We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.

Z_2 Invariants of topological insulators as geometric obstructions / Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 343:3(2016), pp. 1115-1157. [10.1007/s00220-015-2552-0]

Z_2 Invariants of topological insulators as geometric obstructions

FIORENZA, DOMENICO;MONACO, DOMENICO;PANATI, GIANLUCA
2016

Abstract

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to −1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones.
2016
statistical and nonlinear physics; mathematical physics
01 Pubblicazione su rivista::01a Articolo in rivista
Z_2 Invariants of topological insulators as geometric obstructions / Fiorenza, Domenico; Monaco, Domenico; Panati, Gianluca. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 343:3(2016), pp. 1115-1157. [10.1007/s00220-015-2552-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/862487
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