Quantum geometry: a new paradigm in topological quantum matter and unconventional superconductivity
Dr. Alex Kruchkov
Branco Weiss Fellow & Lecturer
Quantum geometry — the metrics of quantum states in Hilbert space — determines the distance between two neighboring quantum states and their entanglement. The concept of quantum geometry (represented by Fubini-Study metric ) has been widely used in the quantum information theory, however, until recently, had been mainly overlooked in the condensed matter environment. This situation has changed after recent discovery  of twisted bilayer graphene (TBG) and similar moiré heterostructures, which host nearly dispersionless quantum states (”flat bands”) characterized by nontrivial topology and quantum geometry [3-5]. Despite the conventional expectation of vanishing conductivity and superconductivity, the dispersionless Bloch electrons in TBG demonstrate a plethora of anomalies ranging from unconventional superconductivity  to giant thermopower  and strange metal behavior [7-8], among others. A new paradigm featuring the quantum geometry of dispersionless quantum states is getting momentum towards understanding these anomalies [9-11]. In this colloquium, we will discuss quantum transport — thermal conductance, thermoelectric response, and superfluid weight — from the old perspective and from the new quantum-geometric (entanglement) perspective. Finally, we discuss recent experimental evidence of significant quantum-geometric effects on the transport anomalies in flat bands of twisted bilayer graphene , and outline new perspectives and challenges.
 J. Provost and G. Vallee, vol. 76, no. 3, pp. 289–301, 1980.
 Y. Cao, V.Fatemi, A.Demir, S.Fang, S.L.Tomarken, J.Y.Luo, J.D.Sanchez-Yamagishi, K.Watanabe, T.Taniguchi…, and P. Jarrilo-Herrero, Nature, vol. 556, no. 7699, pp. 80–84, 2018.
 A. Kruchkov, Physical Review B (Letter), vol. 105, p. L241102, Jun 2022.
 G. Tarnopolsky, A.J. Kruchkov, and A. Vishwanath, Physical Review Letters, vol. 122, 2019.
 Y. Guan, O. V. Yazyev, and A. Kruchkov, Physical Review B (Letter), vol. 106, p. L121115, Sep 2022.
 P. Stepanov, Nature Physics, 18(6), 617-618 (2022)
 Y. Cao, D. Chowdhury, D. Rodan-Legrain, O. Rubies-Bigorda, K. Watanabe, T. Taniguchi, T. Senthil, and P. Jarillo-Herrero, ” Physical Review Letters, vol. 124, no. 7, p. 076801, 2020.
 X. Lu, P. Stepanov, W. Yang,M. Xie, M.A. Aamir, …, and D.K. Efetov , Nature, 574(7780), 653-657, (2019).
 S. Peotta and P. Törmä, Nature Communications, vol.6, p.8944, 2015.
 A. Kruchkov, arXiv:2210.00351 (2022).
 P. Törmä , S.Peotta, and B.A.Bernevig, Nature Reviews Physics, 1–15, (2022).
 H. Tian, S. Che, T. Xu, P. Cheung, K. Watanabe, T. Taniguchi, M. Randeria, F. Zhang, C.N. Lau, and M.W. Bockrath, Nature 614, 440–444 (2023).
Hosted by Prof. Stepanov