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Qijing Zheng
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Molecular Dynamics at Constant Temperature

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 ...

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...

Bravais Lattice

Bravais Lattices in 3D Figure 1. Primitive (red), conventional (blue if any) and Wigner-seitz cell (green) of 14 three-dimensional (3D) Bravais lattices. G...

Brillouin Zone Integration: Linear Tetrahedron Method

Introduction The translational symmetry of solids resulits in a quantum number, i.e. the crystal momentum $\mathbf{k}$. Consequently many quantities of the crystal, e.g. total energy and density...

Phonopy: Rutile TiO2

Phonon Dispersion of Rutile TiO$_2$ This is a summary of my using Phonopy to calculate phonon spectrum of rutile TiO$_2$. 1 Computational Details Below is a list of used packages and computation...

Matplotlib: 1D Chain ARPES Signal

ARPES Signal of 1D Chain within Tight-binding 1 The eigenvalues of 1D mono-atomic chain within the tight-binding model \[\begin{equation*} \varepsilon_\kappa = \varepsilon_0 - 2t\cos(\f...

Peierls Transition

Peierls Transition A Peierls transition or Peierls distortion is a distortion of the periodic lattice of a one-dimensional crystal. Atomic positions oscillate, so that the perfect order of the 1D ...