Conductance distributions in quasi-one-dimensional disordered wires

Area of Science:

• Condensed Matter Physics
• Disordered Systems
• Quantum Transport

Background:

• Understanding electron transport in disordered systems is crucial for materials science.
• The metal-insulator crossover describes the transition between metallic and insulating behavior in materials.
• Quasi-one-dimensional disordered wires present a unique system for studying quantum transport phenomena.

Purpose of the Study:

• To analyze the distribution of conductances P(g) in quasi-one-dimensional disordered wires.
• To investigate the validity of perturbation theory in the metal-insulator crossover regime.
• To compare results from Monte Carlo simulations with numerical calculations and experimental observations.

Main Methods:

• Monte Carlo solution of the Dorokhov, Mello, Pereyra, and Kumar (DMPK) scaling equation.
• Tight-binding numerical calculations for bulk disordered wires.
• Perturbation theory analysis for conductances.

Main Results:

• The distribution of conductances P(g) obtained from DMPK equation matches tight-binding calculations.
• Perturbation theory is valid for mean dimensionless conductances around 1.
• A distinct sharp feature in P(g) at g=1 is observed in the crossover regime, differing from surface-disordered wires.

Conclusions:

• The DMPK equation accurately describes conductance distributions in disordered wires.
• Perturbation theory provides a reliable tool for analyzing transport properties even at low conductances.
• The observed feature at g=1 highlights differences between bulk and surface disorder effects.