Topology dependent quantities at the anderson transition

Area of Science:

• Condensed matter physics
• Disordered systems
• Quantum transport

Background:

• The Anderson transition describes the metal-insulator transition in disordered electronic systems.
• Understanding critical phenomena in such systems is crucial for condensed matter physics.
• Boundary conditions can influence system behavior, particularly near critical points.

Purpose of the Study:

• To investigate the impact of boundary conditions on the critical behavior of the three-dimensional Anderson transition.
• To determine which aspects of critical behavior are sensitive to boundary conditions and which are not.

Main Methods:

• Numerical simulations of the Anderson transition model in three dimensions.
• Analysis of scaling functions and critical conductance distributions.
• Varying boundary conditions (e.g., periodic, anti-periodic, open) to assess their effects.

Main Results:

• A strong dependence of the scaling function on boundary conditions was observed.
• The critical conductance distribution was found to be significantly influenced by boundary conditions.
• The critical disorder and critical exponent were determined to be independent of the boundary conditions studied.

Conclusions:

• Boundary conditions play a crucial role in shaping the detailed characteristics of the Anderson transition, such as scaling functions and conductance distributions.
• Fundamental critical parameters like the critical disorder and critical exponent are robust and do not depend on the chosen boundary conditions for the 3D Anderson transition.