Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

Abstract

Topological insulating (TI) phases were originally highlighted for their disorder-robust bulk responses, such as the quantized Hall conductivity of 2D Chern insulators. With the discovery of time-reversal-(T -) invariant 2D TIs, and the recognition that their spin Hall conductivity is generically non-quantized, focus has since shifted to boundary states as signatures of 2D and 3D TIs and symmetry-enforced topological crystalline insulators (TCIs). However, in T -invariant (helical) 3D TCIs such as bismuth, BiBr, and MoTe2 -termed higher-order TCIs (HOTIs) -the boundary signatures manifest as 1D hinge states, whose configurations are dependent on sample details. It is hence desirable to elucidate bulk signatures of helical TCIs, and their relationship to sample-independent experimental observables. In this work, we introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the bulk topological properties of Iand T -protected helical HOTIs. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetal states with gapless spin spectra, and T -doubled axion insulator (T-DAXI) states with nontrivial partial axion angles θ ± = π indicative of a 3D spin-magnetoelectric bulk response. We provide experimental signatures of each spin-stable regime of helical HOTIs, including surface Fermi arcs in spin-Weyl semimetals under strong Zeeman fields, and half-quantized 2D TI states on the gapped surfaces of T-DAXIs originating from a partial parity anomaly. Lastly, we use ab-initio calculations to demonstrate that the candidate HOTI β-MoTe2 realizes a spin-Weyl state with 8 total spin-Weyl points.

Effective action approach to the filling anomaly in crystalline topological matter

“…IV. Our work can also be extended to (interacting and noninteracting) time-reversal invariant HOTI phases in 2D, where we expect to find spinresolved responses [112][113][114] and charge-neutral defect states [56,69]. Such an extension would be particularly relevant to experimental searches for non-magnetic obstructed atomic limit phases [115][116][117].…”

BerryEasy: a GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects

“…Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. supported built-in functionality for computing state-of-the-art topological diagnostics including the nested Wilson loop [13,14] and the spin-resolved Wilson loop [15,16]. Both computations are critical for a comprehensive analysis of band topology.…”

“…Both computations are critical for a comprehensive analysis of band topology. Recently, an auxiliary code was constructed to work in conjunction with the PythTB package for the computation of these quantities [16]. However, as mentioned, each code has separate strengths.…”

“…It is thus ideal for investigating the effects of external fields, disorder and impurities on transport and density of states, but to this point it has lacked functionality for diagnosing band topology. In this paper, we detail how BerryEasy offers a simple interface for the computation of the Wilson loop [6,[17][18][19][20][21][22][23][24][25][26], nested Wilson loop [13,14], and spin-resolved Wilson loop [15,16] for models defined in PyBinding. Given its popularity, we note that BerryEasy can additionally be interfaced with Kwant, although not all functionalities available via PyBinding are available with Kwant at this point.…”

Interacting second-order topological insulators in one-dimensional fermions with correlated hopping

“…The key role of inversion symmetry has been further explored in highdimensional systems in the context of fragile topology both in free [21][22][23][24][25][26][27][28][29] and in interacting systems [30][31][32][33][34][35]. Moreover, it has been shown that the combination of inversion and time reversal symmetries plays a central role in various kinds of higher-order topological insulators (HOTIs) in high dimensionality [27,[36][37][38][39][40][41][42][43][44][45]. Topological states of matter result to be much less understood in presence of interactions.…”