Topology-Bounded Superfluid Weight in Twisted Bilayer Graphene

Xie, Fang; Song, Zhida; Lian, Biao; Bernevig, B. Andrei

doi:10.1103/physrevlett.124.167002

Topology-Bounded Superfluid Weight in Twisted Bilayer Graphene

Journal Article · Fri Apr 24 00:00:00 EDT 2020 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.124.167002· OSTI ID:1802878

Xie, Fang ^[1]; Song, Zhida ^[2]; Lian, Biao ^[2]; Bernevig, B. Andrei ^[3]

Princeton Univ., NJ (United States); OSTI
Princeton Univ., NJ (United States)
Princeton Univ., NJ (United States); Freie Universitat Berlin (Germany); Max Planck Institute of Microstructure Physics, Halle (Germany)

While regular flat bands are good for enhancing the density of states and hence the gap, they are detrimental to the superfluid weight. We show that the predicted nontrivial topology of the two lowest flat bands of twisted bilayer graphene (TBLG) plays an important role in the enhancement of the superfluid weight and hence of superconductivity. We derive the superfluid weight (phase stiffness) of the TBLG superconducting flat bands with a uniform pairing, and show that it can be expressed as an integral of the Fubini-Study metric of the flat bands. This mirrors results already obtained for nonzero Chern number bands even though the TBLG flat bands have zero Chern number. We further show that the metric integral is lower bounded by the topological $$C_{2z}T$$ Wilson loop winding number of TBLG flat bands, which renders that the superfluid weight is also bounded by this topological index. In contrast, trivial flat bands have a zero superfluid weight. The superfluid weight is crucial in determining the Berezinskii-Kosterlitz-Thouless transition temperature of the superconductor. Based on the transition temperature measured in TBLG experiments, we estimate the topological contribution of the superfluid weight in TBLG.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: National Oceanic and Atmospheric Administration (NOAA); National Science Foundation (NSF); Packard Foundation; Schmidt Fund for Innovative Research; USDOE Office of Science (SC)

Grant/Contract Number:: SC0016239

OSTI ID:: 1802878

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 16 Vol. 124; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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