Related papers: Geometric phases and Wannier functions of Bloch el…
We extend the Intrinsic Atomic Orbital (IAO) method for localisation of molecular orbitals to calculate well-localised generalised Wannier functions in crystals using the Pipek--Mezey locality metric. We furthermore present a one-shot…
We consider the applicability of phase space Wannier functions" to electronic structure calculations. These generalized Wannier functions are analogous to localized plane waves and constitute a complete, orthonormal set which is…
A recently proposed ab initio Hartree-Fock approach aimed at directly obtaining the Wannier functions of a crystalline insulator is applied to polymers. The systems considered are the LiH chain and trans-polyacetylene. In addition to being…
We have constructed maximally-localized Wannier functions for prototype structures of solid molecular hydrogen under pressure, starting from LDA and tight-binding Bloch wave functions. Each occupied Wannier function can be associated with…
The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law…
Wannier functions of the one dimensional Schroedinger equation with elliptic one gap potentials are explicitly constructed. Properties of these functions are analytically and numerically investigated. In particular we derive an expression…
An exact analytical expression is derived for Bloch states in three dimensions, based on the only assumption that the electronic wavefunction can be expanded in terms of Gaussian type orbitals. The resulting expression features…
In the present letter, we report the extension of our Wannier-function-based ab initio Hartree-Fock approach---meant originally for three-dimensional crystalline insulators---to deal with quasi-one-dimensional periodic systems such as…
In this work, we use Wannier functions to analyze topological phase transitions in one dimensional photonic crystals. We first review the construction of exponentially localized Wannier functions in one dimension, and show how to…
The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements. Recently, it was predicted that topology can also give rise to a…
We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a 1D quantum walk, where one spatial dimension plays the role of time. In this mapping a magnetic field B perpendicular to the…
Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch bundles, we obtain decay rates of Wannier functions in…
The electronic ground state of a periodic crystalline solid is usually described in terms of extended Bloch orbitals; localized Wannier functions can alternatively be used. These two representations are connected by families of unitary…
We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally-localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave…
In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both…
In the Hermitian regime, the Wannier-Stark ladder characterizes the eigenstates of an electron in a periodic potential with an applied static electric field. In this work, we extend this concept to the complex regime for a periodic…
Motivated by recent developments in quantum simulation of synthetic dimensions, e.g. in optical lattices of ultracold atoms, we discuss here $d$-dimensional periodic, gapped quantum systems for $d \le 4$, with focus on the topology of the…
Wannier functions provide a localized representation of spectral subspaces of periodic Hamiltonians, and play an important role for interpreting and accelerating Hartree-Fock and Kohn-Sham density functional theory calculations in quantum…
The Bloch wavefunction leads either to mathematically impossible consequences or suggests that the ground state energy is a function of size and shape when the geometry of large crystals is considered in detail. It is incompatible with the…
We present a first-principles calculation of the electronic properties of crystalline silicon and gallium arsenide in a uniform electric field. Polarized Wannier-like functions which are confined in a finite region are obtained by…