Week 5: Number of modes M(E)

Number of modes M(E): wavelengths that fit across the width (Datta Sec. 6.4, Eq. 6.20)

An electron of energy E has de Broglie wavelength λ = h/p. Across a strip of width W only standing waves whose transverse wavelength 2W/n is longer than λ fit, so the number of modes is M = floor(2W/λ). Each mode (per spin) adds q²/h to the ballistic conductance.

Dispersion:

Width W Energy above band edge, E − E_c Effective mass m/m₀ Temperature T

Wavelength λ = h/p–

2W/λ (continuous)–

Modes M (per spin)–

G_B = g(q²/h)M · R_B–