Preformed Cooper Pairs Research Articles

Onset of magnetization in the one-dimensional Fermi gas with attractive [formula omitted]-function potential

The magnetic field dependence of the ground state of the one-dimensional spin-1/2 Fermi gas is studied with emphasis on the onset of the magnetization. The Bethe Ansatz solution shows that the system has three phases, namely, spin–singlet bound states (preformed Cooper pairs), spin-polarized particles and a mixed phase of the above. For small fields the ground state consists of paired states. At the critical field the band of unpaired (spin-up) particles starts to get gradually populated following the square-root dependence of the van Hove singularity of the empty parabolic band. The filled unpaired states correspond to the rapidity interval −B0≤k≤B0. We show that the square of the magnetization and B02 are initially linear in the field. For the case of spin-3/2 the Bethe Ansatz solution for the ground state has four fundamental bands: The particles can be either unpaired or bound in states of two, three and four fermions. The onset of the population of the first three bands again follows the square-root dependence of the one-dimensional van Hove singularity of the respective band. Our results are compared with previous studies where the magnetization is linear in the field.

Microscopic evidence for preformed Cooper pairs in pressure-tuned organic superconductors near the Mott transition

Microscopic evidence for preformed Cooper pairs in pressure-tuned organic superconductors near the Mott transition

Hybridization-Controlled Pseudogap State in the Quantum Critical Superconductor CeCoIn_{5}.

The origin of the partial suppression of the electronic density states in the enigmatic pseudogap behavior, which is at the core of understanding high-T_{c} superconductivity, has been hotly contested as either a hallmark of preformed Cooper pairs or an incipient order of competing interactions nearby. Here, we report the quasiparticle scattering spectroscopy of the quantum critical superconductor CeCoIn_{5}, where a pseudogap with energy Δ_{g} was manifested as a dip in the differential conductance (dI/dV) below the characteristic temperature of T_{g}. When subjected to external pressure, T_{g} and Δ_{g} gradually increase, following the trend of increase in quantum entangled hybridization between the Ce 4f moment and conduction electrons. On the other hand, the superconducting (SC) energy gap and its phase transition temperature shows a maximum, revealing a dome shape under pressure. The disparate dependence on pressure between the two quantum states shows that the pseudogap is less likely involved in the formation of SC Cooper pairs, but rather is controlled by Kondo hybridization, indicating that a novel type of pseudogap is realized in CeCoIn_{5}.

Unconventional superconductivity with preformed pairs in twisted bilayer graphene

We present a theory of superconductivity in magic-angle twisted bilayer graphene and analyze the superconducting phase diagram in presence of the magnetic field. Namely, we consider a model of a granular array hosting localized states, which are hybridized via the delocalized fermions in the inter-grain regions. We study a strong coupling situation when the interactions lead to an incoherent state with preformed Cooper pairs inside the grains. The Andreev scattering among different grains manifests itself through the global phase-coherent superconducting state at lower temperatures. We demonstrate that a new phase transition between the preformed Cooper pairing state and the Larkin-Ovchinnikov-Fulde-Ferrell state might be induced by the spin pair-breaking effect of in-plane magnetic field. The upper critical magnetic field is shown to be enhanced in the strong coupling case.

Preformed Cooper pairs in flat-band semimetals

We study conditions for the emergence of the preformed Cooper pairs in materials hosting flat bands. As a particular example, we consider a semimetal, with a pair of three-band crossing points at which a flat band intersects with a Dirac cone, and focus on the s-wave intervalley pairing channel. The nearly dispersionless nature of the flat band at strong attraction between electrons promotes local Cooper pair formation so that the system may be modeled as an array of superconducting grains. Due to dispersive bands, Andreev scattering between the grains gives rise to the global phase-coherent superconductivity at low temperatures. We develop a mean-field theory to calculate transition temperature between the preformed Cooper pair state and the phase-coherent state for different interaction strengths in the Cooper channel. The transition temperature between semimetal and preformed Cooper pair phases is proportional to the interaction constant, the dependence of the transition temperature to the phase-coherent state on the interaction constant is weaker.

Electronic nature of the pseudogap in electron-doped Sr2IrO4

In high-temperature (Tc) cuprate superconductors, many exotic phenomena are rooted in the enigmatic pseudogap state, which has been interpreted as consisting of preformed Cooper pairs or competing orders or a combination thereof. Observation of pseudogap phenomenologically in electron-doped Sr2IrO4—the 5d electron counterpart of the cuprates, has spurred intense interest in the strontium iridates as a testbed for exploring the exotic physics of the cuprates. Here, we examine the pseudogap state of electron-doped Sr2IrO4 by angle-resolved photoemission spectroscopy (ARPES) and parallel theoretical modeling. Our analysis demonstrates that the pseudogap state of Sr2IrO4 appears without breaking the particle–hole symmetry or inducing spectral broadening which are telltale signatures of competing orders in the cuprates. We find quasiparticle dispersion and its temperature dependence in the pseudogap state of Sr2IrO4 to point to an electronic order with a zero scattering wave vector and limited correlation length. Particle–hole symmetric preformed Cooper pairs are discussed as a viable mechanism for such an electronic order. The potential roles of incommensurate density waves are also discussed.

Theory of coupled dual dynamics of macroscopic phase coherence and microscopic electronic fluids: Effect of dephasing on cuprate superconductivity

By using the gauge-invariant kinetic equation approach [Yang and Wu, Phys. Rev. B {\bf 98}, 094507 (2018); {\bf 100}, 104513 (2019)], we construct the coupled dual dynamics of macroscopic phase coherence and microscopic electronic fluids in cuprate superconductors. We prove that the developed dual dynamics provides an efficient and simplified approach to formulate the dephasing process of macroscopic superconducting phase coherence, as well as its influence on microscopic electronic fluids (including gap, densities of superfluid and normal fluid, and in particular, the transport property to determine superconducting transition temperature $T_c$). We then present theoretical description of the preformed Cooper pairs in pseudogap state. The key origin of pseudogap state comes from the quantum effect of disorder, which excites the macroscopic inhomogeneous phase fluctuation through Josephson effect. Influenced by this phase fluctuation, there exist normal fluid and viscous superfluid below $T_c$ in cuprate superconductors, in addition to conventional non-viscous superfluid. The normal fluid always emerges around nodal points even at zero temperature, whereas the viscous superfluid emerges due to the friction between superfluid and normal fluid. Particularly, the non-viscous superfluid gets suppressed when the phase fluctuation is enhanced by increasing temperature, until vanishes at $T_c$. Then, the system enters the pseudogap state, showing the nonzero resistivity as well as the finite gap from the viscous superfluid. By further increasing temperature to $T^{\rm os}$, the viscous superfluid and hence gap vanish. An experimental scheme to distinguish the densities of normal fluid as well as viscous and non-viscous superfluids is proposed. Finally, this theory is also applied to low-dimensional disordered $s$-wave superconductors.

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized pre-formed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number $Z\gg1$ of similar neighboring pairs. We derived integral equations for the probability distribution $P\left(\Delta\right)$ of local superconducting order parameter $\Delta\left(\boldsymbol{r}\right)$ and analyzed their solutions in the limit of small dimensionless Cooper coupling constant $\lambda\ll1$. The shape of the order-parameter distribution is found to depend crucially upon the effective number of nearest neighbors $Z_{\text{eff}}=2\nu_{0}\Delta_{0}Z$. The solution we provide is valid both at large and small $Z_{\text{eff}}$; the latter case is nontrivial as the function $P\left(\Delta\right)$ is heavily non-Gaussian. The discovery of a broad parameter range where the distribution function $P\left(\Delta\right)$ is non-Gaussian but also non-critical (in the sense of SIT criticality) is one of our key findings. The analytic results are supplemented by numerical data, and good agreement between them is observed.

Mechanisms of screening or enhancing the pseudogap throughout the two-band Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover

We demonstrate the rise-and-fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multi-band configuration suppresses pairing fluctuations and the pseudogap opening in the strongly-interacting shallow band at small pair-exchange couplings by screening effects, with possible connection to the pseudogap phenomenology in iron based superconductors. On the other hand, the multiple pseudogap mechanism accompanies with the emergence of binary preformed Cooper pairs originating from interplay between intra-band and pair-exchange couplings.

Preformed Cooper Pairs in Layered FeSe-Based Superconductors.

Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- T_{c} cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO_{3} substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below T_{p}∼60 K in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high-T_{c} cuprate superconductors.

Superconducting fluctuations probed by the Higgs mode in Bi2Sr2CaCu2O8+x thin films

Superconducting (SC) fluctuations in cuprate superconductors have been extensively studied to gain a deep insight into preformed Cooper pairs above the SC transition temperature $T_{\text{c}}$. While the various measurements, such as the terahertz (THz) optical conductivity, Nernst effect, angle-resolved photoemission spectroscopy (ARPES), and scanning tunneling microscopy (STM) measurements have provided the signature of the SC fluctuations, the onset temperature of the SC fluctuations depends on the measurement scheme. Here, we shed light on the Higgs mode to investigate the SC fluctuations, as it is the direct fingerprint of SC order parameter and can help elucidate the development of SC phase coherence. We perform THz pump-optical probe spectroscopy for underdoped and overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212) thin films. The oscillatory behavior in the pump-probe signal (THz Kerr signal) observed in the SC phase has been identified as the Higgs mode in single crystals in our previous work [K. Katsumi et al., Phys. Rev. Lett. 120, 117001 (2018)], but two onset temperatures are identified above $T_{\text{c}}$. Combined with the results of the single crystals in a wide range of doping, we find that the first onset $T_1^{\text{ons}}$ is 10-30 K above $T_{\text{c}}$. $T_1^{\text{ons}}$ coincides with that of the superfluid density $N_s$ extracted from the THz optical conductivity. Hence, $T_1^{\text{ons}}$ is interpreted as the onset of macroscopic SC phase stiffness. On the other hand, the second onset $T_2^{\text{ons}}$ is identified at substantially higher than $T_{\text{c}}$, whose origin is discussed in terms of preformed Cooper pairs.

Enhancement of the thermal-transport figure of merit and breakdown of the Wiedemann-Franz law in unitary Fermi gases

We theoretically investigate the thermo-particle transport properties of an unitary Fermi gas be- tween two reservoirs connected by a quantum point contact. We find several distinguished properties that are qualitatively different from those of weak or non-interacting gas systems. The particle trans- port figure of merit is drastically enhanced in the unitary regime and it increases as the transmission coefficient increases, exactly opposite to the behavior in the weak or non-interacting gas systems. The Lorentz number violates the Wiedemann-Franz law, demonstrating the breakdown of Fermi liquid. These transport properties are the hallmarks of the unitary Fermi gas and are attributed to the existence of preformed Cooper pairs.

Anomalous mesoscopic kinetics in disordered superconductors

We study anomalous mesoscopic transport effects at the onset of the superconducting transition focusing on the observed large Nernst-Ettinghausen signal in disordered thin films. In the vicinity of the transition, as the Ginzburg-Landau coherence length of preformed Cooper pairs diverges, short-range mesoscopic fluctuations are equivalent to local fluctuations of the critical temperature. As a result, the dynamical susceptibility function of pair propagation acquires a singular mesoscopic component, and consequently, superconducting correlations give rise to enhanced mesoscopic fluctuations of thermodynamic and transport characteristics. In contrast to disordered normal metals, the root-mean-square value of mesoscopic conductivity fluctuations ceases to be universal and displays strong dependence on dimensionality, temperature, and under certain conditions can exceed its quantum normal state value by a large factor. Interestingly, we find different universality as magnetic susceptibility, conductivity, and transverse magnetic thermopower coefficients all display the same temperature dependence. Finally, we discuss an enhancement of mesoscopic effects in the Seebeck thermoelectricity and Hall conductivity fluctuations as mediated by emergent superconductivity.

Collective energy gap of preformed Cooper pairs in disordered superconductors

In most superconductors the transition to the superconducting state is driven by the binding of electrons into Cooper-pairs. The condensation of these pairs into a single, phase coherent, quantum state takes place concomitantly with their formation at the transition temperature, $T_c$. A different scenario occurs in some disordered, amorphous, superconductors: Instead of a pairing-driven transition, incoherent Cooper pairs first pre-form above $T_c$, causing the opening of a pseudogap, and then, at $T_c$, condense into the phase coherent superconducting state. Such a two-step scenario implies the existence of a new energy scale, $\Delta_{c}$, driving the collective superconducting transition of the preformed pairs. Here we unveil this energy scale by means of Andreev spectroscopy in superconducting thin films of amorphous indium oxide. We observe two Andreev conductance peaks at $\pm \Delta_{c}$ that develop only below $T_c$ and for highly disordered films on the verge of the transition to insulator. Our findings demonstrate that amorphous superconducting films provide prototypical disordered quantum systems to explore the collective superfluid transition of preformed Cooper-pairs pairs.

Isothermal Compressibility of an Ultracold Fermi Gas in the BCS–BEC Crossover

We theoretically investigate the isothermal compressibility $$\kappa _{\mathrm{T}}$$ in the normal state of an ultracold Fermi gas with a tunable attractive interaction. We calculate this thermodynamic quantity by considering fluctuations in the Cooper channel, within the framework of the self-consistent T-matrix approximation (SCTMA). For comparison, we also evaluate this quantity in a “non”-self-consistent T-matrix approximation (TMA). We show that the calculated $$\kappa _{\mathrm{T}}$$ diverges at $$T_{\mathrm{c}}$$ in the BCS–BEC crossover region. On the other hand, such a singular behavior is absent when we deal with this quantity in SCTMA. We point out that the origin of this difference is the neglect of an effective inter-pair interaction in the former approximation. We also explicitly show how such an interaction is involved in the theory when one deals with pairing fluctuations in SCTMA. Our results indicate that the isothermal compressibility is a useful quantity in considering how preformed Cooper pairs interact with one another in the BCS–BEC crossover regime of an ultracold Fermi gas.

Molecular Beam Epitaxy Growth of Tetragonal FeS Films on SrTiO3 (001) Substrates**Supported by the National Natural Science Foundation of China, the Ministry of Science and Technology of China, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No 20130002120033.

We report the successful growth of the tetragonal FeS film with one or two unit-cell (UC) thickness on SrTiO3(001) substrates by molecular beam epitaxy. Large lattice constant mismatch with the substrate leads to high density of defects in single-UC FeS, while it has been significantly reduced in the double-UC thick film due to the lattice relaxation. The scanning tunneling spectra on the surface of the FeS thin film reveal the electronic doping effect of single-UC FeS from the substrate. In addition, at the Fermi level, the energy gaps of approximately 1.5 meV are observed in the films of both thicknesses at 4.6 K and below. The absence of coherence peaks of gap spectra may be related to the preformed Cooper-pairs without phase coherence.

Kink Structure in Nodal Quasiparticle Dispersion in a Boson-Fermion Model of Superconductivity

At temperatures below a certain T ∗, single unbound electrons in high- T c cuprates are assumed to coexist with bosonic Cooper pairs (CPs) of electrons emerging incoherently from an attractively interacting system of fermions. Due to both simultaneous interfermion attractions (as in BCS theory) and depairings, the conductive electrons at temperatures higher than the T c of a Bose-Einstein condensation of preformed CPs fluctuate unceasingly between single-fermionic states and states of two bound electrons considered actual bosonic objects. We explore how these interactions in a background of such “frustrated electrons,” i.e., those electrons appearing both as unbound (free) electrons and as constituents of the bosonic CPs, affect the dispersion of a fermion moving in the assembly of other electrons and, in particular, how the recently observed “kinks” in the dispersion curves emerge.

Attractive Hubbard model: Homogeneous Ginzburg–Landau expansion and disorder

We derive Ginzburg - Landau (GL) expansion in disordered attractive Hubbard model within the combined Nozieres - Schmitt-Rink and DMFT+Sigma approximation. Restricting ourselves to the case of homogeneous expansion, we analyze disorder dependence of GL expansion coefficients on disorder for the wide range of attractive potentials U, from weak BCS coupling region to the strong coupling limit, where superconductivity is described by Bose - Einstein condensation (BEC) of preformed Cooper pairs. We show, that for the case of semi - elliptic "bare" density of states of conduction band, disorder influence on GL coefficients A and B before quadratic and fourth -- order terms of the order parameter, as well as on the specific heat discontinuity at superconducting transition, is of universal nature at any strength of attractive interaction and is related only to the general widening of the conduction band by disorder. In general, disorder growth increases the values of coefficients A and B, leading either to the suppression of specific heat discontinuity (in the weak coupling limit), or to its significant growth (in the strong coupling region). However, this behavior actually confirms the validity of the generalized Anderson theorem, as disorder dependence of superconducting critical temperature T_c, is also controlled only by disorder widening of conduction band (density of states).

Attractive Hubbard Within the Generalized DMFT: Normal State Properties, Disorder Effects and Superconductivity

Using the generalized DMFT+ Σ approach, we have studied disorder influence on the density of states, optical conductivity of the normal phase, superconducting transition temperature, and Ginzburg–Landau coefficients in the attractive Hubbard model. The wide range of attractive potentials U was studied—from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong coupling region, where superconducting transition is due to the Bose–Einstein condensation (BEC) of preformed Cooper pairs. For semi-elliptic “bare” density of states of conduction band, the disorder influence on all single-particle properties (e.g., density of states) is universal for arbitrary strength of electronic correlations and is due only to the general disorder widening of conduction band. Using the combination of DMFT +Σ and Nozieres–Schmitt-Rink approximations, we have studied the disorder influence upon superconducting transition temperature Tc for the range of characteristic values of U and disorder including the BCS-BEC crossover region. Disorder can either suppress Tc (in the weak coupling region) or significantly increase Tc (in strong coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of superconducting critical temperature are essentially due only to the general disorder widening of the conduction band.

Specific heat and effects of pairing fluctuations in the BCS-BEC-crossover regime of an ultracold Fermi gas

We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived {\it stable} molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a $^6$Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas, to eventually become stable, as one passes through the BCS-BEC crossover region.