Canonical Ensemble In a canonical ensemble, the particle number $N$, the volume $V$ and the temperature $T$ are fixed. The temperature of the system is connected to the averaged kinetic energy via...

# Hefei-NAMD Training

In this training session, we will learn how to do an NAMD calculation using Hefei-NAMD. Outline of the session: A bit of theory Installation of Hefei-NAMD ...

# Band Unfolding Tutorial

Introduction The supercell (SC) method is the ubiquitous approach for the study of solid-state periodic boundary condition systems. In the simplest case, one just construct an SC by repeating the ...

# Ewald Summation

Introduction Let’s consider an ionic crystal with atomics charges $q_\alpha$ at $\boldsymbol\tau_\alpha$ and $\sum q_\alpha = 0$, where $\alpha$ runs from 1 to the number of atoms in a unit cell....

# Angular Momentum in Solids

Conservation of Crystal Total Angular Momentum Einstein-De Haas Effect The Einstein–de Haas effect is a physical phenomenon in which a change in the magnetization causes mechanical rotation of t...

# Light-Matter Interaction and Dipole Transition Matrix

Quantum theory of light-matter interaction Let us consider an atom in the presence of an external classical electromagnetic fields, the gauge invariant Schrödinger equation writes 1 [\begin{equa...

# PAW All-Electron Wavefunction in VASP

Introduction In the PAW method, the all-electron (AE) wavefunction (AEWFC) $\psi_{n\mathbf{k}}$ is related to the pseudo-wavefucntion (PSWFC) $\tilde\psi_{n\mathbf{k}}$ by means of a linear trans...

# NAC Calculation for 1D Model Hamiltonian

Introduction Let’s start with a parametric 1D Hamiltonian $H(r)$ [\begin{equation} H(r) = \begin{pmatrix} \varepsilon_1^d(r) & \lambda(r) \[6pt] \lambda(r) & \varepsilon_2^d(r) \end{pmat...

# Evaluating Overlap Integral in Momentum Space

Introduction Suppose $\chi_{l,m}(\mathbf{r})$ is a atomic orbital of the form: [\begin{equation} \chi_{l,m}(\mathbf{r}) = f_{l}(r)\cdot Y_l^m(\hat{\mathbf{r}}) \end{equation}] where $f_l(...

# General Wigner Crystal in Moiré Superlattice

Ratio of Potential and Kinetic Energy The dimensionless ratio of the potential energy ($U$) and the kinetic energy $K$, known as $\gamma_s$, can be written as 1 [\begin{align} \gamma_s &= \f...