Question

The tight binding energy dispersion (E-k) relation for electrons in a one-dimensional array of atoms having lattice constant 'a' and total length 'L' is :

E=E0−β−2γcoska

Where E0,β and γ are constants and k is the wave vector.
The effective mass of electrons in the band is given by?

Answer 1

Given:

$$E(k)=E_0-\beta-2\gamma\cos ka$$

The effective mass of electron is given by

$$m^{*}=\frac{\hbar^2}{d^2E(k)/dk^2}$$

Hence

$$m^{*}=\frac{\hbar^2}{a^2*2\gamma \cos ka}=\frac{\hbar^2}{a^2(E_0-E+\beta)}$$