Related papers: Quantum Geometry Phenomena in Condensed Matter Sys…
In quantum mechanics, a quantum wavepacket may acquire a geometrical phase as it evolves along a cyclic trajectory in parameter space. In condensed matter systems, the Berry phase plays a crucial role in fundamental phenomena such as the…
We investigate the quantum geometric tensor, which is comprised of the Berry curvature and quantum metric, in a generalized Dirac two-band system with non-integer dispersion $E(\mathbf{k})\sim k^{\alpha}$. Our analysis reveals that this…
Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
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 optical properties of solids are governed not only by their energy band dispersions but also by the quantum geometry of Bloch states. While the role of energy bands in determining the perceived optical appearance of materials, such as…
The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the…
Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase (M.V. Berry (1984), Proc. Royal. Soc.…
In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT), whose imaginary part is the Berry curvature and real part is the quantum metric tensor. Here, we propose and experimentally implement a…
Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions, encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport…
Exploring the topological characteristics of electronic bands is essential in condensed matter physics. Moir\'e materials featuring flat bands provide a versatile platform for engineering band topology and correlation effects. In moir\'e…
Optoelectronic and nonlinear transport experiments probe the quantum geometric tensor of Bloch states, whose real and imaginary components -- the quantum metric and the Berry curvature -- are typically constrained by symmetry. Here, we show…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
The quantum geometric tensor, which has the quantum metric and Berry curvature as its real and imaginary parts, plays a key role in the transport properties of condensed matter systems. In the nonlinear regime, the quantum metric dipole and…
Quantum geometric tensor (QGT), including a symmetric real part defined as quantum metric and an antisymmetric part defined as Berry curvature, is essential for understanding many phenomena. We studied the photogalvanic effect of a…
We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…
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…