Related papers: Geometry of chiral temporal structures I: Physical…

We use the recently developed kinetic theory with Berry curvature to describe the fermions and antifermions of a chiral relativistic plasma. We check that this transport approach allows to reproduce the chiral anomaly equation of…

Sub-laser cycle time scale of electronic response to strong laser fields enables attosecond dynamical imaging in atoms, molecules and solids. Optical tunneling and high harmonic generation are the hallmarks of attosecond imaging in optical…

We study topological properties of one-dimensional non-Hermitian systems without chiral symmetry and give phase diagrams characterized by topological invariants $\nu_E$ and $\nu_{total}$, associated with complex energy vorticity and…

We present a two-dimensional (2D) lattice model that exhibits a nontrivial topological phase in the absence of the Berry curvature. Instead, the Berry connection provides the topological nontrivial phase in the model, whose integration over…

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…

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…

Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where…

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…

Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a…

Two-dimensional compounds with non-zero Berry curvature are ideal systems to study exotic and technologically favourable thermoelectric and magnetoelectric properties. Within this class of materials, the topological trivial and non-trivial…

We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a 4-dimensional Euclidean…

We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes…

Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…

Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase…

Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components:…

Theoretical and experimental studies of Berry and Pancharatnam phases are reviewed. Basic elements of differential geometry are presented for understanding the topological nature of these phases. The basic theory analyzed by Berry in…

Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field…

The fundamental concepts of Riemannian geometry, such as differential forms, vielbein, metric, connection, torsion and curvature, are generalized in the context of non-commutative geometry. This allows us to construct the…

The quantum geometric properties of a Bloch state in momentum space are usually described by the Berry curvature and quantum metric. In realistic gapped materials where interactions and disorder render the Bloch state not a viable starting…

The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric…