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arXiv:2007.04913 · Physical review. B./Physical review. B

Fermi surface resonance and quantum criticality in strongly interacting Fermi gases

Dmitry Miserev, Jelena Klinovaja, Daniel Loss

Published Feb 1, 2021• 6 citations
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Abstract

Fermions in a Fermi gas obey the Pauli exclusion principle restricting any two fermions from occupying the same quantum state. Strong interactions between fermions can completely change the properties of the Fermi gas. In our theoretical study we find an exotic quantum phase in strongly interacting Fermi gases subject to a certain condition imposed on the Fermi surfaces that we call the Fermi surface resonance. The phase is quantum critical in time and space and can be identified by the power-law dependence of the spectral density in frequency and momentum. The linear-response functions are singular in the static limit and at the Kohn anomalies. We analyze the quantum critical state at finite temperatures $T$ and finite size $L$ of the Fermi gas and provide a qualitative $L\ensuremath{-}T$ phase diagram. The quantum critical phase can be experimentally found in typical semiconductor heterostructures.

DOI
10.1103/physrevb.103.075104

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Fermions in a Fermi gas obey the Pauli exclusion principle restricting any two fermions from occupying the same quantum state. Strong interactions between fermions can completely change the properties of the Fermi gas. In our theoretical study we find an exotic quantum phase in strongly interacting Fermi gases subject to a certain condition imposed on the Fermi surfaces that we call the Fermi surface resonance. The phase is quantum critical in time and space and can be identified by the power-law dependence of the spectral density in frequency and momentum. The linear-response functions are singular in the static limit and at the Kohn anomalies. We analyze the quantum critical state at finite temperatures TTT and finite size LLL of the Fermi gas and provide a qualitative L\ensuremath−TL\ensuremath{-}TL\ensuremath−T phase diagram. The quantum critical phase can be experimentally found in typical semiconductor heterostructures.
Quantum criticality of strongly attractive Fermi gas with SU(3)SU(3)SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential μμμ, effective magnetic field H1H_1H1​, H2H_2H2​ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2z=2z=2 and correlation length exponent ν=1/2ν=1/2ν=1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with SU(N)SU(N)SU(N) symmetry.
We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gases for all parameter regimes in current experiments. From the equation of state, we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate the physical origin of quantum criticality. It turns out that the critical properties of the system are described by those of free fermions and those of mixtures of fermions with masses mmm and 2m2m2m. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gases at finite temperatures and can be used to determine the T=0T=0T=0 phase boundaries without any arbitrariness.
In this Letter we consider spinless Fermi gases placed inside a cavity and study the critical strength of a pumping field for driving a superradiance transition. We emphasize that the Fermi surface nesting effect can strongly enhance the superradiance tendency. Around certain fillings, when the Fermi surface is nearly nested with a relevant nesting momentum, the susceptibility of the system toward a checkboard density-wave ordered state is greatly enhanced in comparison with a Bose gas with the same density, because of which a much smaller (sometime even vanishingly small) critical pumping field strength can give rise to superradiance. This effect leads to interesting reentrance behavior and a topologically distinct structure in the phase diagram. Away from these fillings, the Pauli exclusion principle brings about the dominant effect for which the critical pumping strength is lowered in the low-density regime and increased in the high-density regime. These results open the prospect of studying the rich phenomena of degenerate Fermi gases in a cavity.
This thesis presents a theoretical study of strongly-interacting Fermi systems with population imbalance, which is motivated by some differences in cold atoms experiments. We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization, the limit of resonance superfluidity in traps. Our findings contribute to understanding some experimental discrepancies as finite-size and confinement effects. For an imbalanced gas in the uniform system, we calculate the energy of adding an impurity, and construct the equation of state of the partially-polarized normal Fermi liquid. Finally, we study the properties of a spin-down polaron in a trapped gas containing arbitrary numbers of spin-up and spin-down fermions, and derive a self-consistent equation for the polaron energy.
Opportunities for topological phase transitions in strongly correlated Fermi systems near a quantum critical point are explored as an alternative to collective scenarios for experimentally observed departures from standard Fermi-liquid behavior. Attention is focused on a quantum critical point at which the effective mass is divergent due to vanishing of the quasiparticle group velocity at the Fermi surface. Working within the original Landau quasiparticle theory, it is demonstrated that the quasiparticle picture can remain meaningful beyond the quantum critical point through rearrangements of the unstable normal Fermi surface and quasiparticle spectrum. Two possibilities emerge at zero temperature, depending on whether the quasiparticle interaction is regular or singular at zero momentum transfer. In the regular case, one type of topological phase transformation leads to a state with a multiconnected Fermi surface. In the singular case, another type of topological phase transition leads to an exceptional state containing a fermion condensate – the Fermi surface swells into a volume in momentum space, within which partial occupation prevails and quasiparticle energies are pinned to the chemical potential. As the temperature increases from zero to a characteristic value Tm, a crossover can occur from the state with multiple Fermi surfaces to that containing a fermion condensate.
We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization, and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field H<Hc1H<{H}_{c1}H<Hc1​. A completely ferromagnetic phase without pairing occurs when the external field H>Hc2H>{H}_{c2}H>Hc2​. In the region Hc1<H<Hc2{H}_{c1}<H<{H}_{c2}Hc1​<H<Hc2​, we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.