Quantum geometry: a new paradigm in anomalous electronic transport and unconventional superconductivity
Quantum geometry — the metric of quantum states in Hilbert space — determines the distance between two neighbouring quantum states. The concept of quantum geometry, represented by Fubini-Study metric, had been used in the quantum information theory, however, had been mainly overlooked in the condensed matter environment. This situation has changed after discovery of twisted bilayer graphene (TBG) and twisted transition metal dichalcogenides, which host nearly dispersionless quantum states (”flat bands”) characterized by nontrivial topology and quantum geometry. Despite the conventional expectation of vanishing conductivity and absent superconductivity, the dispersionless electrons in moiré materials demonstrate a plethora of anomalies ranging from unconventional superconductivity to giant thermopower, strange metal behaviour, Fractional Chern Insulator states, among others. A new paradigm featuring the quantum geometry of dispersionless quantum states is getting momentum towards understanding these anomalies. In this talk, we will discuss quantum transport — thermal conductance, thermoelectric response, and superfluid weight — from the old perspective and from the new quantum-geometric perspective. Time permitting, 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.
 A. Kruchkov, Physical Review B (Letter), vol. 105, p. L241102, Jun 2022.
 A. Kruchkov, arXiv:2210.00351, under review in PRL (2023).
 Y. Guan, O. V. Yazyev, and A. Kruchkov, Physical Review B (Letter), vol. 106, p. L121115, Sep 2022.