High frequency conductivity in the quantum hall regime.

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect Studies
• Low-Temperature Physics

Background:

• The quantum Hall effect (QHE) is a hallmark of two-dimensional electron systems (2DES) under strong magnetic fields.
• Understanding the dynamic conductivity is crucial for characterizing electronic transport and phase transitions in 2DES.
• Previous studies often focused on static conductivity or lower frequencies.

Purpose of the Study:

• To measure and analyze the complex conductivity, sigma(xx), of a 2DES in the QHE regime up to 6 GHz.
• To investigate the scaling behavior of conductivity across different frequencies and QHE plateau transitions.
• To directly evaluate the electron localization length (xi) using conductivity data in the variable-range hopping regime.

Main Methods:

• Utilized precise measurements of complex conductivity, sigma(xx), in a 2DES.
• Conducted experiments at electron temperatures below 100 mK to ensure quantum effects dominate.
• Employed variable-range hopping regime analysis for localization length determination.

Main Results:

• Demonstrated that sigma(xx) exhibits universal scaling behavior with frequency across different QHE plateau transitions.
• Showcased the ability to scale both the real and imaginary parts of conductivity to a single function.
• Provided a direct evaluation of the localization length, xi, in the variable-range hopping regime.

Conclusions:

• The complex conductivity of 2DES in the QHE regime displays frequency-independent scaling.
• The study offers a robust method for determining the electron localization length.
• Results provide critical insights into the nature of electronic states and transitions in quantum Hall systems.