Bosonic Superfluid on the Lowest Landau Level

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory

Background:

• Superfluidity in two-dimensional systems is crucial for understanding quantum phenomena.
• The lowest Landau level provides a unique setting for studying interacting bosons.

Purpose of the Study:

• To develop a low-energy effective field theory for a 2D bosonic superfluid.
• To investigate the role of a Berry term in superfluid dynamics and responses.
• To analyze the impact on collective excitations and transport properties in a vortex crystal.

Main Methods:

• Formulation of a low-energy effective field theory.
• Identification of a Berry term governing coarse-grained superfluid dynamics.
• Calculation of low-energy spectrum and Hall responses for Tkachenko oscillations.

Main Results:

• A Berry term was identified, influencing the dynamics of superfluid degrees of freedom.
• The Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations.
• Nondissipative Hall responses of particle number current and stress tensor were computed.
• A quadratic in momentum term was found in the Hall conductivity.
• No nondissipative Hall viscosity was generated by this term.

Conclusions:

• The developed theory provides insights into the collective behavior of 2D superfluids.
• The Berry term is essential for understanding momentum-dependent Hall conductivity in vortex crystals.
• The study clarifies the absence of nondissipative Hall viscosity in this system.