Related papers: Topological classification with additional symmetr…
The relation between bulk topological invariants and experimentally observable physical quantities is a fundamental property of topological insulators and superconductors. In the case of chiral symmetric systems in odd spatial dimensions…
We study topological transitions in one dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises due to the structure of the internal spin degrees of freedom of…
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e. with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs…
Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac…
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological…
The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the non-associativity and non-commutativity of this division algebra…
Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground…
We discuss the effects of disorder in time-reversal invariant topological insulators and superconductors in three spatial dimensions. For three-dimensional topological insulator in symplectic (AII) symmetry class, the phase diagram in the…
The topological non-triviality of insulating phases of matter is by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev…
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…
We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of $\mathbb{Z}$…
The electronic band structure of iron pnictides exhibits four Dirac cones, which are due to crystal symmetry and orbital bonding orientation. This hallmark signature presents the pnictide family as an ideal candidate in the search for…
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…
The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…
The connection of (split-)division algebras with Clifford algebras and supersymmetry is investigated. At first we introduce the class of superalgebras constructed from any given (split-)division algebra. We further specify which real…
Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define seven binary eigenvalues that distinguish the $2^7=128$ states of 32 fermions, and determine their parity, electric charge and interactions. Three commuting elements of the…
The modern algebra concepts are used to construct tables of algebraic spinors related to Clifford algebra multivectors with real and complex coefficients. The following data computed by Mathematica are presented in form of tables for…
Topological crystalline insulators are phases of matter where the crystalline symmetries solely protect the topology. In this work, we explore the effect of many-body interactions in a subclass of topological crystalline insulators, namely…
Pseudo $H$-type Lie algebras are a special class of 2-step nilpotent metric Lie algebras, intimately related to Clifford algebras $\Cl_{r,s}$. In this work we propose the classification method for integral orthonormal structures of pseudo…