Quantum geometry: a new paradigm in topological quantum matter and unconventional superconductivity
Dr. Alex Kruchkov
Branco Weiss Fellow & Lecturer
EPFL/ETHZ
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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Hosted by Prof. Stepanov