arXiv subjects

M. Iskin

Publications and source records attributed to M. Iskin.

At least 37 records · Page 2Linked to original sources

arXiv2022

Three-body problem in a multiband Hubbard model

We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-$\uparrow$ fermions and a spin-$\downarrow$ fermion due to an onsite attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically-stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band linear-chain model. In particular we also reveal that the trimers have a nearly-flat dispersion when formed in a flat band, which is unlike the highly-dispersive spectrum of its dimers.

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arXiv2022

Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states

By considering an onsite attraction between a spin-$\uparrow$ and a spin-$\downarrow$ fermion in a multiband tight-binding lattice, here we study the two-body spectrum, and derive an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states. In addition to the intraband (or the so-called conventional) contribution that depends only on the single-particle spectrum and the interband (or the so-called geometric) contribution that is controlled by the quantum metric, our generalized relation has an additional interband contribution that depends on the so-called band-resolved quantum metric. All of our analytical expressions are applicable to those multiband lattices that simultaneously exhibit time-reversal symmetry and fulfill the condition on spatially-uniform pairing. As a nontrivial illustration we analyze the two-body problem in a Kagome lattice with nearest-neighbor hoppings, and show that the exact relation provides a perfect benchmark.

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arXiv2022

Quantum-geometric perspective on spin-orbit-coupled Bose superfluids

We employ the Bogoliubov approximation to study how the quantum geometry of the helicity states affects the superfluid properties of a spin-orbit-coupled Bose gas in continuum. In particular we derive the low-energy Bogoliubov spectrum for a plane-wave condensate in the lower helicity band and show that the geometric contributions to the sound velocity are distinguished by their linear dependences on the interaction strength, i.e., they are in sharp contrast to the conventional contribution which has a square-root dependence. We also discuss the roton instability of the plane-wave condensate against the stripe phase and determine their phase transition boundary. In addition we derive the superfluid density tensor by imposing a phase-twist on the condensate order parameter and study the relative importance of its contribution from the interband processes that is related to the quantum geometry.

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arXiv2021

Two-body problem in a multiband lattice and the role of quantum geometry

We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a variational approach, we obtain the exact solution of the dispersion in the form of a set of self-consistency equations, and apply it to tight-binding Hamiltonians with onsite interactions. We pay special attention to the bipartite lattices with a two-point basis that exhibit time-reversal symmetry, and show that the lowest-energy bound states disperse quadratically with momentum, whose effective-mass tensor is partially controlled by the quantum metric tensor of the underlying Bloch states. In particular, we apply our theory to the Mielke checkerboard lattice, and study the special role played by the interband processes in producing a finite effective mass for the bound states in a non-isolated flat band.

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arXiv2021

Atom-dimer and dimer-dimer scatterings in a spin-orbit coupled Fermi gas

Using the diagrammatic approach, here we study how spin-orbit coupling (SOC) affects the fermion-dimer and dimer-dimer scattering lengths in the Born approximation, and benchmark their accuracy with the higher-order approximations. We consider both isotropic and Rashba couplings in three dimensions, and show that the Born approximation gives accurate results in the $1/(m αa_s) \ll -1$ limit, where $m$ is the mass of the fermions, $α$ is the strength of the SOC, and $a_s$ is the $s$-wave scattering length between fermions. This is because the higher-loop contributions form a perturbative series in the $1/(m αa_s) < 0$ region that is controlled by the smallness of the residue $Z$ of the dimer propagator. In sharp contrast, since $Z$ grows with the square-root of the binding energy of the dimer in the $1/(m αa_s) > 0$ region, all of the higher-loop contributions are of similar order.

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arXiv2021

Non-Hermitian BCS-BEC evolution with a complex scattering length

Having both elastic and inelastic two-body processes that are characterized by a complex $s$-wave scattering length between $\uparrow$ and $\downarrow$ fermions in mind, here we apply the non-Hermitian extension of the mean-field theory to the BCS-BEC evolution at zero temperature. We construct the phase diagram of the system, where we find a reentrant superfluid (SF) transition that is intervened by a normal and/or a metastable phase as a function of increasing inelasticity. This transition occurs in a large parameter regime away from the unitarity, i.e., both on the BCS and BEC sides of the resonance, and it is mostly governed by the exceptional points. In addition, except for the strongly-inelastic regime, we also show that the SF phase can be well-described by the condensation of weakly-interacting bosonic pairs in the two-body bound state with a complex binding energy.

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arXiv2020

Bardeen-Cooper-Schrieffer--type pairing in a spin-$\frac{1}{2}$ Bose gas with spin-orbit coupling

We apply the functional path-integral approach to analyze how the presence of a spin-orbit coupling (SOC) affects the basic properties of a BCS-type paired state in a two-component Bose gas. In addition to a mean-field theory that is based on the saddle-point approximation for the inter-component pairing, we derive a Ginzburg-Landau theory by including the Gaussian fluctuations on top, and use them to reveal the crucial roles played by the momentum-space structure of an arbitrary SOC field in the stability of the paired state at finite temperatures. For this purpose, we calculate the critical transition temperature for the formation of paired bosons, and that of the gapless quasiparticle excitations for a broad range of interaction and SOC strengths. In support of our results for the many-body problem, we also benchmark our numerical calculations against the analytically-tractable limits, and provide a full account of the two-body limit including its non-vanishing binding energy for arbitrarily weak interactions and the anisotropic effective mass tensor.

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arXiv2020

Collective excitations of a BCS superfluid in the presence of two sublattices

We consider a generic Hamiltonian that is suitable for describing a uniform BCS superfluid on a lattice with a two-point basis, and study its collective excitations at zero temperature. For this purpose, we first derive an effective-Gaussian action for the pairing fluctuations, and then extract the low-energy dispersion relations for the in-phase Goldstone and out-of-phase Leggett modes along with the corresponding amplitude (i.e., the so-called Higgs) ones. We find that while the Goldstone mode is gapless at zero momentum and propagating in general, the Leggett mode becomes undamped only with sufficiently strong interactions. Furthermore, we show that, in addition to the conventional contribution that is controlled by the energy of the Bloch bands, the velocity of the Goldstone mode has a geometric contribution that is governed by the quantum metric tensor of the Bloch states. Our results suggest that the latter contribution dominates the velocity when the former one becomes negligible for a narrow- or a flat-band.

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arXiv2019

Geometric contribution to the Goldstone mode in spin-orbit coupled Fermi superfluids

The so-called quantum metric tensor is a band-structure invariant whose measure corresponds to the quantum distance between nearby states in the Hilbert space, characterizing the geometry of the underlying quantum states. In the context of spin-orbit coupled Fermi gases, we recently proposed that the quantum metric has a partial control over all those superfluid properties that depend explicitly on the mass of the superfluid carriers, i.e., the effective-mass tensor of the corresponding (two- or many-body) bound state. Here we scrutinize this finding by analyzing the collective phase and amplitude excitations at zero temperature. In particular to the Goldstone mode, we present extensive numerical calculations for the Weyl and Rashba spin-orbit couplings, revealing that, despite being small, the geometric contribution is solely responsible for the nonmonotonic evolution of the sound velocity in the BCS-BEC crossover.

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arXiv2019

Origin of flat-band superfluidity on the Mielke checkerboard lattice

The Mielke checkerboard is known to be one of the simplest two-band lattice models exhibiting an energetically flat band that is in touch with a quadratically dispersive band in the reciprocal space, i.e., its flat band is not isolated. Motivated by the growing interest in understanding the origins of flat-band superfluidity in various contexts, here we provide an in-depth analysis showing how the mean-field BCS correlations prevail in this particular model. Our work reveals the quantum-geometric origin of flat-band superfluidity through uncovering the leading role by a band-structure invariant, i.e., the so-called quantum metric tensor of the single-particle bands, in the inverse effective mass tensor of the Cooper pairs.

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arXiv2019

Geometric mass acquisition via quantum metric: an effective band mass theorem for the helicity bands

By taking the virtual inter-band transitions along with the intra-band ones into full account, here we first propose an effective band mass theorem that is suitable for a wide-class of single-particle Hamiltonians exhibiting multiple energy bands. Then, for the special case of two-band systems, we show that the inter-band contribution to the effective band mass of a particle at a given quantum state is directly controlled by the quantum metric of the corresponding state. As an illustration, we consider a spin-orbit coupled spin-$1/2$ particle and calculate its effective band mass at the band minimum of the lower helicity band. Independent of the coupling strength, we find that the bare mass $m_0$ of the particle jumps to $2m_0$ for the Rashba and to $3m_0$ for the Weyl coupling. This geometric mass enhancement is a non-perturbative effect, uncovering the mystery behind the effective mass of the two-body bound states in the non-interacting limit. As a further illustration, we show that a massless Dirac particle acquires a linearly dispersing band mass (equivalent to the effective cyclotron one up to a prefactor) with its momentum through the same mechanism.

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arXiv2019

Superfluid stiffness for the attractive Hubbard model on a honeycomb optical lattice

In addition to the conventional contribution that is directly controlled by the single-particle energy spectrum, the superfluid phase stiffness of a two-component Fermi gas has a geometric contribution that is governed by the quantum metric of the honeycomb's band structure. Here, we take both contributions into account, and construct phase diagrams for the critical superfluid transition temperature as a function of the chemical potential, particle filling, onsite interaction and next-nearest-neighbor hopping. Our theoretical approach is based on a self-consistent solution of the BCS mean-field theory for the stationary Cooper pairs and the universal BKT relation for the phase fluctuations.

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arXiv2018

Exposing the quantum geometry of spin-orbit coupled Fermi superfluids

The coupling between a quantum particle's intrinsic angular momentum and its center-of-mass motion gives rise to the so-called helicity states that are characterized by the projection of the spin onto the direction of momentum. In this paper, by unfolding the superfluid-density tensor into its intra-helicity and inter-helicity components, we reveal that the latter contribution is directly linked with the total quantum metric of the helicity bands. We consider both Rashba and Weyl spin-orbit couplings across the BCS-BEC crossover, and show that the geometrical inter-helicity contribution is responsible for up to a quarter of the total superfluid density. We believe this is one of those elusive effects that may be measured within the highly-tunable realm of cold Fermi gases.

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arXiv2018

Spin-susceptibility of spin-orbit coupled Fermi superfluids

Under the self-consistent mean-field approach for the BCS-BEC crossover problem, we derive a closed-form analytical expression for the general spin response of noncentrosymmetric Fermi superfluids with arbitrary spin-orbit coupling and Zeeman fields. In addition to the paramagnetic, i.e., the Pauli intra-helicity and Van Vleck type inter-helicity, contributions to the spin-susceptibility tensor that have normal-state counterparts, we identify a diamagnetic inter-helicity contribution that is unique to the superfluid state. Our extensive numerical calculations for the Weyl, Rashba and equal Rashba-Dresselhaus spin-orbit couplings illustrate that it is this diamagnetic contribution that grows gradually with pairing and cancels precisely the Van Vleck contribution away from the BCS regime in general.

cond-mat.quant-gas↗

arXiv2018

Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature, and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum metric contribution accounts for a sizeable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-BEC crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables as well.

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arXiv2018

Berezinskii-Kosterlitz-Thouless transition in the time-reversal-symmetric Hofstadter-Hubbard model

Assuming that two-component Fermi gases with opposite artificial magnetic fields on a square optical lattice are well-described by the so-called time-reversal-symmetric Hofstadter-Hubbard model, we explore the thermal superfluid properties along with the critical Berezinskii-Kosterlitz-Thouless (BKT) transition temperature in this model over a wide-range of its parameters. In particular, since our self-consistent BCS-BKT approach takes the multi-band butterfly spectrum explicitly into account, it unveils how dramatically the inter-band contribution to the phase stiffness dominates the intra-band one with an increasing interaction strength for any given magnetic flux.

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arXiv2017

Hofstadter-Hubbard model with opposite magnetic fields: Bardeen-Cooper-Schrieffer pairing and superfluidity in the nearly flat butterfly bands

Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BCS and BKT transition temperatures.

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arXiv2017

BCS theory of time-reversal-symmetric Hofstadter-Hubbard model

The competition between the length scales associated with the periodicity of a lattice potential and the cyclotron radius of a uniform magnetic field is known to have dramatic effects on the single-particle properties of a quantum particle, e.g., the fractal spectrum is known as the Hofstadter butterfly. Having this intricate competition in mind, we consider a two-component Fermi gas on a square optical lattice with opposite synthetic magnetic fields for the components, and study its effects on the many-body BCS-pairing phenomenon. By a careful addressing of the distinct superfluid transitions from the semi-metal, quantum spin-Hall insulator or normal phases, we explore the low-temperature phase diagrams of the model, displaying lobe structures that are reminiscent of the well-known Mott-insulator transitions of the Bose-Hubbard model.

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