Anomalous Phase Shift of Quantum Oscillations in 3D Topological Semimetals

TL;DR

This paper investigates how topological properties of 3D semimetals influence quantum oscillation phase shifts, revealing nonmonotonic behavior and beating patterns that enhance understanding of Berry phase effects in these materials.

Contribution

It provides a theoretical analysis of phase shifts in quantum oscillations of Weyl and Dirac semimetals, highlighting effects of topological band inversion and inter-Landau band scattering.

Findings

Phase shift varies nonmonotonically in Weyl semimetals.

Topological band inversion causes beating patterns without Zeeman splitting.

Resistivity peaks correspond to integer Landau indices.

Abstract

Berry phase physics is closely related to a number of topological states of matter. Recently discovered topological semimetals are believed to host a nontrivial $\pi$ Berry phase to induce a phase shift of $\pm 1/8$ in the quantum oscillation ($+$ for hole and $-$ for electron carriers). We theoretically study the Shubnikov-de Haas oscillation of Weyl and Dirac semimetals, taking into account their topological nature and inter-Landau band scattering. For a Weyl semimetal with broken time-reversal symmetry, the phase shift is found to change nonmonotonically and go beyond known values of $\pm 1/8$ and $\pm 5/8$. For a Dirac semimetal or paramagnetic Weyl semimetal, time-reversal symmetry leads to a discrete phase shift of $\pm 1/8$ or $\pm 5/8$, as a function of the Fermi energy. Different from the previous works, we find that the topological band inversion can lead to beating patterns in the absence of Zeeman splitting. We also find the resistivity peaks should be assigned integers in the Landau index plot. Our findings may account for recent experiments in Cd$_2$As$_3$ and should be helpful for exploring the Berry phase in various 3D systems.