Peierls instability, periodic Bose-Einstein condensates and density waves in quasi-one-dimensional boson-fermion mixtures of atomic gases

TL;DR

This paper investigates Peierls instability in quasi-one-dimensional boson-fermion atomic gases, revealing how coupling between bosonic and fermionic excitations leads to periodic density waves and lower-energy states.

Contribution

It demonstrates the occurrence of Peierls instability in Q1D boson-fermion mixtures and characterizes the resulting periodic density wave states.

Findings

Peierls instability appears at wave-number 2k_F in bosonic excitation spectra.

Periodic BEC and fermionic density waves lower the system's energy.

Conditions for Peierls instability are derived for harmonic oscillator confinement.

Abstract

We study the quasi-one-dimensional (Q1D) spin-polarized bose-fermi mixture of atomic gases at zero temperature. Bosonic excitation spectra are calculated in random phase approximation on the ground state with the uniform BEC, and the Peierls instabilities are shown to appear in bosonic collective excitation modes with wave-number $2k_F$ by the coupling between the Bogoliubov-phonon mode of bosonic atoms and the fermion particle-hole excitations. The ground-state properties are calculated in the variational method, and, corresponding to the Peierls instability, the state with a periodic BEC and fermionic density waves with the period $\pi/k_F$ are shown to have a lower energy than the uniform one. We also briefly discuss the Q1D system confined in a harmonic oscillator (HO) potential and derive the Peierls instability condition for it.