The recent realization of twisted, two-dimensional, bilayers exhibiting strongly correlated stateshas 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 thatthese systems allow an unprecedented control of the electronic bands properties, for exampleby varying the relativetwist angle between the layers forming the system. In particular, in twisted bilayers the low energy bands canbe tuned to be very flat and with a nontrivial quantum metric. This allows the quantitativeand experimental exploration of the relation between the metric of Bloch quantum statesand the properties of correlated states. In this work we first review the general connectionbetween 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 superconductivityin magic angle twisted bilayer graphene.We conclude by discussing possible research directions to further elucidatethe connection between quantum metric and correlated states properties.
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