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It has been recently established that transport measurements in the nonlinear regime can give direct access to the quantum metric (QM): the real part of the quantum geometric tensor characterizing the geometry of the electronic…
Berry curvature fundamentally dictates the topological ground state, anomalous transport and optical properties of quantum materials. However, directly mapping its momentum-space distribution in real materials remains an outstanding…
Topological Physics relies on the specific structure of the eigenstates of Hamiltonians. Their geometry is encoded in the quantum geometric tensor containing both the celebrated Berry curvature, crucial for topological matter, and the…
The quantum geometry plays a crucial role in the nonlinear transport of quantum materials. Here, we use the Boltzmann transport formalism to study the magnetic control of nonlinear transport induced by the quantum metric in two-dimensional…
Probing ground-state quantum geometry and topology through optical response is not only of fundamental interest, but it can also offer several practical advantages. Here, using first-principles calculations on antiferromagnetic topological…
Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of…
We experimentally observe the quantum geometric tensor, namely the quantum metric and the Berry curvature, for a square lattice of radiatively coupled plasmonic nanoparticles. We observe a non-zero Berry curvature and show that it arises…
Two-dimensional materials are a fertile ground for exploring quantum geometric phenomena, with Berry curvature and its first moment, the Berry curvature dipole, playing a central role in their electronic response. These geometric properties…
We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the…
In a magnetic topological insulator, nontrivial band topology conspires with magnetic order to produce exotic states of matter that are best exemplified by quantum anomalous Hall (QAH) insulators and axion insulators. Up till now, such…
The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian…
The geometric characteristics of Bloch wave functions play a crucial role in electronic transport properties. We show that the thermoelectric performance of materials is governed by the geometric structure of Bloch wave functions within the…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…
The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…
The Berry curvature characterizes one aspect of the geometry of quantum states. It materializes, among other consequences, as an anomalous velocity of wave packets. In non-Hermitian systems, wave packet dynamics is enriched by additional…
Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the…
The intricate interplay between nontrivial topology and magnetism in two-dimensional (2D) materials has led to the emergence of many novel phenomena and functionalities. An outstanding example is the quantum anomalous Hall (QAH) effect,…
Quantized transport not only exist in gapped topological states but also in metallic states. Recently, Kane proposed a quantized nonlinear conductance in ballistic metals whose value is determined by the Euler characteristic of the Fermi…
In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…