Tunneling phase diagrams in anisotropic Multi-Weyl semimetals

TL;DR

This paper investigates tunneling phenomena in anisotropic Multi-Weyl semimetals, revealing phase transition-like behavior in transmission modes and establishing a formal analogy with statistical mechanics phase transitions.

Contribution

It introduces phase diagrams for tunneling in anisotropic Multi-Weyl semimetals and connects these phenomena to dynamical phase transitions, providing a new classification framework.

Findings

Different anisotropy parameters yield varying transmitted modes.

Identified non-analytical behavior indicative of phase transitions.

Established a formal analogy with statistical mechanics phase transitions.

Abstract

Motivated by the exciting prediction of Multi-Weyl topological semimetals that are stabilized by point group symmetries [Phys. Rev. Lett. 108 (2012) 266802], we study tunneling phenomena for a class of anisotropic Multi-Weyl semimetals. We find that a distant detector for different ranges of an anisotropy parameter $\lambda$ and incident angle $\theta$ will measure a different number of propagating transmitted modes. We present these findings in terms of phase diagrams that is valid for an incoming wave with fixed wavenumber $k$--energy is not fixed. To gain a deeper understanding of this phenomenon we then focus on the simplest case of an anisotropic quadratic Weyl-semimetal and analyze tunneling coefficients analytically and numerically to confirm the observations from the phase diagram. Our results show non-analytical behavior, which is the hallmark of a phase transition. This serves as a motivation to make a formal analogy with phase transitions that are known from statistical mechanics. Specifically, we argue that the long distance limit in our tunneling problem takes the place of the thermodynamic limit in statistical mechanics. More precisely, find a direct formal connection to the recently developed formalism for dynamical phase transitions [Reports on Progress in Physics 81 (5) (2018) 054001]. We propose that this analogy to phase transitions can help classify transport properties in exotic semimetals.