# 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/πh^{2}

(b) Show that the sheet density is related to the Fermi wave vector by: n_{s} = k^{2}_{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/e^{2}) (kFℓ) where ℓ = v_{μ}τ is the mean free path.

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