Quantum Metric and Correlated States in Two-dimensional Systems

Abstract

The recent realization of twisted, two-dimensional, bilayers exhibiting strongly correlated states has created a platform in which the relation between the properties of the electronic bands and the nature of the correlated states can be studied in unprecedented ways. The reason is that these systems allow extraordinary control of the electronic bands' properties, for example by varying the relative twist angle between the layers forming the system. In particular, in twisted bilayers the low energy bands can be tuned to be very flat and with a nontrivial quantum metric. This allows the quantitative and experimental exploration of the relation between the metric of Bloch quantum states and the properties of correlated states. In this work we first review the general connection between quantum metric and the properties of correlated states that break a continuous symmetry. We then discuss the specific case when the correlated state is a superfluid and show how the quantum metric is related to the superfluid stiffness. To exemplify such relation we show results for the case of superconductivity in magic angle twisted bilayer graphene. We conclude by discussing possible research directions to further elucidate the connection between quantum metric and correlated states' properties.

Review article, submitted to Current Opinion in Solid State & Materials Science

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Cited by in corpus (10)

• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Quantum geometry induced second harmonic generation
• Nontrivial quantum geometry of degenerate flat bands
• Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
• Pair Density Waves from Local Band Geometry
• Fractional Chern insulators with a non-Landau level continuum limit
• Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion
• Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials
• Topological Superfluid Responses of Superconducting Dirac Semimetals
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings