A. Alexandradinata

Parafermionic phases with symmetry breaking and topological order

Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech., P11020 (2012)]. The first essential property is that the groundstates are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the groundstates. These two properties are shown to be topologically robust, and applicable to a wider family of topologically-ordered Hamiltonians than has been previously considered. An an application of these edge modes, we formulate a new notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain groundstate is topological, i.e., it originates from the topological manifold of degenerate states on the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalizes Cooper pairing in superconductors. The stability of these condensates are investigated on both open and closed chains.

Tilted Dirac Fermions

We introduce the notion of a band-inverted, topological semimetal in two-dimensional nonsymmorphic crystals. This notion is materialized in the monolayers of MTe

Spin-orbit-free topological insulators

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Topological Nonsymmorphic Metals from Band Inversion

(M

Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry

=

Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators

W, Mo) if spin-orbit coupling is neglected. We characterize the Dirac band touching topologically by the Wilson loop of the non-Abelian Berry gauge field. An additional feature of the Dirac cone in monolayer MTe

Topological Insulators from Group Cohomology

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Trace index and spectral flow in the entanglement spectrum of topological insulators

is that it tilts over in a Lifshitz transition to produce electron and hole pockets, a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently-reported, non-saturating magnetoresistance in WTe

Topological nonsymmorphic metals from band inversion

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Topological invariants for nonsymmorphic symmetries

, as well as its circular dichroism in photoemission. We complement our analysis and first-principle bandstructure calculations with an