Related papers: Topological Crystalline Materials - General Formul…
Many materials crystallize in structure types that feature a square-net of atoms. While these compounds can exhibit many different properties, some members of this family are topological materials. Within the square-net-based topological…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
Three dimensional (3D) topological insulators are novel states of quantum matter that feature spin-momentum locked helical Dirac fermions on their surfaces and hold promise to open new vistas in spintronics, quantum computing and…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Since topological insulators were theoretically predicted and experimentally observed in semiconductors with strong spin-orbit coupling, more and more attention has been drawn to topological materials which host exotic surface states. These…
The established diversity of electronic topology classes lends the opportunity to pair them into dual topological complexes. Bulk-surface correspondence then ensures the coexistence of a combination of boundary states that cannot be…
Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on…
We provide a manifestly topological classification scheme for generalised Weyl semimetals, in any spatial dimension and with arbitrary Weyl surfaces which may be non-trivially linked. The classification naturally incorporates that of Chern…
Chiral symmetry on bipartite lattices with different numbers of $A$-sites and $B$-sites is exceptional in condensed matter, as it gives rise to zero-energy flat bands. Crystalline systems featuring chiral symmetry with non-equal sublattices…
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
We propose a general formula for the group of invertible topological phases on a space $Y$, possibly equipped with the action of a group $G$. Our formula applies to arbitrary symmetry types. When $Y$ is Euclidean space and $G$ a…
In this article we describe the equivariant and ordinary topological $K$-ring of a toric bundle with fiber a $T$-{\it cellular} toric variety. This generalizes the results in \cite{su} on $K$-theory of smooth projective toric bundles. We…
Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…
While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections…
Topological phases of matter$\unicode{x2013}$comprising both insulators and semimetals$\unicode{x2013}$offer great potential for quantum applications, but identifying new candidates remains challenging due to expensive first-principles…
When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a…
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i)…