Topological depletions and sub-leading scalings across topological phase transitions

TL;DR

This paper investigates universal scaling functions and topological depletions across topological quantum phase transitions in fermionic systems with Weyl spin-orbit coupling, revealing non-analytic corrections and experimental signatures.

Contribution

It introduces the concept of topological depletions and sub-leading scalings in topological phase transitions, providing universal relations and experimental detection methods.

Findings

Identifies third-order topological phase transition with universal critical exponents.

Derives scaling functions for specific heat, compressibility, and magnetic susceptibilities.

Reveals topological depletions as non-analytic, non-Fermi liquid corrections in quantum critical regimes.

Abstract

It remains an open problem if there are universal scaling functions across a topological quantum phase transition (TPT) without an order parameter, but with extended Fermi surfaces (FS ). Here, we study a simple system of fermions hopping in a cubic lattice subject to a Weyl type spin-orbit coupling (SOC). As one tunes the SOC parameter at the half filling, the system displays Weyl fermions and also various TPT due to the collision of particle-particle or hole-hole Weyl Fermi Surface (WFS). At the zero temperature, the TPT is found to be a third order one whose critical exponent is determined. We derive the scaling functions of the specific heat, compressibility and magnetic susceptibilities. In contrast to all the previous cases in quantum or topological transitions, although the leading terms are non-universal and cutoff dependent, the sub-leading terms satisfy universal scaling relations. The sub-leading scaling leads to the topological depletions (TD) which show non-analytic and non-Fermi liquid corrections in the quantum critical regime, can be easily distinguished from the analytic leading terms and detected experimentally. One can also form a topological Wilson ratio from the TD of two conserved quantities such as the specific heat and the compressibility. As a byproduct, we also find Type II Weyl fermions appearing as the TPT due to the collision of the extended particle-hole WFS. Experimental realizations and detections in cold atom systems and materials with SOC are discussed.