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- W2798801395 abstract "We present a general methodology to systematically characterize crystalline insulating phases with time reversal symmetry (TRS). In particular, we study windings of Wilson loop spectra over cuts in the Brillouin zone that are dictated by the underlying lattice symmetries. Our approach finds a prominent use in elucidating and quantifying the recently proposed topological quantum chemistry (TQC) concept. Namely, it evaluates whether a split of an elementary band representation (EBR) must lead to a phase. After lifting the exhaustive classification of two-band spinless phases into four-band spinful phases, we additionally extend the classification beyond the sectors adiabatically connected to the inversion symmetric phases. In particular, we show that in addition to the Fu-Kane-Mele $mathbb{Z}_2$ classification, there is an obstructed $mathbb{Z}$-type classification protected by crystalline symmetries that accounts for all nontrivial Wilson loop windings of split EBRs. Then, by systematically embedding all combinatorial four-band phases into six-band phases, we reveal a generic fragility of higher Wilson loop windings so that the topology of split EBRs can be trivialized under the addition of extra trivial bands. We hence conclude that the premises of TQC are unstable under the inclusion of extra bands. More generally, our work sets the basis of a systematic classification of crystalline phases with TRS by rigorously positioning fragile phases as the bridge in crystalline systems between unstable topology pertaining to few-band models (as captured by e.g. homotopy theory), and stable topology, i.e. unaffected by the addition of an arbitrary number of bands (as described by e.g. K-theories). We constructively illustrate all these results for the honeycomb lattice." @default.
- W2798801395 created "2018-05-07" @default.
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- W2798801395 date "2018-04-25" @default.
- W2798801395 modified "2023-09-26" @default.
- W2798801395 title "Wilson loop approach to topological crystalline insulators with time reversal symmetry" @default.
- W2798801395 hasPublicationYear "2018" @default.
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