Week 14: The quantum of conductance, modes of a 2D wire

The quantum of conductance: modes of a 2D wire (Datta Part B, Ch. 20, Figs. 20.1–20.4)

A ballistic 2D conductor with N sites across its width is a set of 1D wires in parallel, one per subband E_n(k_x) = ε_n − 2t₀cos k_xa with ε_n = 4t₀ − 2t₀cos[nπ/(N+1)] (Eq. 20.4). Transmission is the number of modes M(E): half the number of times the energy line crosses a subband. Add a magnetic field (Peierls phases) to see the subbands bend into Landau levels and edge states.

Width: N sites across (a = 2.5 nm) Energy E − E_c (units of t₀) Magnetic field B (T), m = 0.067 m₀ Right panel

Modes M(E) = T(E)–

Conductance M q²/h (×2 with spin)–

Resistance h/(M q²)–

t₀, width W = (N+1)a–