Kelvin-Mach Wake in a Two-Dimensional Fermi Sea.

Area of Science:

• Condensed matter physics
• Plasma physics
• Mesoscopic systems

Background:

• Plasma oscillations in two-dimensional electron gas (2DEG) exhibit complex dispersion relations.
• Hydrodynamic approximations are crucial for understanding collective electron behavior.
• Supersonic electric currents introduce unique phenomena due to the Mach cone effect.

Purpose of the Study:

• To investigate the wake patterns formed downstream of a charged impurity in a 2DEG with supersonic electric current.
• To analyze how the Mach number (M) influences the geometry of the induced charge density and potential wake.
• To characterize the nature of wave fronts within and outside the Mach cone.

Main Methods:

• Utilizing the hydrodynamic approximation for plasma oscillations in a 2DEG.
• Analyzing the dispersion law of plasma oscillations as a function of wave vector (q).
• Investigating the wake structure for different Mach numbers (M).

Main Results:

• The dispersion law interpolates between Ω∝sqrt[q] and Ω∝q.
• A wake pattern of induced charge density and potential is formed downstream of a charged impurity.
• For 1
• For M>√2, an additional wake resembling a Kelvin ship wake appears outside the Mach sector.

Conclusions:

• The geometry of the wake pattern is directly controlled by the Mach number.
• The study identifies distinct wake structures dependent on whether the flow is subsonic, sonic, or supersonic.
• These findings have implications for understanding charge transport and wake formation in 2D electronic systems.