Resonances in the superconducting properties, in a regime of crossover from BCS to mixed Bose-Fermi superconductivity, are investigated in a two-band superconductor where the chemical potential is tuned near the band edge of the second mini-band generated by quantum confinement effects. The shape resonances at T=0 in the superconducting gaps (belonging to the class of Feshbach-like resonances) is manifested by interference effects in the superconducting gap at the first large Fermi surface when the chemical potential is in the proximity of the band edge of the second mini-band. The case of a superlattice of quantum wells is considered and the amplification of the superperconducting gaps at the 3D-2D Fermi surface topological transition is clearly shown. The results are found to be in good agreement with available experimental data on a superlattice of honeycomb boron layers intercalated by Al and Mg spacer layers.
Motivated by recent experiments on heavy fermion materials CeCu$_2$Si$_2$ and UBe$_{13}$, we develop a framework to capture generic properties of multiband superconductors with strong Pauli paramagnetic effect (PPE). In contrast to the single band case, the upper critical field $H_{\rm c2}$ can remain second order transition even for strong PPE cases. The expected first order transition is hidden inside $H_{\rm c2}$ and becomes a crossover due to the interplay of multibandness. The present theory based on full self-consistent solutions of the microscopic Eilenberger theory explains several mys…
The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal Fe$_{1+y}$Se$_x$Te$_{1-x}$ by tuning the Fermi energy, $ε_F$, via chemical doping, which permits us to systematically change $Δ/ ε_F$ from 0.16 to 0.5 were $Δ$ is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap and characteristic chang…
The upper critical field Hc2(T) of the multiband superconductor KFe2As2 has been studied via low-temperature thermal expansion and magnetostriction measurements. We present compelling evidence for Pauli-limiting effects dominating Hc2(T) for H || a, as revealed by a crossover from second- to first-order phase transitions to the superconducting state in the magnetostriction measurements down to 50 mK. Corresponding features were absent for H || c. To our knowledge, this crossover constitutes the first confirmation of Pauli limiting of the Hc2(T) of a multiband superconductor. The results are su…
Scanning tunneling experiments on single crystals of superconducting FeTe$_{0.55}$Se$_{0.45}$ have recently provided evidence for discrete energy levels inside vortices. Although predicted long ago, such levels are seldom resolved due to extrinsic (temperature, instrumentation) and intrinsic (quasiparticle scattering) limitations. We study a microscopic multiband model with parameters appropriate for FeTe$_{0.55}$Se$_{0.45}$. We confirm the existence of well-separated bound states and show that the chemical disorder due to random occupation of the chalcogen site does not affect significantly t…
In multiband systems, such as iron-based superconductors, the superconducting states with locking and anti-locking of the interband phase differences, are usually considered as mutually exclusive. For example, a dirty two-band system with interband impurity scattering undergoes a sharp crossover between the $s_{\pm}$ state (which favors phase anti locking) and the $s_{++}$ state (which favors phase locking). We discuss here that the situation can be much more complex in the presence of an external field or superconducting currents. In an external applied magnetic field, dirty two-band supercon…
In a superconductor the third-harmonic generation (THG) of a strong THz pulse is enhanced below Tc by the resonant excitation of lattice-modulated charge fluctuations (LCF), which modulate the response according to the polarization of the field. Here we compute the THG within a multiband model for the prototype NbN superconductor. We show that the non-resonant contribution coming from the instantaneous electronic response and the finite width of the pulse significantly suppress the polarization dependence of the signal, challenging its observation in real systems.
We examine the resonant activation of a current-biased Josephson junction near the crossover temperature in order to show the way in which the device transitions from the classical regime to the quantum regime. We use microwaves to probe the quantum energy states that exist in the potential well. The quantum features are visible until the junction is heated up to the crossover temperature, at which point the line widths of the energy levels overlap and become indistinguishable from one another. When well above this temperature, the junction behaves classically when resonantly activated with mi…
We present measurements of the specific heat coefficient γ(= C/T) in the low temperature limit as a function of an applied magnetic field for the Fe-based superconductor BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$. We find both a linear regime at higher fields and a limiting square root $H$ behavior at very low fields. The crossover from a Volovik-like $\sqrt{H}$ to a linear field dependence can be understood from a multiband calculation in the quasiclassical approximation assuming gaps with different momentum dependence on the hole- and electron-like Fermi surface sheets.
We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential, $μ$), which w…
Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux. In the absence of pinning such paramagnetic response is weak, and ceases with increasing sample thickness. Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field. We link the appearance of this giant paramagnetic response to the broad crossover between conventiona…
We investigate theoretically the properties of s-wave multiband superconductors in the weak coupling (BCS) limit in the presence of pair-breaking effects of magnetic field. It is shown that a qualitatively new gapless superconducting state must appear in quasi-2D superconductors in magnetic fields parallel to the plane, corresponding to a Sarma state induced on one of the Fermi surfaces. The emergence of the new state in s-wave multiband superconductors in the absence of anisotropy or spin-orbit interaction is usually accompanied by a zero-temperature first-order metamagnetic phase transition.…
We examine the effect of a single, non-magnetic impurity in a multiband, extended s-wave superconductor allowing for anisotropy of the gaps on the Fermi surfaces. We derive analytic expressions for the Green's functions in the continuum and analyse the conditions for the existence of sharp impurity-induced resonant states. Underlying band structure is more relevant for the multiband than for single band case, and mismatch between the bands generically makes the formation of the impurity states less likely in the physical regime of parameters. We confirm these conclusions by numerically solving…
Within the two-band model of superconductivity, we study the dependence of the critical temperature Tc and of the isotope exponent alpha in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband of the diborides. Our results agree with the observed dependence of Tc on Mg content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be interpreted as due to the proximity to a "shape resonance". Moreover we have calculated a possible variation of the isotope effect on the s…
We theoretically investigate coherent optical excitations of collective modes in two-band BCS superconductors, which accommodate two Higgs modes and one Leggett mode corresponding, respectively, to the amplitude and relative-phase oscillations of the superconducting order parameters associated with the two bands. We find, based on a mean-field analysis, that each collective mode can be resonantly excited through a nonlinear light-matter coupling when the doubled frequency of the driving field coincides with the frequency of the corresponding mode. Among the two Higgs modes, the higher-energy o…
The problem of Andreev reflection between a normal metal and a multiband superconductor is addressed. The appropriate matching conditions for the wave function at the interface are established on the basis of an extension of quantum waveguide theory to these systems. Interference effects between different bands of the superconductor manifest themselves in the conductance and the case of FeAs superconductors is specifically considered, in the framework of a recently proposed effective two-band model, in the sign-reversed s-wave pairing scenario. Resonant transmission through surface Andreev bou…
In several parent iron-pnictide compounds the resistivity has an extended range of linear magnetic field dependence. We argue that there is a simple and natural explanation of this behavior. Spin density wave transition leads to Fermi-surface reconstruction corresponding to strong modification of the electronic spectrum near the nesting points. It is difficult for quasiparticles to pass through these points during their orbital motion in magnetic field, because they must turn sharply. As the area of the Fermi surface affected by the nesting points increases proportionally to magnetic field, th…
Superfluidity in coupled electron-hole sheets of bilayer graphene is predicted here to be multicomponent because of the conduction and valence bands. We investigate the superfluid crossover properties as functions of the tunable carrier densities and the tunable energy band gap $E_g$. For small band gaps there is a significant boost in the two superfluid gaps, but the interaction driven excitations from the valence to the conduction band can weaken the superfluidity, even blocking the system from entering the BEC regime at low densities. At a given larger density, a band gap $E_g\sim 40$-$60$ …
There is a tacit assumption that multiband superconductors are essentially the same as multigap superconductors. More precisely, it is usually assumed that the number of excitation gaps in the single-particle energy spectrum of a uniform superconductor determines the number of contributing bands in the corresponding superconducting model. Here we demonstrate that contrary to this widely accepted viewpoint, the superconducting magnetic properties are sensitive to the number of contributing bands even when the corresponding excitation gaps are degenerate and cannot be distinguished. In particula…
We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen--Cooper--Schrieffer--Bose--Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic $T$ matrix approach, we~report how thermodynamic quantities such as the critical temperature, chemical potential, {and~momentum distributions} undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan's contact to a two band system and report the two contac…
Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The…
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, $a_{F},$ and the effective range parameter, $r_{\mathrm{e}}.$ In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances.…
We discuss the shape resonance in the superconducting gaps of a two band superconductor by tuning the chemical potential at a Lifshitz transition for Femi surface neck collapsing and for spot appearing. The high temperature superconducting scenario for complex matter shows the coexistence of a first BCS condensate made of Cooper pairs in the first band and a second boson-like condensate made of bosons like bipolarons, in the second band where the chemical potential is tuned near a Lifshitz transition. The interband coupling controls the shape resonance in the pair exchange between the two cond…
The physics of the crossover between weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein-condensate (BEC) limits gives a unified framework of quantum bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature $T_{\rm c}=8.5$ K has been found to be deep inside the BCS-BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe below $T…
We investigate pairing and superconductivity in the attractive Fermi Hubbard model on the one-dimensional sawtooth lattice, which exhibits a flat band by fine-tuning the hopping rates. We first solve the two-body problem, both analytically and numerically, to extract the binding energy and the effective mass of the pairs. Based on the DMRG method, we address the ground-state properties of the many-body system, assuming equal spin populations. We compare our results with those available for a linear chain, where the model is integrable by Bethe ansatz, and show that the multiband nature of the …
We investigate single-particle excitation properties in the normal state of a two-band superconductor or superfluid throughout the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein-condensation (BEC) crossover, within the many-body T-matrix approximation for multi-channel pairing fluctuations. We address the single-particle density of states and the spectral functions consisting of two contributions associated with a waekly interacting deep band and a strongly interacting shallow band, relevant for iron-based multiband superconductors and multicomponent fermionic superfluids. We show how the ps…
Spin excitations in the overdoped high temperature superconductors Tl$_2$Ba$_2$CuO$_{6+δ}$ and (Bi,Pb)$_2$(Sr,La)$_{2}$CuO$_{6+δ}$ were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-$L_3$ absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle/hole e…
We map out the detuning-magnetization phase diagram for a ``magnetized'' (unequal number of atoms in two pairing hyperfine states) gas of fermionic atoms interacting via an s-wave Feshbach resonance (FR). For large positive FR detuning a normal magnetized Fermi gas is stable above an exponentially small value of the population difference. Below this critical value the phase diagram is dominated by coexistence of a magnetized normal gas and a singlet paired superfluid with the latter exhibiting a BCS-Bose Einstein condensate crossover with reduced detuning. On the BCS side of strongly overlappi…
Recently, a test for a sign-changing gap function in a candidate multiband unconventional superconductor involving quasiparticle interference data was proposed. The test was based on the antisymmetric, Fourier transformed conductance maps integrated over a range of momenta $\bf q$ corresponding to interband processes, which was argued to display a particular resonant form, provided the gaps changed sign between the Fermi surface sheets connected by $\bf q$. The calculation was performed for a single impurity, however, raising the question of how robust this measure is as a test of sign-changin…
We study thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the non-monotonic dependence of the chemical potential on detuning and…
We present a detailed study of the superconducting properties in the beta-phase Mo$_{1-x}$Re$_x$ (x = 0.25 and 0.4) solid solution alloys pursued through magnetization and heat capacity measurements. The temperature dependence of the upper critical field H$_{C2}$(T) in these binary alloys shows a deviation from the prediction of the Werthamer-Helfand-Hohenberg (WHH) theory. The temperature dependence of superfluid density estimated from the variation of lower critical field H$_{C1}$ with temperature, cannot be explained within the framework of a single superconducting energy gap. The heat capa…
We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the $ab$ plane. At low temperatures, the upper critical field $μ_0 H_{c2}^{ab}$ shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at $μ_0 H^{\ast}\approx 24$ T well below $μ_0 H_{c2}^{ab}$, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes…
Sideband fingerprint of the Leggett mode in terahertz two-dimensional coherent spectroscopy of multiband superconductors
Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；University of Tokyo（东京大学）；Cryogenic Research Center, University of Tokyo（东京大学低温研究中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所涌现物质科学中心）；Trans-scale Quantum Science Institute, University of Tokyo（东京大学跨尺度量子科学研究所）
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature $T_{cr}$ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux $Φ$. Beyond that we predict a narrow peak in the dependence of $T_{cr}(Φ)$ occurring in …
Multiband superconductivity, involving resonant pair scattering between different bands, has emerged as a possible explanation of some of the main characteristics of the recently discovered iron pnictides. A key feature of such interband pairing mechanism is that it can generate or enhance superconducting pairing irrespective of whether it is attractive or repulsive. The latter case typically leads to the superconducting gap switching its sign among different sections of the Fermi surface. In iron pnictides, the natural scenario is that the gap changes sign between the hole and the electron Fe…
We use a model of vortex dynamics and collective weak pinning theory to study the residual dissipation due to trapped magnetic flux in a dirty superconductor. Using simple estimates, approximate analytical calculations, and numerical simulations, we make predictions and comparisons with experiments performed in CERN and Cornell on resonant superconducting radio-frequency NbCu, doped-Nb and Nb$_3$Sn cavities. We invoke hysteretic losses originating in a rugged pinning potential landscape to explain the linear behavior of the sensitivity of the residual resistance to trapped magnetic flux as a f…
Superconductors are classified by their pairing mechanism and the coupling strength, measured as the ratio of the energy gap to the critical temperature, Tc. We present an extensive comparison of the gap ratios among many single- and multiband superconductors from simple metals to high-Tc cuprates and iron pnictides. Contrary to the recently suggested universality of this ratio in Fe-based superconductors, we find that the coupling in pnictides ranges from weak, near the BCS limit, to strong, as in cuprates, bridging the gap between these two extremes. Moreover, for Fe- and Cu-based materials,…
We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial harmonic trap with frequencies $Ω_\perp$, $Ω_z$. Our primary prediction is the upper-critical angular velocity, $ω_{c2} (δ,T)$, as a function of temperature $T$ and resonance detuning $δ$, ranging across the BEC-BCS crossover. The rotation-driven suppression of superfluidity at $ω_{c2}$ is quite distinct in the BCS and BEC regimes, with the former controlled by Cooper-pair depairing and the latter by the dilution of bosonic molecules. At low $T$ and $Ω_z\llΩ_\perp$, in the BCS and crossover regimes of $0…
While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size o…
Eigen oscillations in a superconducting parallel plate resonator with the Josephson-coupled plates are investigated. While the insulator thickness S changes from tens of microns down to the decay lengthscale of the superconducting wavefunction into a dielectric, ξ~1 nm, both the resonant frequency and Q-factor vary non-monotonically by up to three orders in magnitude. A crossover between the Swihart waves and Josephson plasmons causes a global minimum in the resonant frequency and a local maximum in the Q-factor at S~10ξ.
We present a theory of a degenerate atomic Fermi gas, interacting through a narrow Feshbach resonance, whose position and therefore strength can be tuned experimentally, as demonstrated recently in ultracold trapped atomic gases. The distinguishing feature of the theory is that its accuracy is controlled by a dimensionless parameter proportional to the ratio of the width of the resonance to Fermi energy. The theory is therefore quantitatively accurate for a narrow Feshbach resonance. In the case of a narrow s-wave resonance, our analysis leads to a quantitative description of the crossover bet…
We have produced high-quality complex microwave circuits, such as multiplexed resonators and superconducting phase qubits, using a "vacuum-gap" technology that eliminates lossy dielectric materials. We have improved our design and fabrication strategy beyond our earlier work, leading to increased yield, enabling the realization of these complex circuits. We incorporate both novel vacuum-gap wiring crossovers (VGX) for gradiometric inductors and vacuum-gap capacitors(VGC) on chip to produce resonant circuits that have large internal quality factors (30,000<Q<165,000) at 50 mK, outperforming mos…
We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson-fermion model). The calculations of the superconducting phase transition temperature ($T_{c}$) and the phase diagram are the main concern. The self-consistent $T$-matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The $T$-matrix results for $T_{c}$ are given for a 3D cubic lattice with tight-binding dispersion of electrons and standard…
This thesis presents theoretical work in s- and p-wave resonantly paired Fermi gases at zero temperature. In the BEC regime of the wide-resonance s-wave BCS-BEC crossover, the chemical potential, speed of sound, condensate depletion, and ground state energy are computed. The quantities are calculated in a low density approximation. The bosonic scattering length is computed diagrammatically to be approximately 0.60a with a the fermionic scattering length, confirming a well-known result. The perturbative approach breaks down in the intermediate BCS-BEC crossover regime which is not investigated.…
We investigate the conductance through and the spectrum of ballistic chaotic quantum dots attached to two s-wave superconductors, as a function of the phase difference $ϕ$ between the two order parameters. A combination of analytical techniques -- random matrix theory, Nazarov's circuit theory and the trajectory-based semiclassical theory -- allows us to explore the quantum-to-classical crossover in detail. When the superconductors are not phase-biased, $ϕ=0$, we recover known results that the spectrum of the quantum dot exhibits an excitation gap, while the conductance across two normal leads…
We present a detailed analysis of the two-channel atom-molecule effective Hamiltonian for an ultracold two-component homogeneous Fermi gas interacting near a Feshbach resonance. We particularly focus on the two-body and many-body properties of the dressed molecules in such a gas. An exact result for the many-body T-matrix of the two-channel theory is derived by both considering coupled vertex equations and the functional integral methods. The field theory incorporates exactly the two-body physics of the Feshbach scattering by means of simple analytical formulas without any fitting parameters. …
The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in Tc versus pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The a high-order anisotropic van Hove singularity near the Fermi level observed in band structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wires modules forming a nanoscale heterostructure at atomic limit called superstripes phase. Here we propose that pressurized sulfur hyd…
Resonant Raman scattering below Tc has been discovered in several Bi-, Hg-, Tl-based high-Tc superconductors with three or four CuO2-layers. For Bi2Si2Ca2Cu3O10+d, we found an unexpected crossover of the pair-breaking peak in the A1g-spectrum from a broad bump at hw = 6kBTc for Eexc = 2.54eV to a sharp peak at hw = 8kBTc for Eexc = 2.18eV, together with a strong enhancement of the Ca-phonons. Under resonant conditions, the relative positions of the pair breaking peaks in A1g, B1g, and B2g channels are 2Delta(A1g) = 2Delta(B1g) > 2Delta(B2g). This relation implies that the A1g Raman channel is …
High-temperature superconductivity and a wide variety of exotic superconducting states discovered in FeSe-based materials have been at the frontier of research on condensed matter physics over the past decade. Unique properties originating from the multiband electronic structure, strongly orbital-dependent phenomena, extremely small Fermi energy, electronic nematicity, and topological aspects give rise to many distinct and fascinating superconducting states. Here, we provide an overview of our current understanding of the superconductivity of {\it bulk} FeSe-based materials, focusing on FeSe a…
