Wannier Charge Center in Bloch representation

The Wannier Charge Centers (WCCs) can be used to calculate the polarization of a ferroelectric material. Alternatively, it can be expressed using Bloch functions. This post derive the link between these two representations and show that the choice of gauge doesn't affect the final results. »

Polar metals and hybrid Wannier functions

Polar metals are metallic systems that have non-centrosymmetric polar structures. It has been theorized to exist and experimentally demonstrated to be possible. This post discusses the options of calculating the polarization of these materials using Berryphase or Wannier charge center method. »

The evolution of bond index

Bond index(BI) is a measurement of the "average number of electron pairs shared between atoms". It provides an intuitive description of the covalency between atoms. This post provides a birds-eye-view of the development of the bond index formalism. »

From Green's function to Dyson equation

Dyson equation provides a perturbative approach for solving the electron-electron correlation problems. It's intimately related to the one-particle green's function. This post provides an easy to understand derivation of the Dyson equation by considering the potential term as a perturbation to the Schrödinger quation. »

From Greens function to DOS

Green's function (or sometimes called correlation functions and propagator) can be used to measures frequency of the transition between state, hence it can also measure the intrinsic "oscillation" energy of a state. This post provides the link to get density of state from one-particle green's functions. »