Search for plasmons in isotropic Luttinger semimetals

Abstract

Luttinger semimetals include materials like gray tin (α-Sn) and mercury telluride, which are three-dimensional gapless semiconductors having a quadratic band crossing point (QBCP). Due to a growing interest in QBCPs and new experimental efforts, it is essential to study the finite-temperature properties of such systems. In this paper, we investigate the emergence of plasmons in the presence of Coulomb interactions in isotropic Luttinger semimetals, for zero as well as generic nonzero temperatures. When the Fermi level lies right at the QBCP, which is the point where twofold degenerate conduction and valence bands touch each other quadratically, we find that plasmons cannot appear at zero temperature.However, for nonzero temperatures, thermal plasmons are generated. Whether they are long-lived or not depends on the values of temperature, effective electron mass and effective fine-structure constant, and the number of fermion flavors. We also numerically estimate the behavior of the inelastic scattering rate at nonzero temperatures, as a function of energy, where the signatures of the QBCP thermal plasmons show up as a sharp peak. Our results will thus serve as a guide to experimental probes on these systems.

Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals

“…Luttinger semimetals refer to a class of strongly spin-orbit coupled fermions with pseudospin-3/2 in three dimensions, whose normal state exhibits quadratic touching of Kramers-degenerate valence and conduction bands at the Brillouin zone center (i.e., the Γ-point). Due to the growing relevance of these strongly correlated compounds nowadays in the field of topological quantum materials, there has been a recent surge of theoretical works investigating various aspects of the physics of these systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Important examples of these compounds include HeTe [16][17][18], some pyrochlore iridates [19,20], grey-tin [21], half-Heusler compounds [22,23], etc.…”

Thermoelectric and thermal properties of the weakly disordered non-Fermi liquid phase of Luttinger semimetals

“…This node exhibits a quadratic band-touching (QBT) of doubly-degenerate valence and conduction bands in the three-dimensional Brillouin zone. The unconventional properties of these compounds that emerge due to the nontrivial topology of its electronic states, have attracted considerable attention in recent years in the field of topological quantum matter [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Examples of these materials include some pyrochlore iridates [5,19], half-Heusler compounds [21,22], and grey-Sn [23], among others.…”

Dielectric function and plasmons of doped three-dimensional Luttinger semimetals

“…Fermi energy located at the quadratic band touching point) at finite T have been recently calculated in Ref. 55.…”