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 ...
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...
Numerical Solutions to the Time-dependent Schrödinger Equation
Time-dependent Schrödinger Equation The single-particle time-dependent Schrödinger equation of an electron under an external potential read [\begin{align} i\hbar \frac{\partial}{\partial t} \psi...