ZHEJIANG UNIVERSITYDepartment of Physics

Issued: 2013/05/16Solid State Physics I Problem Set #7 Due: 2013/05/23

1. Hall effect with two carrier types.

(a) (Kittel 8.3) Assuming concentrationsn, p; relaxation timeτe, τh; and massesme, mh; show that the weak field limit (ωcτ ≪ 1), the Hall coefficient in thedrift velocity approximation is

RH =1

ec·p− nb2

(p+ nb)2(1)

in CGS unit, whereb = µe/µh is the mobility ratio.

(b) A silicon sample of resistivity10−3 Ω cm has zero Hall voltage at small mag-netic field strengths. Assumeµn = 1300 cm2/Vs andµp = 300 cm2/Vs anddetermine the carrier concentrations.

2. Ashcroft / Mermin Chapter 13 Problem 2

3. De Haas-van Alphen period of ptassium

(a) Calculate the period(1/B) expected for ptassium on the free elctron model.

(b) What is the area in real space of the extremal orbit forB = 10 kG?

4. Open orbits

An open orbit in a monovalent tetragonal metal connects opposite faces on theboundaries of a BZ. The faces are separated byG = 2 × 108 cm−1. A magneticfield B = 103 gauss is normal to the plane of the orbit.

(a) What is the order of magnitude of the period of the motion in k-space? Takev ∼ 108 cm/s.

(b) Describe in real space the motion of an electron on this orbit in the presenceof a magnetic field.

5. Ashcroft / Mermin Chapter 14 Problem 1

1