Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-line Semimetals

TL;DR

This paper systematically analyzes the phase shifts in quantum oscillations of topological nodal-line semimetals, providing general rules to interpret experimental results and resolve contradictory observations.

Contribution

It introduces a comprehensive model and analytical framework for understanding phase shifts in SdH oscillations in nodal-line semimetals, accounting for various experimental conditions.

Findings

Derived general rules for phase shifts in SdH oscillations.

Applied rules to ZrSiS and Cu$_3$PdN systems.

Revealed dependence of phase shifts on magnetic field, carrier type, and Fermi surface geometry.

Abstract

Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial $\pi$ Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W=Zr/Hf, H=Si/Ge, M=S/Se/Te). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu$_3$PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help exploring transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.