Quantum chaos in nano-sized billiards in layered two-dimensional semiconductor structures

Area of Science:

• Condensed Matter Physics
• Mesoscopic Physics
• Quantum Chaos

Background:

• Two-dimensional electron-rich cavities at semiconductor interfaces are crucial for quantum devices.
• Modeling these cavities requires accounting for electrostatic confinement (soft walls) and impurity disorder.

Purpose of the Study:

• Investigate the impact of soft confining walls and disorder on the dynamic behavior of electrons in semiconductor cavities.
• Explore the transition between Wigner and Poisson distributions in energy level spacing.
• Examine the influence of leads on electron behavior and its relation to experimental observations.

Main Methods:

• Numerical modeling of two-dimensional electron-rich cavities with soft walls and ionized impurity disorder.
• Analysis of nearest-level spacing distributions (Wigner vs. Poisson).
• Investigation of chaotic Robnik dots and the effect of attached leads (stubs).

Main Results:

• Softening confining walls induces a crossover from Wigner to Poisson distributions for nearest level spacing.
• Disorder effects are negligible in high-mobility samples with ballistic electron motion.
• Chaotic Robnik dots do not exhibit this crossover. Wide leads lead to Wigner statistics, indicating irregular behavior.

Conclusions:

• The softening of confining walls is a key factor in controlling electron energy level statistics in semiconductor cavities.
• Lead effects can induce transitions to irregular behavior, consistent with experimental magnetoresistance measurements.
• Findings have implications for understanding conductance fluctuations in mesoscopic systems.