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

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 π 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 explore transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.

Surface termination dependent quasiparticle scattering interference and magneto-transport study on ZrSiS

“…This behaviour may be related to the fine structures in the 2D tubular Fermi surface shown as the blue area in figure 1(f). The observed major SdH frequency F1 agrees with several previous reports [24,29,34], but we do note that the 3D diamond-shaped band (the green area in figure 1(f)) was not seen in our SdH measurements, which is likely due to its reported unusual mass enhancement [29,35] and our limited field strength.…”

Quantum oscillations probe the Fermi surface topology of the nodal-line semimetal CaAgAs

“…Quantum oscillations in TNLSMs have been predicted to exhibit a peculiar behavior [21][22][23] and can accumulate a topological Berry phase. A qualitative understanding of the quantum oscillations of CaAgAs can be gained by considering the limit of a circular torus FS [ Fig.…”

“…For hole carriers, φ 3D = ±π/4 depends on whether the extremal orbit has locally minimum or maximum area respectively [24]. The phase shifts, in the absence SOC, can be predicted for each frequency branch [21], and are summarized in Table I. To address the topological character of δ, we directly fit the oscillatory torque signal in the high-angle regime (over the field range 18-35 T as shown in Orbit…”

Spin and charge transport in topological nodal-line semimetals

“…When this single mode is incident on the right interface, it will cause a definite transmitted wave as described by Eq. (29). The reflected wave by the right interface will then be reflected alternatively by the left and right interfaces.…”