Quantum oscillations and Berry's phase in topological insulator surface states with broken particle-hole symmetry

Abstract

Quantum oscillations can be used to determine properties of the Fermi surface of metals by varying the magnitude and orientation of an external magnetic field. Topological insulator surface states are an unusual mix of normal and Dirac fermions. Unlike in graphene and simple metals, Berry's geometric phase in topological insulator surface states is not necessarily quantized. We show that reliably extracting this geometric phase from the phase offset associated with the quantum oscillations is subtle. This is especially so in the presence of a Dirac gap such as that associated with the Zeeman splitting or interlayer tunneling. We develop a semiclassical theory for general mixed normal-Dirac systems in the presence of a gap, and in doing so clarify the role of topology and broken particle-hole symmetry. We propose a systematic procedure of fitting Landau-level index plots at large filling factors to reliably extract the phase offset associated with Berry's phase.

Magnetization of the metallic surface states in topological insulators

“…While there can be a significant Schrödinger contribution to the low-energy Hamiltonian of a topological insulator, we find here [Eqn. (53)] that the phase offset γ of the magnetic oscillations is essentially zero; this is in agreement with previous semiclassical considerations 10,13,14,40 . This is the same result as for pure relativistic particles for which the Berry phase is π.…”

Quantum oscillations of the topological surface states in low carrier concentration crystals of Bi2−xSbxTe3Pan1, Никитин2, Wu3 et al. 2016Solid State Communications7100View full textAdd to dashboardCite

“…However, obtaining n x by linear extrapolation is not justified in all cases. While it is appropriate for light-element materials, such as graphene [34], it is generally not suitable for 3D Bi-based TIs where deviations from the linear dispersion relation, E(k), and the large Zeeman term should be taken into account [24,25]. We first investigate the effect of a nonideal-Dirac E(k).…”

“…The SdH effect is a powerful tool to discriminate between 2D and 3D Fermi surfaces [23]. At the same time, it may give direct access to the topological nature of the surface states via the geometric phase (Berry phase) [24,25] of the quantum oscillations. Therefore, the SdH effect in TIs has received ample attention in the literature, notably through experiments carried out on bulk crystals of Bi 2 Te 3 , Bi 2 Se 3 and Bi 2 Te 2 Se [12,11,26,27,28].…”

“…In most cases, the phase offset of the quantum oscillations obtained from a linear Landau level plot has been interpreted as a finite Berry phase. However, such an interpretation is not straight-forward because of the non-ideal Dirac dispersion and the sizeable Zeeman effect due to the large g s -factor [24,25]. Therefore, care should be taken when using the phase offset of the SdH oscillations as direct evidence for topological surface states.…”

Thermodynamic signature of Dirac electrons across a possible topological transition in ZrTe5

“…The Berry's phase associated with this quantization is often used as evidence for the existence of non-trivial topology, which can in principle be extracted from a plot of the Landau indices versus inverse magnetic field [19]. However, the influence of Zeeman splitting, the complicating effects of conductivity contributions from other bands and the presence of a Dirac mass can make this extraction unreliable, particularly in three dimensions [20,21]. Instead, a robust consequence of Eq.…”