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, in the Drude model, the sheet resistance, i e , the resistance of a square segment of the ZDEG can be written as R s (h e 2 ) (kF) where v is the mean free path

Question: 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

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: n_s = k²_F/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: R_s = (h/e²) (kFℓ) where ℓ = v_μτ is the mean free path.

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