Square-root higher-order Weyl semimetals

Song, Lianchun; Yang, Huanhuan; Cao, Yong; Yan, Ping

doi:10.48550/arxiv.2202.07833

Cited by 1 publication

(3 citation statements)

References 27 publications

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“…The off-diagonal Hamiltonian block can be expressed in terms of σ y,z and the identity matrix using Eq. (12). In that regard, our model with the rational power of σ y can be reinterpreted as the Kitaev chain with an additional nearest-neighbour coupling term that mixes the hopping and pairing strengths:…”

Section: Rational Powers Of Bdg Hamiltoniansmentioning

confidence: 99%

“…In the context of topological materials, there has been a resurgence of Dirac's original intuition with the advent of square-root topological insulators and also square-root Weyl semi-metals. Both systems emerge by taking the square root of either an appropriate tight-binding model [3] which can lead to a new class of topological insulator that allows robust edge states with codimension larger than one [4][5][6][7][8][9][10][11] or by stacking such two-dimensional (2D) squareroot higher-order topological insulators with interlayer couplings in a double-helix pattern [12]. While both might seem artificial, the former has been observed in a photonic cage [13].…”

Section: Introductionmentioning

confidence: 99%

“…The key prediction of the square-root Weyl semimetal proposal [12] is the presence of Fermi arcs and hinge states that connect the projection of the Weyl points. Even the latter [12] has had an experimental realization.…”

Section: Introductionmentioning

confidence: 99%

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Kitaev Chain with a Fractional Twist

Basa,

La Nave,

Phillips

2022

Preprint

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The topological non-triviality of insulating phases of matter are 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 chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudo-metallic component to the topological phase diagram within which the winding number is valued in Q. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a non-integral winding number. We remark that this is in correspondence with Ref.[1] demonstrating that projective Dirac operators defined in the absence of spin C structure have rational indices.

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Section: Rational Powers Of Bdg Hamiltoniansmentioning

confidence: 99%