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• W4313304004 abstract "In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to nontrivial quantized responses. Here we study a particular invariant, the discrete shift 풮, for the square lattice Hofstadter model of free fermions. 풮 is associated with a Z_{M} classification in the presence of M-fold rotational symmetry and charge conservation. 풮 gives quantized contributions to (i) the fractional charge bound to a lattice disclination and (ii) the angular momentum of the ground state with an additional, symmetrically inserted magnetic flux. 풮 forms its own Hofstadter butterfly, which we numerically compute, refining the usual phase diagram of the Hofstadter model. We propose an empirical formula for 풮 in terms of density and flux per plaquette for the Hofstadter bands, and we derive a number of general constraints. We show that bands with the same Chern number may have different values of 풮, although odd and even Chern number bands always have half-integer and integer values of 풮, respectively." @default.
• W4313304004 created "2023-01-06" @default.
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• W4313304004 date "2022-12-30" @default.
• W4313304004 modified "2023-09-30" @default.
• W4313304004 title "Fractional Disclination Charge and Discrete Shift in the Hofstadter Butterfly" @default.
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• W4313304004 doi "https://doi.org/10.1103/physrevlett.129.275301" @default.
• W4313304004 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/36638282" @default.
• W4313304004 hasPublicationYear "2022" @default.
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