Anderson Localization Length Calculator

Weak-disorder approximation

Anderson localization describes exponential confinement of electronic wavefunctions due to random onsite potentials. In one dimension, perturbation theory yields the approximate localization length $\xi$ for weak disorder:

Conductance follows the scaling relation , measured in units of the conductance quantum $e$²/ h . The calculator reports both quantities, offering a quick check on how disorder and sample length suppress transport.

Scenario comparison

Different experiments probe localization by varying disorder strength or sample length. The table below compares a baseline case with 20 % weaker and stronger disorder to illustrate sensitivity.

Localization shrinks rapidly with increasing disorder: doubling W cuts ξ by a factor of four. The conductance column highlights how even modest changes in ξ translate into orders of magnitude difference in transport for long chains.