Topological depletions and sub-leading scalings across topological phase transitions

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.

5 pages + 3 pages SM, 5 + 3 figures, REVTEX4-1

References in corpus (5)

• Fermi arcs and their topological character in the candidate type-II Weyl semimetal MoTe2
• Spin gradient demagnetization cooling of ultracold atoms
• Topological Lifshitz transitions
• A long-lived spin-orbit-coupled degenerate dipolar Fermi gas
• Pairing sizes in attractively interacting Fermi gases with Spin-orbit Couplings

Cited by in corpus (6)

• Multi-critical Behavior in Topological Phase Transitions
• Multi-critical topological transition at quantum criticality
• Magnetic properties of Type I and II Weyl Superconductors
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Aslamazov Larkin Conductivity in Weyl Semimetals