximation is independent of energy ω in some certain region: for upper branch, nonzero constant DOS requires ω + µ i > D, while for lower branch, nonzero constant DOS requires ω + µ i < D. This is different to both the intrinsic Dirac systems (or some other graphene-related complex junction structures [94,100]) which has a DOS linear with energy in low-energy regime [97,92], and the semi-Dirac systems whose DOS is proportional to √ ω as we stated above. Such special phenomenon in DOS (constant, but not follow the power law behavior) is similar to the normal 2D electron gas, and can also be found in the bilayer graphene [98,113] or other bilayer Dirac-like systems under magnetic field [99,114] (if we ignore the largest peak in zero energy which is contributed by a doubly degenerated level). That also implies in low carrier density approximation the semi-Dirac system can be approximately treated as 2D electron gas although with different effective masses in different directions.…”

“…We investigate the electronic properties of semi-Dirac system as well as the related polaronic dynamics as a semi-Dirac quasiparticle (impurity) immersed into a medium (two-dimensional (2D) electron gas). Semi-Dirac 2D material, which exhibits a relativistic dispersion in one direction and nonrelativistic in another, has surge a great research interest [125,114]. Besides, due to the existence of nonadiabatic feature in the nonrelativistic direction, the polaronic effect would be foud as the minority semi-Dirac quasiparticles interact with the quadratic majority particles (particle-hole excitations) in 2D electron gas.…”

Unfolding optical transition weights of impurity materials for first-principles LCAO electronic structure calculations

“…The optical properties contain fundamental features of materials, including optical conductivity, dielectric function, refractive index, reflectivity, and transmission that can be measured by experiments [1][2][3][4][5][6][7][8][9], and have been widely studied for a variety of compounds, such as solids [10][11][12][13], nanoparticles [14,15], 2D materials [16][17][18][19][20], superconductors [21][22][23][24], and biological tissues [25]. The optical conductivity and dielectric function of materials are two important measurable quantities for understanding natural phenomena, such as current density caused by an alternative electric field, optical transitions, and energy dissipation [26][27][28][29][30].…”