Universal conductance and conductivity at critical points in integer quantum Hall systems.

Area of Science:

• Condensed matter physics
• Quantum Hall effect

Background:

• The integer quantum Hall regime exhibits distinct electronic properties.
• Understanding transport at quantum critical points is crucial for condensed matter physics.

Purpose of the Study:

• To calculate longitudinal two-terminal conductance and Kubo conductivity at quantum critical points.
• To investigate the universality of transport quantities in different Landau bands.
• To explore the role of multifractal wave functions in conductance.

Main Methods:

• Numerical calculations of transport quantities.
• Analysis in the limit of large system sizes.
• Comparison of results across different Landau bands.

Main Results:

• Longitudinal conductance and Kubo conductivity are identical in the lowest Landau band.
• A critical conductance value supporting universality is found in the second-lowest Landau band.
• Obtained values differ significantly from previously accepted values.

Conclusions:

• The multifractal structure of critical wave functions likely causes the discrepancy in conductance values.
• This multifractality is a generic property affecting conductance at quantum critical points.