TY - JOUR
T1 - Topology-Bounded Superfluid Weight in Twisted Bilayer Graphene
AU - Xie, Fang
AU - Song, Zhida
AU - Lian, Biao
AU - Bernevig, B. Andrei
N1 - Funding Information:
We acknowledge helpful discussion with Nai Phuan Ong, Ali Yazdani, Guorui Chen, Sebastiano Peotta, Päivi Törmä, Aleksi Julku, and Long Liang. Z. D. S. and B. B. is supported by the Department of Energy Grants No. de-sc0016239 and No. noaawd1004957, Simons Investigator Grants No. ONRN00014-14-1-0330, the Packard Foundation, the Schmidt Fund for Innovative Research. The National Science Foundation EAGER and No. NSF-MRSEC DMR-1420541 also supported the work. B. L. is supported by Princeton Center for Theoretical Science at Princeton University.
Publisher Copyright:
© 2020 American Physical Society. © 2020 American Physical Society.
PY - 2020/4/24
Y1 - 2020/4/24
N2 - 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 C2zT 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.
AB - 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 C2zT 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.
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U2 - 10.1103/PhysRevLett.124.167002
DO - 10.1103/PhysRevLett.124.167002
M3 - Article
C2 - 32383962
AN - SCOPUS:85084720634
SN - 0031-9007
VL - 124
JO - Physical review letters
JF - Physical review letters
IS - 16
M1 - 167002
ER -