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arXiv:1312.6453

Non-Fermi liquid behavior in Bose-Fermi mixtures at two dimensions

Xiao-Yong Feng, Tai Kai Ng

Published Dec 23, 2013• 0 citations
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Abstract

In this paper we study the low temperature behaviors of a system of Bose-Fermi mixtures at two dimensions. Within a self-consistent ladder diagram approximation, we show that at nonzero temperatures $T\rightarrow0$ the fermions exhibit non-fermi liquid behavior. We propose that this is a general feature of Bose-Fermi mixtures at two dimensions. An experimental signature of this new state is proposed.

DOI
10.48550/arxiv.1312.6453

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In this paper we study the low temperature behaviors of a system of Bose-Fermi mixtures at two dimensions. Within a self-consistent ladder diagram approximation, we show that at nonzero temperatures T→0T\rightarrow0T→0 the fermions exhibit non-fermi liquid behavior. We propose that this is a general feature of Bose-Fermi mixtures at two dimensions. An experimental signature of this new state is proposed.
We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic T T -matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan’s contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan’s contact parameter with respect to the density ratio is also found.
Using numerical methods, we study the formation of self-bound quantum Bose-Fermi droplets at nonzero temperatures. We describe an attractive atomic Bose-Fermi mixture using quantum hydrodynamics enriched by beyond-mean-field corrections and thermal fluctuations, together with a simplified self-consistent Hartree-Fock model. With these models, we determine that low-temperature droplets with finite lifetimes can exist in free space when the attraction between bosons and fermions is sufficiently strong. Additionally, Bose-Fermi droplets at nonzero temperatures can exist in a box potential in equilibrium with bosonic and fermionic vapor. We discuss the properties of Bose-Fermi droplets at nonzero temperatures in terms of the initial condensate fraction, total atom number, and interspecies attraction strength.
Non-Fermi liquid behavior is found for the first time in a two-dimensional (2D) system with non-singular interactions using Haldane’s bosonization scheme. The bosonized system is solved exactly by a generalized Bogoliubov transformation. The fermion momentum distribution, calculated using a generalized Mattis-Lieb technique, exhibits a non-universal power law in the vicinity of the Fermi surface for intermediate interaction strengths. In recent years, there has been great interest in possible non-Fermi-liquid-like behavior in the ground state of two-dimensional (2D) strongly correlated fermionic systems [1]. It is well-known that in one dimension the ground state of a fermionic system with arbitrarily weak interactions is not a Fermi liquid but a state usually known as a Luttinger liquid [2]. For the 2D case, many studies have suggested that, in the limit of weak interactions, this behavior does not appear [3]. Studies of systems with a small number of particles also suggest Fermi liquid behavior in 2D [4]. Although Khveshchenko et al have found non-Fermi-liquid behavior in 2D, they worked only with a singular long-range current-current interaction [5]. The one-dimensional Luttinger liquid solution can be obtained by a bosonization
An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-lll channels. It has been found that the onset of the superconducting phase can occur at temperatures (>100nK)(>100\mathrm{nK})(>100nK) of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.
The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study the quantum phase diagram, equation of state, and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behavior at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in a harmonic trap is also studied within the local-density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insight into understanding the universal features of many-body critical phenomena.
Understanding non-Fermi liquids in dimensions higher than one has been a subject of great interest. Such phases may serve as parent states for other unconventional phases of quantum matter, in a similar manner that conventional broken symmetry states can be understood as instabilities of the Fermi liquid. In this work, we investigate the emergence of an exotic non-Fermi liquid in two dimensions, where the fermions with quadratic band-touching dispersion interact with Bose metal. The bosonic excitations in Bose metal possess an extended nodal-line spectrum in momentum space, which arises due to the subsystem symmetry or the restricted motion of bosons. Using renormalization group analysis and direct computations, we show that the extended infrared singularity of Bose metal leads to a line of interacting fixed points of an exotic non-Fermi liquids, where the anomalous dimension of the fermions varies continuously, akin to the Luttinger liquid in one dimension. Further, the generalization of the model with multiple low-energy excitations is used to explore other unusual features of the resulting ground state.