A central result in superconductivity is that flat bands, though dispersionless, can still host a
nonzero superfluid weight due to quantum geometry. We show that the derivation of the …

We study superconductivity of twisted bilayer graphene with local and nonlocal attractive
interactions. We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) …

Semiclassical quantization of electronic states under a magnetic field, as proposed by
Onsager, describes not only the Landau level spectrum but also the geometric responses of …

We investigate relations between topology and the quantum metric of two-dimensional
Chern insulators. The quantum metric is the Riemannian metric defined on a parameter …

The topology of two-dimensional materials traditionally manifests itself through the
quantization of the Hall conductance, which is revealed in transport measurements …

Nonlinear optical response is well studied in the context of semiconductors and has gained
a renaissance in studies of topological materials in the recent decade. So far it mainly deals …

A Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is
well studied in many branches of modern physics; however, the quantum metric as a real …

We study Chern insulators from the point of view of Kähler geometry, ie, the geometry of
smooth manifolds equipped with a compatible triple consisting of a symplectic form, an …

Geometry and topology are fundamental concepts, which underlie a wide range of
fascinating physical phenomena such as topological states of matter and topological …

We propose a computationally efficient method to derive the unitary evolution that a
quantum state is most sensitive to. This allows one to determine the optimal use of an …