We present a detail theoretical study of the Drude weight and optical conductivity of 8-P mmn borophene having tilted anisotropic Dirac cones. We provide exact analytical expressions of xx and yy components of the Drude weight as well as maximum optical conductivity. We also obtain exact analytical expressions of the minimum energy (ǫ1) required to trigger the optical transitions and energy (ǫ2) needed to attain maximum optical conductivity. We find that the Drude weight and optical conductivity are highly anisotropic as a consequence of the tilted Dirac cone. The tilted parameter can be extracted by knowing ǫ1 and ǫ2 from optical measurements. The maximum values of the components of the optical conductivity do not depend on the carrier density and the tilted parameter. The product of the maximum values of the anisotropic conductivities has the universal value (e 2 /4 ) 2 . The tilted anisotropic Dirac cones in 8-P mmn borophene can be realized by the optical conductivity measurement.

We show that the gap parameter in semi-Dirac material induces a large degree of sensitivity for inter-band optical conductivity with respect to the polarization direction. The optical conductivity reveals an abruptly large value at a certain frequency for light along a particular polarization direction while it is significantly suppressed along the direction orthogonal to the former. The direction-dependent optical conductivity may, in turn, be used to uniquely predict the dispersive nature of the 2D semi-Dirac materials, in addition to other possible applications in the field of transparent conductors.

We show that a gap parameter can fully describe the merging of Dirac cones in semi-Dirac materials from K-and K -points into the common M -point in the Brillouin zone. We predict that the gap parameter manifests itself by enhancing the thermoelectric figure of merit zT as the chemical potential crosses the gap followed by a sign change in the Seebeck coefficient around the same point. Subsequently, we show that there is also a trade-off feature between the maximum power delivered and the efficiency when the chemical potential crosses the gap parameter. An optimal operating point that minimizes the power-efficiency trade-off is consequently singled out for the best thermoelectric performance. Our work paves the way for the use of 2D semi-Dirac materials for thermoelectric applications. arXiv:1905.11039v1 [cond-mat.mes-hall]

The spin-orbit interaction in heavy hole gas formed at p-doped semiconductor heterojunctions and electron gas at SrTiO3 surfaces is cubic in momentum. Here we report magnetotransport properties of k-cubic Rashba spin-orbit coupled two-dimensional fermionic systems. We study longitudinal and Hall component of the resistivity tensor analytically as well as numerically. The longitudinal resistivity shows beating pattern due to different Shubnikov-de Haas (SdH) oscillation frequencies f± for spin-up and spin-down fermions. We propose empirical forms of f± as exact expressions are not available, which are being used to find location of the beating nodes. The beating nodes and the number of oscillations between any two successive nodes obtained from exact numerical results are in excellent agreement with those calculated from the proposed empirical formula. In the Hall resistivity, an additional Hall plateau appears in between two conventional ones as spin-orbit coupling constant increases. The width of this additional plateau increases with spin-orbit coupling constant.

We present detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas(2DHG) with k-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of k-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with k-linear spin-orbit couplings. For large hole density and strong k-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional electron gas with k-linear spin-orbit couplings, we explicitly show that the optical conductivity does not vanish even for equal strength of the two spin-orbit couplings. We attribute this fact to the non-zero Berry phase for equal strength of k-cubic spin-orbit couplings. The least photon energy needed to set in the optical transition in hole gas is one order of magnitude smaller than that of electron gas. Types of two van Hove singularities appear in the optical spectrum are also discussed.