Expan ane two method to calculate effective mass in tight binding approximation nnsion method n this method we assume k to be small and expand near cenitre of 7

Expan ane two method to calculate effective mass in tight binding approximation nnsion Method n this method we assume k to be small and expand near cenitre of 77here ere iven by te : Let E =E,21cos ka + cos kal is enerqy expression of square lattice. Example eXpression of cos term we can write 7hen by exp E-E-2y1 Ka 1a 2 -5,-22a (where k =k +k) 2 E = E-4y + yk2a? Now at centre of B.Z. (K, k,) = (0, 0) dE =2ya dk lo le.com Thus, m lo.o) 2a At top of B.Z (k, k) = a'a -h* m 2/a -= -m I(0,0) From here we conclude that m top m mbottom