[2-2]固體物理導(dǎo)論 introduction to solid state physics

1、11.2. BASIC PROPERTIES 2431200.10.20.30.40.50.61 2 3 4 5 6 7 ζFigure 11.5: Normalized electron densities An|χn(z/?F)|2 for the first (1) and second (2)subbands in a triangle potential with the slope F, ?F = (?2/2mF)1/3.v

2、 (for n-type materials), and in-plane quasimomentum k. If the spectrum is degenerate with respect to spin and valleys one can define the spin degeneracy νs and valley degeneracy νv to getg(?) = νsνv(2π)d?n?ddk δ (? ? En,

3、k) .Here we calculate the number on states per unit volume, d being the dimension of the space. For 2D case we obtain easilyg(?) = νsνvm2π?2?n Θ(? ? En) .Within a given subband it appears energy-independent. Since there

4、can exist several subbands in the confining potential (see Fig. 11.6, inset), the total density of states can be represented as a set of steps, as shown in Fig. 11.6. At low temperature (kT ? EF) all the states are fille

5、d up to the Fermi level. Because of energy-independent density of states the sheet electron density is linear in the Fermi energy,ns = N νsνvmEF2π?2 + const11.2. BASIC PROPERTIES 245Figure 11.7: Density of states for a q

6、uasi-1D system (solid line) and the number of states (dashed lines).Motion in a perpendicular magnetic field2DEG in a perpendicular magnetic field gives an example of 0-dimensional electronic sys- tem. Indeed, according

7、to the classical theory the Hamilton’s function of a charged particle in an external electromagnetic field isH = 12m? p ? ecA ?2 + eφ ,where φ is the scalar and A is the vector potential of the field, and p is the genera

8、lized momentum of the particle. According to the rules of quantum mechanics, one should replace the canonical momentum p by the operatorp → ? p = ?i??and add also an extra spin term ?µH where µ = µB? s/s.

9、Here µB = e/2mc is the Bohr magneton while ? s is the spin operator. Generally, interaction with periodic potential of the crystalline lattice leads to renormalization of the spin splitting µB → µ=gfµ