Abstract
We study two-dimensional spinful insulating phases of matter that are protected by time-reversal and crystalline symmetries. To characterize these phases we employ the concept of corner charge fractionalization: Corners can carry charges that are fractions of even multiples of the electric charge. The charges are quantized and topologically stable as long as all symmetries are preserved. We classify the different corner charge configurations for all point groups, and match them with the corresponding bulk topology. For this we employ symmetry indicators and (nested) Wilson loop invariants. We provide formulas that allow for a convenient calculation of the corner charge from Bloch wavefunctions and illustrate our results using the example of arsenic and antimony monolayers. Depending on the degree of structural buckling, these materials can exhibit two distinct obstructed atomic limits. We present density functional theory calculations for open flakes to support our findings.
Highlights
The classification of insulating phases of matter by topological invariants has been refined in important ways recently
An example foundational to the field are the Z2 topological insulators in two dimensions (2D) and three dimensions (3D) [1,2,3,4], whose topology is protected by time-reversal symmetry (TRS) and manifests in edge and surface states, respectively, which are immune to Anderson localization
We are concerned with 2D TRS spin-orbit coupled crystalline solids that admit a band structure description in terms of free fermions and fall in category (2) above, i.e., obstructed atomic limit [20] (OAL). (This excludes, in particular, Z2 topological insulators protected by TRS and phases with a mirror Chern number, where the mirror plane is the plane of the 2D solid itself.) Our aim is to classify OALs with fractional corner charges and filling anomalies in all 2D layer groups and to provide topological invariants which allow to infer the presence or absence of such charges from the knowledge of the bulk band structure alone
Summary
The classification of insulating phases of matter by topological invariants has been refined in important ways recently. (This excludes, in particular, Z2 topological insulators protected by TRS and phases with a mirror Chern number, where the mirror plane is the plane of the 2D solid itself.) Our aim is to classify OALs with fractional corner charges and filling anomalies in all 2D layer groups and to provide topological invariants which allow to infer the presence or absence of such charges from the knowledge of the bulk band structure alone Such invariants are either computed from the irreducible representations of the Bloch states, in which case we speak of symmetry indicators, or expressed as integrals of a connection obtained from the Bloch states over (subsets of) the Brillouin zone, which will be referred to as Berry phase or Wilson loop type invariants.
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