Related papers: Reduced Wannier representation for topological ban…
In this Article we address the definition and values of topological numbers of the manifolds of wavefunctions - bands obtained by quantum superposition of the wavefunctions that belong to topologically distinct manifolds. The problem,…
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension $d \leq 3$, vanishing Chern classes of bundles of Bloch eigenfunctions characterize operators with exponentially…
We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs posses improved symmetry and…
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with…
The characteristics of topologically protected wave propagation is typically predicted via the band structure of the primitive unit cell, using Berry curvature to predict localized interface or boundary states (as well as their degree of…
Second-order topological insulators can be characterized by their bulk polarization, which is believed to be intrinsically connected to the center of the Wannier function. In this study, we demonstrate the existence of second-order…
We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari…
The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features.…
Since the seminal work of Marzari and Vanderbilt, maximally localized Wannier functions have become widely used as a real-space representation of the electronic structure of periodic materials. In this paper we introduce selectively…
The fundamental building blocks in band theory are band representations (BRs): bands whose infinitely-numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a…
A remarkable feature of the band structure of bilayer graphene at small twist angle is the appearance of isolated bands near neutrality, whose bandwidth can be reduced at certain magic angles (eg. $\theta\sim 1.05^\circ$). In this regime,…
The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic…
One-dimensional superlattices with modulated coupling constants show rich topological properties and tunable edge states. Beyond the dimeric case, probing the topological properties of superlattices is a challenge. Here we suggest a rather…
Recently there is a surge of interests in the so-called topologically protected corner states in 2D and 3D systems. Such systems are considered as high order topological insulators. Wannier centers are used as topological invariants to…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected…
Accurate prediction of fundamental band gaps of crystalline solid state systems entirely within density functional theory is a long standing challenge. Here, we present a simple and inexpensive method that achieves this by means of…
The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and…
Maximally localized Wannier functions (MLWFs) are conventionally constructed by iteratively minimizing a spread functional over a high-dimensional gauge landscape. In this work, we present a non-variational constructive algorithm that…
We propose a general method of constructing Wannier functions in disordered systems directly out of energy eigenstates. This method consists of two successive operations: (i) a phase transformation setting the proper localization center;…
Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…