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Occupation probabilities as variables in electronic structure theory: cooper pairing, OP-NSOFT-Cs,t, and the homogeneous electron liquid
The energy functional of a novel electronic structure theory, OP-NSOFT, has as variables the natural spin orbitals (NSO) of the trial function and their joint occupation probabilities in the search for the ground state energy. When occupancy is restricted to the spin-paired NSOs of DOCI, the resulting theory, OP-NSOFT-0, scales as M 3 , with M the size of the one-electron basis set. Accurate results were obtained for small molecules, particularly near dissociation where single reference theories like DFT are inaccurate. The homogeneous electron liquid (HEL) could serve as a test bed of OP-NSOFT for condensed systems, but OP-NSOFT-0 reduces to the Hartree–Fock approximation for the HEL. Cooper pairing is introduced instead, both singlet pairing, OP-NOFT-Cs, and fully polarized triplet pairing, OP-NSOFT-Ct. The former yields 1/3 of the diffusion-Monte-Carlo correlation energy, the latter 1/2 to 1/3 with decreasing electron density for r s values between 1 and 10. Both yield the discontinuity in the single-particle occupation number required by the Luttinger theorem. Furthermore, two-state joint occupation probabilities illustrate the importance of electron–electron small-angle scattering in establishing electron correlation in the unpolarized HEL.
Detection of a Cooper-pair density wave in Bi 2 Sr 2 CaCu 2 O 8+x
The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold 6 Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a ‘pair density wave’ state. In this paper we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi 2 Sr 2 CaCu 2 O 8+x . We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi 2 Sr 2 CaCu 2 O 8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors Q P ≈ (0.25, 0)2π/a 0 and (0, 0.25)2π/a 0 in Bi 2 Sr 2 CaCu 2 O 8+x . The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. Finally, this phenomenology is consistent with Ginzburg–Landau theory when a charge density wave with d-symmetry form factor and wavevector Q C = Q P coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.
Time-resolved measurements of Cooper-pair radiative recombination in InAs quantum dots
We studied InAs quantum dots (QDs) where electron Cooper pairs penetrate from an adjacent niobium (Nb) superconductor with the proximity effect. With time-resolved luminescence measurements at the wavelength around 1550 nm, we observed luminescence enhancement and reduction of luminescence decay time constants at temperature below the superconducting critical temperature (T{sub C}) of Nb. On the basis of these measurements, we propose a method to determine the contribution of Cooper-pair recombination in InAs QDs. We show that the luminescence enhancement measured below T{sub C} is well explained with our theory including Cooper-pair recombination.
Thermoelectric-induced unitary Cooper pair splitting efficiency
Thermoelectric effect is exploited to optimize the Cooper pair splitting efficiency in a Y-shaped junction, which consists of two normal leads coupled to an s-wave superconductor via double noninteracting quantum dots. Here, utilizing temperature difference rather than bias voltage between the two normal leads, and tuning the two dot levels such that the transmittance of elastic cotunneling process is particle-hole symmetric, we find current flowing through the normal leads are totally contributed from the splitting of Cooper pairs emitted from the superconductor. Such a unitary splitting efficiency is significantly better than the efficiencies obtained in experiments so far.
Out-of-phase Andreev transports in a double-quantum-dot Cooper-pair splitter
We investigate the Andreev transports through a double-quantum-dot Cooper-pair splitter with an additional direct coupling between the dots. It is found that when finite magnetic flux is applied through this structure, its induced phase adjusts the local and crossed Andreev reflections in different manners. Moreover, in the presence of appropriate magnetic flux, the crossed Andreev reflection can be efficiently enhanced, accompanied by the suppression of the local Andreev reflection. Such a result exists in both the linear and nonlinear transport regions, even in the case of strong intradot Coulomb interaction. Therefore, such a work provides a promising scheme to enhance the splitting of the Cooper pair.
Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands
Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at “ghost crossings” of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron–electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.
Hyperbolic Cooper-Pair Polaritons in Planar Graphene/Cuprate Plasmonic Cavities
Hyperbolic Cooper-pair polaritons (HCP) in cuprate superconductors are of fundamental interest due to their potential for providing insights into the nature of unconventional superconductivity. In this study, we critically assess an experimental approach using near-field imaging to probe HCP in Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212) in the presence of graphene surface plasmon polaritons (SPP). Our simulations show that inherently weak HCP features in the near-field can be strongly enhanced when coupled to graphene SPP in layered graphene/hexagonal boron nitride (hBN)/Bi-2212 heterostructures. This enhancement arises from our multilayered structures effectively acting as plasmonic cavities capable of altering collective modes of a layered superconductor by modifying its electromagnetic environment. The degree of enhancement can be selectively controlled by tuning the insulating spacer thickness with atomic precision. Finally, we verify the expected renormalization of room-temperature graphene SPP using near-field infrared imaging. Our modeling, augmented with data, attests to the validity of our approach for probing HCP modes in cuprate superconductors.
A Study on the Wiedemann-Franz Law in a Granular s-Wave Superconductor, Given the Tunneling Between the Grains in Cooper Pair Fluctuation Propagator and Impurity Vertex
The present study tries to investigate Wiedemann-Franz law near and far from the critical temperatures, given the tunneling between the grains in Cooper pair fluctuation propagator and impurity vertex. By means of Dyson’s equation, the Cooper pair fluctuation propagator, L(qkΩ{sub μ}) and the Cooperon (impurity vertex), λ(q, k, ε{sub 1}, ε{sub 2}), are initially calculated in the presence of tunneling between the grains. Then, the three distinct contributions of density of states, Maki-Thompson, and Aslamazov-Larkin, are calculated in the frameworks of the Green’s functions formalism and the Kubo formula technique. The evaluation is conducted under the limited tunneling conductance between the grains. Findings show that although the tunneling is efficient near the critical temperature, it is not effective when it is far from the critical temperature Compared to that in high temperatures, moreover, the deviation from the Wiedemann-Franz law is much more evident in low temperatures.
Two-Electron and Two-Hole Cooper Pairs in Superconductivity
We revisit the generalized Bose-Einstein condensation (GBEC) theory which addresses a ternary boson-fermion gas including two-hole Cooper pairs (2hCPs) as an essential component in superconductivity. Here, we extend the BCS-Bose crossover theory, itself subsumed in BEC, by explicitly including 2hCPs. Shown here are phase diagrams of T{sub c}/T{sub F}, where T{sub c} is the critical temperature and T{sub F} the Fermi temperature and Δ(0)/E{sub F}vsn/n{sub f}, where Δ(0) is the energy gap at zero temperature and E{sub F} is the Fermi energy of an ideal Fermi gas, with n the total electron number density and n{sub f} is that of unbound electrons at zero temperature. These phase diagrams are obtained for two pure phases, one with two-electron Cooper pairs (2eCPs) and the other with 2hCPs, plus a mixed phase with arbitrary proportions of 2e/2hCPs. We find that the extended BCS-Bose crossover predicts T{sub c}/T{sub F} as well Δ(0)/E{sub F} values for the elemental superconductors (SCs) Al, In, Sn, Pb, Hg, and Nb which compare reasonably well with experimental data.
Stimulated emission of Cooper pairs in a high-temperature cuprate superconductor
The concept of stimulated emission of bosons has played an important role in modern science and technology, and constitutes the working principle for lasers. In a stimulated emission process, an incoming photon enhances the probability that an excited atomic state will transition to a lower energy state and generate a second photon of the same energy. It is expected, but not experimentally shown, that stimulated emission contributes significantly to the zero resistance current in a superconductor by enhancing the probability that scattered Cooper pairs will return to the macroscopically occupied condensate instead of entering any other state. Here, we use time- and angle-resolved photoemission spectroscopy to study the initial rise of the non-equilibrium quasiparticle population in a Bi 2 Sr 2 CaCu 2 O 8+δ cuprate superconductor induced by an ultrashort laser pulse. Our finding reveals significantly slower buildup of quasiparticles in the superconducting state than in the normal state. The slower buildup only occurs when the pump pulse is too weak to deplete the superconducting condensate, and for cuts inside the Fermi arc region. We propose this is a manifestation of stimulated recombination of broken Cooper pairs, and signals an important momentum space dichotomy in the formation of Cooper pairs inside and outside the Fermi arc region.
Dimension Effects in Insulating NbTiN Disordered Films and the Asymptotic Freedom of Cooper Pairs
This study investigates the evolution of the electronic transport in disordered NbTiN films at the insulating side of the superconductor-insulator transition as function of the effective system size along the current direction. We demonstrate that both, the threshold voltage characterizing low-temperature superinsulating phase, and the Berezinskii-Kosterlitz-Thouless criticality of the conductance above the superinsulator critical temperature, vanish upon increasing disorder taking the system far from the disorder-driven superconductor-insulator transition. We find that decrease in the system's effective size suppresses its insulating and superinsulating properties and that threshold voltage drops linearly with the diminishing system size. We demonstrate that this linear dependence can be used for experimental measurement of the linear tension of the electric string binding Cooper pairs and anti-Cooper pairs in a superinsulator.
Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing
We find exact analytic expressions for the energies and wave functions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of A A and A B / B A tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of the form factors of the active bands in TBG. The two-charge excitation energy and wave functions are also obtained, and a sufficient condition on the graphene eigenstates for obtaining a Cooper pair from Coulomb interactions is obtained. For the actual TBG bands at the first magic angle, we can analytically show that the Cooper pair binding energy is zero in all such projected Coulomb models, implying that either phonons and/or nonzero kinetic energy are needed for superconductivity. Since Vafek and Kang [Phys. Rev. Lett. 125, 257602 (2020)] showed that the kinetic energy bounds on the superexchange energy are less 10 -3 in Coulomb units, the phonon mechanism becomes then very likely. If nonetheless the superconductivity is due to kinetic terms which render the bands nonflat, one prediction of our theory is that the highest T c would not occur at the highest DOS.
Discovery of orbital-selective Cooper pairing in FeSe
The superconductor iron selenide (FeSe) is of intense interest owing to its unusual nonmagnetic nematic state and potential for high-temperature superconductivity. But its Cooper pairing mechanism has not been determined. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the electronic bands surrounding the Γ = (0, 0) and X = (π/ a Fe , 0) points of FeSe and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless and that they exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique, we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing that, in FeSe, is based preferentially on electrons from the d yz orbitals of the iron atoms.
Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions
Abstract Unconventional superconductivity arising from the interplay between strong spin–orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the three-dimensional topological insulator Bi 2 Se 3 . We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi 2 Se 3 and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the emergence of an anomalous Fraunhofer pattern. We describe how the anomalous Fraunhofer patterns evolve for different device parameters, and we use this to understand the microscopic origin of the oscillating order parameter. The agreement between the experimental data and simulations shows that the finite momentum pairing originates from the coexistence of the Zeeman effect and Aharonov–Bohm flux.
Simulating exotic phases of matter with bond-directed interactions with arrays of Majorana-Cooper pair boxes
It is suggested that networks of Majorana-Cooper pair boxes connected by metallic nanowirescan simulate various exotic states of matter. In this simulations Majorana-Cooper boxes play therole of effective spins S=1/2 and the metallic connections generate the Kondo screening and theRuderman-Kittel-Kasuya-Yosida (RKKY) interaction. Depending on what prevails - whether it isthe Kondo effect or the RKKY exchange, one will have either an effective spin model or a Kondolattice. The list of exotic stets includes the famous hexagonal Kitaev model, a generalization of thismodel for a Kondo lattice and various spin models with three-spin interactions. A special emphasizeis made on the discussion of the Kondo lattice scenario.
Controlling the transmitted information of a multi-photon interacting with a single-Cooper pair box
We study a model of a multi-photon interaction of a single Cooper pair box with a cavity field. The exchange of the information using this system is studied. We quantify the fidelity of the transmitted information. The effect of the system parameters (detuning parameter, field photons, state density and mean photon number) in the fidelity of the transmitted information is investigated. We found that the fidelity of the transmitted information can be controlled using the system parameters.
Confinement and asymptotic freedom with Cooper pairs
One of the most profound aspects of the standard model of particle physics, the mechanism of confinement binding quarks into hadrons, is not sufficiently understood. The only known semiclassical mechanism of confinement, mediated by chromo-electric strings in a condensate of magnetic monopoles still lacks experimental evidence. Here we show that the infinite resistance superinsulating state, which emerges on the insulating side of the superconductor insulator transition in superconducting films offers a realization of confinement that allows for a direct experimental access. We find that superinsulators realize a single-color version of quantum chromodynamics and establish the mapping of quarks onto Cooper pairs. We reveal that the mechanism of superinsulation is the linear binding of Cooper pairs into neutral “mesons” by electric strings. Here, our findings offer a powerful laboratory for exploring and testing the fundamental implications of confinement, asymptotic freedom, and related quantum chromodynamics phenomena via the desktop experiments on superconductors.