I have a question about how the Berry connection and the velocity operator are computed in continuum models versus in tight-binding models. Let me start with my understanding of the definitions in ...

My question's notation and equation is based on Condensed Matter Field Theory Third Edition (Altland and Simons).In P54-P56,the book shows how to change the basis between Bloch states and Wannier ...

I am trying to write down a minimal model of the electronic band structure in G-type antiferromagnet (AFM) ordered Perovskites (specifically $\rm LaFeO_3$). I came across the following paper from ...

As I understand it, a way to create a tight binding model for a bravais lattice is to use Wannier functions, which are neat since they form an orthonormal basis of $L^2(\mathbb{R^3})$ and they can be ...

Consider a tight-binding Hamiltonian, whose k-space matrix is $H(k)$. Its general eigenstate reads\begin{equation} |\psi_{n,k}\rangle=\frac{1}{\sqrt{N}}\sum_{R\alpha}[C_k]_{\alpha n}e^{ik\cdot{R}}...

When considering magnetic field on a lattice, an easy way to accommodate the effect of magnetic field is to use peierls substitution,\begin{equation}t_{ij} \to t_{ij} e^{i \phi_{ij}}\end{equation}...

We know that graphene in a magnetic field shows anomalous integer quantum hall effect. I want to understand where this sits in the tenfold classification of insulators and superconductors. The regular ...

I have been recently trying to get the Hofstadter Butterfly spectrum for the maple leaf lattice, but I am getting stuck somewhere and am unable to proceed with the problem. I was wondering if I could ...

Graphene is known to have the following Dirac Hamiltonian in the tight-binding approximation$$\begin{equation}H = \begin{pmatrix}0 & q_{x} + i q_{y} \\q_{x} - i q_{y} & 0\end{pmatrix}\...

I am studying a 1D quantum system with five lattice sites (can be increased to more sites and more dimensions), containing two distinguishable fermions: one spin-up and one spin-down. I allow double ...

I understand the Bulk-Edge correspondence is essentially the Atiyah-Singer (AS) Index theorem in mathematics. On the physics, side the key requirement is translation symmetry for the lattice so that ...

I am learning on how to use tenfold classification of insulators and superconductors in my research. I am confused about when I can use this table and for what kind of Hamiltonians. I have heard ...

In a homework problem, I was asked to compute the dispersion relation for a 2D CuO$_2$ plane by considering an electron in the $d_{x^2-y^2}$ orbital of Cu, using a tight-binding approach and assuming ...

I am working on a problem where I compute the magnetization as a function of energy for a 1D system in the mean-field approximation, both in k-space and real-space models. The system is a tight-...

I want to convert the Momentum-Space Hamiltonian for a Hopf-Insulator given in Equation 8 of this paper by Moore, Ran, and Wen. The momentum-space representation is$$ \mathcal{H}(k_x, k_y,k_z) = \vec{...