Physics & Astronomy Colloquium: Dr. Alex Kruchkov, EPFL/ETHZ


Location: zoom

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 [1]) 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 [2] 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 [1] to giant thermopower [6] 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 [12], and outline new perspectives and challenges. 

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[3]  A. Kruchkov, Physical Review B (Letter), vol. 105, p. L241102, Jun 2022. 
[4] G. Tarnopolsky, A.J. Kruchkov, and A. Vishwanath, Physical Review Letters, vol. 122, 2019.
[5] Y. Guan, O. V. Yazyev, and A. Kruchkov,  Physical Review B (Letter), vol. 106, p. L121115, Sep 2022.
[6] P. Stepanov, Nature Physics, 18(6), 617-618 (2022)
[7] 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.
[8] X. Lu, P. Stepanov,  W. Yang,M.  Xie, M.A. Aamir, …, and  D.K.  Efetov , Nature, 574(7780), 653-657, (2019).
[9]  S. Peotta and P. Törmä, Nature Communications, vol.6, p.8944, 2015.
[10] A. Kruchkov,  arXiv:2210.00351 (2022). 
[11] P. Törmä , S.Peotta, and B.A.Bernevig, Nature Reviews Physics, 1–15, (2022).
[12] 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