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Topological Classification of Crystalline Insulators through Band Structure Combinatorics
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm
Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe
Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate
Non-Hermitian Boundary Modes and Topology.
TLDR
This work exposes a direct relation between the presence of a point gap invariant and the appearance of skin modes when this gap is trivialized by an edge, and can expose novel non-Hermitian topological regimes beyond the reach of previous methods.
Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry
We present a general methodology toward the systematic characterization of crystalline topological insulating phases with time-reversal symmetry. In particular, taking the two-dimensional spinful h
Unsupervised Machine Learning and Band Topology.
TLDR
An unsupervised machine learning approach that searches for and retrieves paths of adiabatic deformations between Hamiltonians, thereby clustering them according to their topological properties, which is general and readily applicable to any symmetry class.
Geometric approach to fragile topology beyond symmetry indicators
TLDR
This work presents a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands, and makes use of a geometric construction to induce windings in the band structure necessary to facilitate nontrivial topology.
Wilson loop approach to topological crystalline insulators with time reversal symmetry
We present a general methodology to systematically characterize crystalline topological insulating phases with time reversal symmetry (TRS). In particular, we study windings of Wilson loop spectra
The space group classification of topological band-insulators
Topological insulators are now shown to be protected not only by time-reversal symmetry, but also by crystal lattice symmetry. By accounting for the crystalline symmetries, additional topological
Universal probes of two-dimensional topological insulators: dislocation and π flux.
TLDR
It is conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.
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