Questions tagged [tight-binding]
221 questions
13
votes
1 answer
Tight binding model in a magnetic field
The standard way to treat a tight binding method in a magnetic is to replace the hopping matrix element:
$t_{i,j}\rightarrow e^{i\int_i^j\mathbf{A(x)}.d\mathbf{x}}$
the so called "Peierls substitution", How is this justified?
The usual way people…
Yahya Alavirad
- 193
11
votes
1 answer
Does anyone know the difference and relation between $k\cdot p$ method and tight binding (TB) method?
Among the methods of calculating energy bands for crystals, first-principles method is the most accurate. Besides first principles, two commonly used modeling methods are the $k\cdot p$ method and the tight binding (TB) method. They can both give a…
goodluck
- 531
10
votes
1 answer
Tight-binding vs. nearly free electron (NFE) model predictions
I came across the following problem:
Suppose that a certain material consists of $N$ atoms that are ordered in a 2D lattice with a lattice constant $a$, and that each atom donates two conduction electrons at $s$-level. Determine whether the…
grjj3
- 705
10
votes
1 answer
Number of bands in 1D tight-binding model
I was reading about the one-dimensional tight-binding Hamiltonian (TBH) with one quantum state per atom $$H=E_0\sum\limits_{n}|n\rangle\langle n|-t\sum\limits_{n}\Big(|n\rangle\langle n+1|+|n+1\rangle\langle n|\Big)\tag{1}$$ where $E_0$ and $t$…
SRS
- 27,790
- 13
- 115
- 365
8
votes
1 answer
Alternating Tight Binding Hamiltonian
The alternating Hamiltonian may be written as:
$$H = t \sum_{n} (-1)^{n} \left[c^{\dagger}_{n+1}c_{n} + c^{\dagger}_{n}c_{n+1} \right] \; \; .$$
I wanted to know the energy dispersion for this system, so I wrote in mommentum space; After some…
RKerr
- 1,367
7
votes
1 answer
Can we write energy band of square lattice with vertical magnetic field?
I am interested in a square lattice with the vertical magnetic field. Without a magnetic field, we can know the energy dispersion of the square lattice easily. But, how about in case of with magnetic field? My theory shown below is correct or…
Sakurai.JJ
- 227
7
votes
1 answer
explicit representation of creation/annihilation operators & its fourier transform (matrix form) (tight-binding hamiltonian, graphene)
While I'm a mathematician/computer-scientist myself, I've some problems trying to understand some paper about the electronic states of graphene nanoribbons modelled by the tight-binding Hamiltonian…
Nils
- 73
6
votes
1 answer
What's a charge density wave?
I'm reading chapter 2 of Condensed Matter Field Theory by Alexander Altland, Ben D. Simons, Section on Interacting fermions in one dimension.
From what I understood, they considered the system of electrons in one dimension with Coulomb interaction.…
Himanshu
- 12,211
6
votes
2 answers
Numerically transforming Hamiltonian into $k$-space
A rather computational question:
Suppose you have a very simple tight-binding Hamiltonian in matrix form, i.e. for example something like this for a 1D chain with open ends:
$$H =\begin{bmatrix}
0 & t & 0 & \dots & 0 \\
t & 0 & t &…
benfisch
- 103
6
votes
1 answer
Line integral in Peierls substitution
I'm trying to understand the reasoning behind Peierls substitution. The final result seems to be simply replacing the hopping elements
$$t_{ij} \to t_{ij} e^{i \frac{q}{\hbar} \int_i^j \vec{A} \cdot d \vec{r}}$$
The line integral in the exponent is…
Bio
- 944
6
votes
0 answers
Analog of Anderson localization caused by random hopping
Consider the tight-binding Hamiltonian:
$$
H = \sum_i \epsilon_i a^\dagger_i a_i + \sum_i V_i (a^\dagger_i a_{i+1} + a^\dagger_{i+1} a_i)
$$
Random on-site energy $\epsilon_i$ leads to the famous Anderson localization.
I wonder if there's an analog…
liwt31
- 161
6
votes
2 answers
Calculating topological invariants under different conventions of tight-binding models
There are two widely used conventions to construct the Bloch-like basis in a tight-binding model [1].
Convention…
zrysky
- 381
6
votes
1 answer
What is nesting/ what is a nesting vector in energy contour plots?
I am making different plots for a 2-d non-interacting tight binding Hamiltonian
$$ H = - t \sum_{, \sigma} c_{i \sigma}^{\dagger} c_{j \sigma} + h.c$$
I get the dispersion relation $$\epsilon (k) = -2 t ( \cos(k_{x} a) + \cos (k_{y}…
Hoda
- 63
6
votes
4 answers
Getting tight binding density of states more accurately
I calculated numerically the density of states (DoS) for the 3-D tightbinding dispersion $\epsilon(k_x,k_y,k_z)=-2t\,(\cos k_x + \cos k_y + \cos k_z)$ and obtained the following plot [$t=1$ has been chosen].
What I did is summing over $k$-points…
hbaromega
- 307
6
votes
1 answer
Time reversal operator in tight-binding model with second quantization form
In the tight binding model, $H=\sum_{r,r'}ta^{\dagger}_{r}a_{r'}+h.c.$. When conducting a time reversal transformation, what form will this Hamiltonian take? Or how can I express time reversal operator? When the Hamiltonian is transformed into…
Simon
- 311
- 3
- 7