Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
1. (a) Show that along the principal symmetry directions shown in Figure 10.5 the tight- binding expression (10.22) for the energies of an s-band in a face-centered cubic crystał reduces to the following: (i) Ałong rX (k, = k̟ = 0, kg = µ 2m/a, 0 < µ < 1) 8 = E, – B – 4y(1 + 2 cos µn). %3D %3D (ii) Along TL (k, = k, = k, = µ 2n/a, 0 < H< }) %3D %3D 8 = E, – B - 12y cos²µn. (iii) Along TK (k, = 0, kg = k, = µ 27/a, 0 < µ < ) %3D %3D 8 = E, -- B - 4y(cos² µn + 2 cos µn). (iv) Along rW (k̟ = 0, k, = µ 2n/a, ky fu 2n/a, 0 < µ < 1) %3D E-β- 4γ(cos μπ + cos μπ + os μπ cos μπ ).

1. (a) Show that along the principal symmetry directions shown in Figure 10.5 the tight- binding expression (10.22) for the energies of an s-band in a face-centered cubic crystał reduces to the following: (i) Ałong rX (k, = k̟ = 0, kg = µ 2m/a, 0 < µ < 1) 8 = E, – B – 4y(1 + 2 cos µn). %3D %3D (ii) Along TL (k, = k, = k, = µ 2n/a, 0 < H< }) %3D %3D 8 = E, – B - 12y cos²µn. (iii) Along TK (k, = 0, kg = k, = µ 27/a, 0 < µ < ) %3D %3D 8 = E, -- B - 4y(cos² µn + 2 cos µn). (iv) Along rW (k̟ = 0, k, = µ 2n/a, ky fu 2n/a, 0 < µ < 1) %3D E-β- 4γ(cos μπ + cos μπ + os μπ cos μπ ).

icon
Related questions
Question
L X to W K
Transcribed Image Text:L X to W K
1. (a) Show that along the principal symmetry directions shown in Figure 10.5 the tight- binding expression (10.22) for the energies of an s-band in a face-centered cubic crystał reduces to the following: (i) Ałong TX (k, = k̟ = 0, kg =µ 27/a, 0 < µ< 1) %3D 8 = E, - B – 4y(1 + 2 cos µn). (ii) Along FL (k, = k, = k, = µ 2n/a, 0 < µ< ) 8 = E, – B -- 12y cos²µn. ( i) Along ΓΚ (,0, k-k,= μ 2π/α, 0 < µ < ) %3D 8 = -E-β- 4γ(cos μπ +2cos μπ). (iv) Along rW (k, 0, k, = µ 27/a, k, = }µ 2n/a, 0 <µ < 1) 8 = E, – B – 4y(cos µn + cos ¿un + cos µn cos žuT). %3D (b) Show that on the square faces of the zone the normał derivative of ɛ vanishes. (c) Show that on the hexagonał faces of the zone, the normał derivative of Ɛ vanishes onły ałong lines joining the center of the hexagon to its vertices.
Transcribed Image Text:1. (a) Show that along the principal symmetry directions shown in Figure 10.5 the tight- binding expression (10.22) for the energies of an s-band in a face-centered cubic crystał reduces to the following: (i) Ałong TX (k, = k̟ = 0, kg =µ 27/a, 0 < µ< 1) %3D 8 = E, - B – 4y(1 + 2 cos µn). (ii) Along FL (k, = k, = k, = µ 2n/a, 0 < µ< ) 8 = E, – B -- 12y cos²µn. ( i) Along ΓΚ (,0, k-k,= μ 2π/α, 0 < µ < ) %3D 8 = -E-β- 4γ(cos μπ +2cos μπ). (iv) Along rW (k, 0, k, = µ 27/a, k, = }µ 2n/a, 0 <µ < 1) 8 = E, – B – 4y(cos µn + cos ¿un + cos µn cos žuT). %3D (b) Show that on the square faces of the zone the normał derivative of ɛ vanishes. (c) Show that on the hexagonał faces of the zone, the normał derivative of Ɛ vanishes onły ałong lines joining the center of the hexagon to its vertices.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer