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Register a new userBreach pair superfluidity: a brief review
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Added by
Wensheng Vincent Liu
Publication date
2021
fields
Physics
and research's language is
English
Authors
W. Vincent Liu
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Interior gap superfluidity was introduced together with Frank Wilczek. Later on together with our collaborators, we generalized this new possibility of superfluidity to a more broader concept, breach pair superfluidity. In the occasion to celebrate Professor Frank Wilczeks seventieth birthday and his productive career in several major areas in physics, I dedicate this note to recall the exciting times of developing this idea, the main aspects of the proposed phase, and discussion on its stability condition.
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We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the mechanism responsible for the formation of those phases, the crucial role is played by the flat band, wherein particles can readjust their density at zero energy cost. The multiorbital structure of the unit cell is found to stabilize the Sarma phase by allowing for a modulation of the order parameter within a unit cell. We also study the effect of finite temperature and a lattice with staggered hopping parameters on the behaviour of these phases.
Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction between lattice fermions, will suppress the phase separation instability. Taking the honeycomb lattice as an example, we show that our proposal significantly enlarges the stable portion of the topological superfluid phase and increases the critical temperature by an order of magnitude. Our work opens a route to enhance the stability of topological superfluids by engineering inter-particle interactions.
This article provides a focused review of recent findings which demonstrate, in some cases quite counter-intuitively, the existence of bound states with a singularity of the density pattern at the center, while the states are physically meaningful because their total norm converges. One model of this type is based on the 2D Gross-Pitaevskii equation (GPE) which combines the attractive potential ~ 1/r^2 and the quartic self-repulsive nonlinearity, induced by the Lee-Huang-Yang effect (quantum fluctuations around the mean-field state). The GPE demonstrates suppression of the 2D quantum collapse, driven by the attractive potential, and emergence of a stable ground state (GS), whose density features an integrable singularity ~1/r^{4/3} at r --> 0. Modes with embedded angular momentum exist too, and they have their stability regions. A counter-intuitive peculiarity of the model is that the GS exists even if the sign of the potential is reversed from attraction to repulsion, provided that its strength is small enough. This peculiarity finds a relevant explanation. The other model outlined in the review includes 1D, 2D, and 3D GPEs, with the septimal (seventh-order), quintic, and cubic self-repulsive terms, respectively. These equations give rise to stable singular solitons, which represent the GS for each dimension D, with the density singularity ~1/r^{2/(4-D). Such states may be considered as a result of screening of a bare delta-functional attractive potential by the respective nonlinearity.
Realising and probing topological superfluids is a key goal for fundamental science, with exciting technological promises. Here, we show that chiral $p_x+ip_y$ pairing in a two-dimensional topological superfluid can be detected through circular dichroism, namely, as a difference in the excitation rates induced by a clockwise and counter-clockwise circular drive. For weak pairing, this difference is to a very good approximation determined by the Chern number of the superfluid, whereas there is a non-topological contribution scaling as the superfluid gap squared that becomes signifiant for stronger pairing. This gives rise to a competition between the experimentally driven goal to maximise the critical temperature of the superfluid, and observing a signal given by the underlying topology. Using a combination of strong coupling Eliashberg and Berezinskii-Kosterlitz-Thouless theory, we analyse this tension for an atomic Bose-Fermi gas, which represents a promising platform for realising a chiral superfluid. We identify a wide range of system parameters where both the critical temperature is high and the topological contribution to the dichroic signal is dominant.
We consider a mixture of two bosonic species with tunable interspecies interaction in a periodic potential and discuss the advantages of low filling factors on the detection of the pair-superfluid phase. We show how the emergence of such a phase can be put dramatically into evidence by looking at the interference pictures and density correlations after expansion and by changing the interspecies interaction from attractive to repulsive.
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