Vertex corrections to the mean-field electrical conductivity in disordered electron systems

Area of Science:

• Condensed Matter Physics
• Disordered Systems
• Electronic Transport Phenomena

Background:

• Mean-field theory accurately describes equilibrium properties of disordered electron systems.
• Standard mean-field theory fails for transport phenomena due to quantum coherence and backscattering.
• Vertex corrections can lead to unphysical negative conductivity in strong disorder regimes.

Purpose of the Study:

• To develop a stabilized expansion of mean-field theory for disordered electron systems.
• To incorporate vertex corrections that account for quantum coherence and backscattering.
• To ensure non-negative electrical conductivity across all disorder strengths.

Main Methods:

• Utilized the inverse of the number of nearest neighbors on hypercubic lattices as a small parameter.
• Developed a method to include vertex corrections within the mean-field approximation.
• Analyzed the impact of these corrections on electrical conductivity.

Main Results:

• Successfully stabilized the theoretical expansion around the mean-field approximation.
• Incorporated vertex corrections to accurately model transport phenomena.
• Achieved non-negative electrical conductivity predictions in all disorder regimes.

Conclusions:

• The enhanced theory provides a robust framework for understanding transport in disordered electron systems.
• This approach overcomes limitations of standard mean-field theory, particularly in strong disorder.
• The findings are crucial for accurate predictions of material properties in alloys and other disordered materials.