Phenomenology of a semi-Dirac semi-Weyl semi-metal

TL;DR

This paper explores the unique electronic properties of semi-Dirac semi-Weyl semimetals, revealing their anisotropic plasmon behavior, divergent susceptibilities at low doping, and tunneling characteristics, extending understanding of their low-energy physics.

Contribution

It provides a detailed analysis of the low-energy behavior, plasmon anisotropy, and tunneling phenomena in semi-Dirac systems, highlighting their distinct physical responses compared to other Dirac and Weyl materials.

Findings

Plasmon frequency is highly anisotropic.

Orbital to spin susceptibility ratio diverges at low doping.

Perfect transmission in Klein tunneling depends on orientation.

Abstract

We extend the study of fermionic particle-hole symmetric semi-Dirac (alternatively, semi-Weyo) dispersion of quasiparticles, $\varepsilon_K = \pm \sqrt{(k_x^2/2m)^2 + (vk_y)^2)} = \pm \varepsilon_0 \sqrt{K_x^4 + K_y^2}$ in dimensionless units, discovered computationally in oxide heterostructures by Pardo and collaborators. This unique system a highly anisotropic sister phase of both (symmetric) graphene and what has become known as a Weyl semimetal, with $<v_y^2>^{1/2} \approx v$ independent of energy, and $<v_x^2>^{1/2} \propto m^{-1/2}\sqrt{\varepsilon}$ being very strongly dependent on energy ($\varepsilon$) and depending only on the effective mass $m$. Each of these systems is distinguished by bands touching (alternatively, crossing) at a point Fermi surface, with one consequence being that for this semi-Dirac system the ratio $|\chi_{orb}/\chi_{sp}|$ of orbital to spin susceptibilities diverges at low doping. We extend the study of the low-energy behavior of the semi-Dirac system, finding the plasmon frequency to be highly anisotropic while the Hall coefficient scales with carrier density in the usual manner. The Faraday rotation behavior is also reported. For Klein tunneling for normal incidence on an arbitrarily oriented barrier, the kinetic energy mixes both linear (massless) and quadratic (massive) contributions depending on orientation. Analogous to graphene, perfect transmission occurs under resonant conditions, except for the specific orientation that eliminates massless dispersion. Comparisons of the semi-Dirac system are made throughout with both other types of point Fermi surface systems.