We review the topological gauge theory of the superconductor-to-superinsulator transition. The possible intermediate Bose metal phase intervening between these two states is a bosonic topological insulator. We point out that the correct treatment of a bosonic topological insulator requires a normally neglected, additional dimensionless parameter, which arises because of the non-commutativity between the infinite gap limit and phase space reduction. We show that the bosonic topological insulator is a functional first Landau level. The additional parameter drives two Berezinskii–Kosterlitz–Thouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The two BKT correlation scales account for the emergent granularity observed around the transition. Finally, we derive the ground state wave function for a system of charges and vortices in the Bose metal phase.
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February 2023
Review Article|
February 27 2023
Bosonic topological insulators at the superconductor-to-superinsulator transition
Special Collection:
Mathematical Aspects of Topological Phases
M. C. Diamantini
;
M. C. Diamantini
a)
(Conceptualization)
1
NiPS Laboratory, INFN and Dipartimento di Fisica e Geologia, University of Perugia
, via A. Pascoli, I-06100 Perugia, Italy
a)Author to whom correspondence should be addressed: [email protected]
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C. A. Trugenberger
C. A. Trugenberger
(Conceptualization)
2
SwissScientific Technologies SA
, rue du Rhone 59, CH-1204 Geneva, Switzerland
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a)Author to whom correspondence should be addressed: [email protected]
Note: This paper is part of the Special Topic on Mathematical Aspects of Topological Phases.
J. Math. Phys. 64, 021101 (2023)
Article history
Received:
November 20 2022
Accepted:
January 31 2023
Citation
M. C. Diamantini, C. A. Trugenberger; Bosonic topological insulators at the superconductor-to-superinsulator transition. J. Math. Phys. 1 February 2023; 64 (2): 021101. https://doi.org/10.1063/5.0135522
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