Related papers: Simple mechanisms that impede the Berry phase iden…
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…
The Berry phase of mixed states, as neutrino oscillations, is calculated in a accelerating and rotating reference frame. It turns out to be depending on the vacuum mixing angle, the mass--squared difference and on the coupling between the…
We develop a theory of Berry phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential. Here a charge Hall current arises from the Berry phase correction to…
Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material…
Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, ``dressed'' Hamiltonian that is able to treat internal atomic or molecular structure in…
A distinguishing feature of Dirac fermions is the Berry phase of $\pi$ associated with their cyclotron motions. Since this Berry phase can be experimentally assessed by analyzing the Landau-level fan diagram of the Shubnikov-de Haas (SdH)…
The rigid rotor is a classic problem in quantum mechanics, describing the dynamics of a rigid body with its centre of mass held fixed. The configuration space of this problem is $SO(3)$, the space of all rotations in three dimensions. This…
The surface states of 3D topological insulators possess geometric structures that imprint distinctive signatures on electronic transport. A prime example is the Berry curvature, which controls, for instance, electric frequency doubling via…
In this paper, we investigate in general how thermodynamic quantities such as the polarization, magnetization and the magneto-electric tensor are affected by the boundaries. We show that when the calculation with periodic boundary…
The Berry phase acquired by an electromagnetic field undergoing an adiabatic and cyclic evolution in phase space is a purely quantum-mechanical effect of the field. However, this phase is usually accompanied by a dynamical contribution and…
We have shown that the study of topological aspects of the underlying geometry in a ferromagnetic spin system gives rise to an intrinsic Berry phase. This real space Berry phase arises due to the spin rotations of conducting electrons which…
We study phase diagrams of charge-conserving `class A' non-interacting fermions, focusing on the trivial phase in various dimensions. Such phases are usually termed `featureless' to distinguish them from those others with either…
We report on the study of the non-trivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model in the…
We propose classification schemes for characterizing two-dimensional topological phases with nontrivial weak indices. Here, "weak" implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along…
We show that Berry's geometrical (topological) phase for circular quantum dots with an odd number of electrons is equal to \pi and that eigenvalues of the orbital angular momentum run over half-integer values. The non-zero value of the…
By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a…
The presence/absence of a Berry phase depends on the topology of the manifold of dynamical Jahn-Teller potential minima. We describe in detail the relation between these topological properties and the way the lowest two adiabatic potential…
The Berry phase understanding of electronic properties has attracted special interest in condensed matter physics, leading to phenomena such as the anomalous Hall effect and the topological Hall effect. A non-vanishing Berry phase, induced…
A perturbation theory of the static response of insulating crystals to homogeneous electric fields, that combines the modern theory of polarization (MTP) with the variation-perturbation framework is developed, at unrestricted order of…
A notion of the Berry phase is a powerful means to unravel the non-trivial role of topology in various novel phenomena observed in chiral magnetic materials and structures. A celebrated example is the intrinsic anomalous Hall effect (AHE)…