Related papers: Approximate formula for the macroscopic polarizati…
Condensed matter physics is often concerned with determining the response of a solid to an external stimulus. This paper revisits and extends the microscopic formalism for calculating response coefficients -- here referred to as…
The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct…
We discuss characterization of the polarization for insulators under the periodic boundary condition in terms of the Berry phase, clarifying confusing subtleties. For band insulators, the Berry phase can be formulated in terms of the Bloch…
The dipole moment of any finite and neutral system, having a square-integrable wavefunction, is a well defined quantity. The same quantity is ill-defined for an extended system, whose wavefunction invariably obeys periodic (Born-von Karman)…
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…
We demonstrate that polarization-related quantities in semiconductors can be predicted accurately from first-principles calculations using the appropriate approach to the problem, the Berry-phase polarization theory. For III-V nitrides, our…
Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators.…
Berry phase polarization calculations have been investigated for several ferroelectric materials from the point of view of practical calculations. It was shown that interpretation of the results is particular to each case due to the…
Recent theoretical advances have established that the electric polarization in an insulating crystal can be viewed as a multivalued quantity that is determined by certain Berry phases associated with the occupied Bloch bands. The…
Recently, it has been established that Chern insulators possess an intrinsic two-dimensional electric polarization, despite having gapless edge states and non-localizable Wannier orbitals. This polarization, $\vec{P}_{\text{o}}$, can be…
The so-called {\it Modern Theory of Polarization}, which rigorously defines the spontaneous polarization of a period solid and provides a route for its computation in electronic structure codes through the Berry phase, is introduced in a…
This paper represents one contribution to a larger Roadmap article reviewing the current status of the FHI-aims code. In this contribution, the implementation of polarization, Born-effective charges and topological invariants using a…
We derive an analogue of the Berry phase associated with inflationary cosmological perturbations of quantum mechanical origin by obtaining the corresponding wavefunction. We have further shown that cosmological Berry phase can be completely…
We provide a unified semiclassical theory for thermoelectric responses of any observable represented by an operator $\hat{\boldsymbol{\theta}}$ that is well-defined in periodic crystals. The Einstein and Mott relations are established…
We develop the theory and practical expressions for the full quantum-mechanical distribution of the intrinsic macroscopic polarization of an insulator in terms of the ground state wavefunction. The central quantity is a cumulant generating…
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…
We consider the flow of polarization current J(t)=dP/dt produced by a homogeneous electric field E(t) or by rapidly varying some other parameter in the Hamiltonian of a solid. For an initially insulating system and a collisionless time…
By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the…
We formulate a framework for the depolarization of linearly polarized backscattered light based on the concept of geometric phase, {\it i.e} Berry's phase. The predictions of this theory are applied to the patterns formed by backscattered…
We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of…