Abstract
The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional topological properties that do not yield surface spectral features, but manifest themselves as (fractional) quantized electronic charges localized at the crystal boundaries. Here, we formulate such bulk-corner correspondence for the physical relevant case of materials with time-reversal symmetry and spin-orbit coupling. To do so we develop partial real-space invariants that can be neither expressed in terms of Berry phases nor using symmetry-based indicators. These previously unknown crystalline invariants govern the (fractional) quantized corner charges both of isolated material structures and of heterostructures without gapless interface modes. We also show that the partial real-space invariants are able to detect all time-reversal symmetric topological phases of the recently discovered fragile type.
Highlights
The discovery of topological insulators has fundamentally challenged our common classification of materials in terms of electrical insulators and electrical conductors[1,2]
We show that the resulting partial real-space invariants govern the quantized corner charges of insulators that are deformable to atomic limit, and determine the quantized corner charges in heterostructures comprising topologically distinct quantum spin-Hall insulators
Even though the discussion above is informative from a purely Wannier functions, and adiabatically connected to an atomic theoretical point of view and of relevance to metamaterial insulator, the formulation of the topological invariants governing structures, it has a limited value for the large number of insulating the quantized corner charges with time-reversal symmetry only materials which possess time-reversal symmetry
Summary
The discovery of topological insulators has fundamentally challenged our common classification of materials in terms of electrical insulators and electrical conductors[1,2]. Even though the discussion above is informative from a purely Wannier functions, and adiabatically connected to an atomic theoretical point of view and of relevance to metamaterial insulator, the formulation of the topological invariants governing structures, it has a limited value for the large number of insulating the quantized corner charges with time-reversal symmetry only materials which possess time-reversal symmetry This is because requires a bulk expression for the number of Wannier Kramers’. Kramers’ theorem engenders the doubling of the corner charge quantum from 1/n to 2/n; it further guarantees that microscopic details at the edge and corners of a finite size crystal pairs centered at the special Wyckoff positions in the unit cell Such a formulation can be immediately achieved by considering a simple subclass of time-reversal invariant insulators, i.e., systems without sizable spin–orbit coupling.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
