Properties of the two-dimensional electron gas consider a two-dimensional electron gas (2DEG) with twofold spin degeneracy but no valley degeneracy. (a) Show that the number of orbitals per unit energy is given by: D()= m/h 2 (b) Show that the sheet density is related to the Fermi wave vector by: n s = k 2 F /2. (c) Show that,
Properties of the two-dimensional electron gas consider a two-dimensional electron gas (2DEG) with twofold spin degeneracy but no valley degeneracy.
(a) Show that the number of orbital’s per unit energy is given by: D(ε)= m/πh2
(b) Show that the sheet density is related to the Fermi wave vector by: ns = k2F/2π.
(c) Show that, in the Drude model, the sheet resistance, i.e., the resistance of a square segment of the ZDEG can be written as: Rs = (h/e2) (kFℓ) where ℓ = vμτ is the mean free path.
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