Quantum Wire — Conductance Quantization

Material

Confinement

Wire width L 14.0 nm

Fermi energy E_F (gate voltage) 120 meV

Temperature T 4.0 K

Readouts

Conductance G

0.00 G₀ (0.0 µS)

Open channels N

Subband spacing E₀

0.0 meV

G vs E_F

How it works

A quantum wire confines electrons in two transverse directions to a width comparable to their de Broglie wavelength. Treating the cross-section as a hard-wall square of side L quantizes the transverse motion into discrete 1D subbands:

E(n,m) = (ħ²π² / 2m*L²)·(n² + m²),   n, m = 1, 2, 3, …
G(E_F,T) = (2e²/h) · Σ_{n,m} 1 / (1 + exp[(E(n,m) − E_F)/k_BT])
G₀ = 2e²/h ≈ 77.5 µS  (12.9 kΩ per open channel)

Each subband below the Fermi energy acts as one independent ballistic conduction channel and contributes exactly one quantum G₀ = 2e²/h (spin-degenerate). Sweeping the gate voltage (E_F) opens channels one at a time, producing the famous conductance staircase first measured by van Wees and Wharam in 1988 quantum point contacts — a direct electrical signature of 1D quantum confinement.

Wire width L — narrower wires push subbands further apart (E₀ ∝ 1/L²), so steps get wider and fewer channels fit under a given E_F.
Fermi energy E_F — the gate voltage that fills subbands; each crossing opens a new lane (or two, if degenerate).
Temperature T — thermal broadening ~k_BT smooths the sharp steps into a soft staircase as T rises.
Tubes in the 3D view are schematic per-mode channels ranked by increasing energy (not real-space electron density); bright green = open, dim gray = closed, particle brightness tracks occupation.

Open channel Closed channel

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