Tunneling Phase Diagrams in Anisotropic Multi-Weyl Semimetals

Motivated by the exciting prediction of multi-Weyl topological semimetals stabilized by point group symmetries, tunneling in anisotropic multi-Weyl semimetals is studied. It is found that distant detectors for different ranges of an anisotropy parameter λ and incident angle θ will measure different numbers of propagating transmitted modes. These findings are presented as phase diagrams that are valid for incoming waves with fixed wavenumber k. Energy is not held fixed for incoming waves but allowed to vary with choice of incident angle and wavenumber k. To gain a deeper understanding of this phenomenon they focus on the simplest case of anisotropic quadratic Weyl-semimetals and tunneling coefficients are analyzed analytically and numerically to confirm observations extracted from phase diagrams. Results show nonanalytical behavior, which is the hallmark of phase transitions. This serves as motivation to make a formal analogy with phase transitions known from statistical mechanics. Specifically, they argued that the long distance limit in the tunneling problem mimics the thermodynamic limit in statistical mechanics. A direct formal connection is found to the recently developed formalism of dynamical phase transitions. They propose that usage of this analogy with dynamical phase transitions can be fruitful in classifying transport properties of exotic semimetals.