The tremendous efforts to unveil high temperature superconductivity (HTSC) have been devoted to the search of the mechanism underlying Cooper pairs which, however, remains a mysterious subject of vigorous debate, let alone many other mysteries like the pseudogap state, the peculiar Homes law, the unnegligible electron-phonon interaction, the stripe, the universal nodal Fermi velocity, etc. Most of subsequent works either bring in more controversies or swell the list of mysteries. Here I tentatively propose a whole new perspective on the basis of low-dimensional Bose-Einstein Condensation (LDBEC), which possibly makes lots of those mysteries correlated and understood in single picture.
We report a microscopic model wherein the unconventional superconductivity emerges from an incoherent `Cooper-pair glass' state. Driven by the pair-pair interaction, a new type of quasi-Bose phase transition is at work. The interaction leads to the unconventional coupling of the quasiparticles to excited pair states, or `super-quasiparticles', with a non-retarded energy-dependent gap. The model describes quantitatively the quasiparticle excitation spectra of both cuprates and pnictides, including the universal `peak-dip-hump' signatures, and for the pseudogap phase above $T_c$. The results sho…
Shortly after the Gor'kov microscopic derivation of the Ginzburg-Landau (GL) model via a small order parameter expansion in Bardeen-Cooper-Schrieffer theory of superconductivity, the derivation was carried to next-to-leading order in that parameter and its spatial derivatives. The aim was to obtain a generalized GL free energy that approximates the microscopic model better. Since 1960s, multiple works have claimed or implicitly assumed that this extended GL model corresponds to the free energy and has solutions in the form of local minima describing superconductivity, such as vortex solutions.…
A phenomenological description of the high-Tc superconductors based on the Cooperon propagator is presented. This model allows one to study the effects of local pairing correlations and long-range phase fluctuations on the same footing, both above and below Tc. Based on numerical calculations, it is shown that the two types of correlations contribute to the gap/pseudogap in the single-particle excitation spectra. The concourse of these two effects can induce low energy states, which should be observable in underdoped materials at very low temperature.
The electronic states and superconductivity in iron pnictides are studied on the basis of the 16 band $d$-$p$ model which includes both the onsite Coulomb interaction between Fe $d$ electrons and the intersite one between Fe $d$ and pnictogen $p$ electrons. The model well accounts for experimentally observed two fluctuations: the $d$-$d$ interaction-enhanced antiferromagnetic (AFM) fluctuation and the $d$-$p$ interaction-enhanced ferro-orbital (FO) fluctuation responsible for the $C_{66}$ elastic softening. The AFM fluctuation induces the repulsive pairing interaction for $\bm{q}\sim \bm{Q}_{\…
As an extension of our previous work on the holon pairing instability in the t-J Hamiltonian [Phys. Rev. B {\bf 66}, 054427 (2002)], we examine the orbital symmetries of holon pairing order parameters in high $T_c$ superconductivity by examining the energy poles of t-matrix. We find that both $s$- and d-wave symmetries in holon pair order parameter occur at low lying energy states corresponding to the higher energy poles of t-matrix while only the s-wave symmetry appears at the lowest energy pole and that this results in the d-wave symmetry in the Cooper pair order which is a composite of the …
The successful application of the electron-phonon interaction (EPI) mechanism in formulating the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity is among the most outstanding intellectual achievements in theoretical physics because of the successful application of the theory to the conventional superconducting materials. Therefore, its unsuccessful application to the nonconventional superconducting materials has led to the search for new theories which generalized it, include an interplay with other mechanisms or are formulated from non - EPI mechanisms. We observe in this current …
The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-$T_c$ cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-$T_c$ cuprates and other pseudogap mat…
We use first-principles calculations to study pressure effects on the vibrational and superconducting properties of H$_3$S in the cubic $Im\bar{3}m$ phase for the pressure range where the superconducting critical temperature (T$_c$) was measured (155-225 GPa). The pressure effects were incorporated using the Functional Derivative Method (FDM). In this paper, we present for the first time, the Cooper-Pairs Distribution Functions D$_{cp}$($ω,T_c$) for H$_3$S, which will allow to identify the spectral regions where Cooper-Pairs formation at temperature T$_c$ is more favorable. We analyzed in deta…
We study the two-dimensional spin-charge separated Ginzburg-Landau theory containing U(1) gauge interactions as a semi-phenomenological model describing fluctuating condensates in high temperature superconductivity. Transforming the original GL action, we abstract the effective action of Cooper pair. Especially, we clarify how Cooper pair correlation evolves in the normal state from the point of view of spin-charge separation. Furthermore, we point out how Cooper pair couples to gauge field in a gauge-invariant way, stressing the insensitivity of Cooper pair to infrared gauge field fluctuation…
A resonating valence bond RVB approach is taken to demonstrate formation of real-space Cooper pairs and High-TC superconductivity HTS. Non-adiabatic coupling between holes aggregates (super-atoms) and undoped anti-ferromagnet cause virtual excitations in either system due to inter-system coupling. HTS is said to reflect cooperative co-existence of two Bose-Einstein condensates in terms of one real-space Cooper pair condensate, and a second magnon condensate, which form at the same critical temperature. TC is formulated in terms of the super-exchange interaction. Connection is made to an equiva…
The usual formulation of the BCS ansatz for superconductivity in the grand canonical ensemble makes the handling of the Pauli exclusion principle between paired electrons straightforward. It however tends to mask that many-body effects between Cooper pairs interacting through the reduced BCS potential are entirely controlled by this exclusion. To show it up, one has to work in the canonical ensemble. Pauli blocking between a fixed number of composite bosons is however known to be difficult to handle. To do it, we here develop a commutator formalism for Cooper pairs, along the line we used for …
In this letter, we address the impact of the electric field on superconductors which are insulators in the normal state, superconducting semiconductors at low carrier concentration and ultracold gas of fermions in the strongly interacting regime. The electric field penetrates these systems and affects on the Cooper pairs. We show that if there are Cooper pairs above the superconductor critical temperature the electric field forces the Cooper pairs to Bose condensate and the onset of the superconductivity, thereby increasing the critical temperature. To study this phenomenon we numerically solv…
Evidence against superconductivity in flux trapping experiments on hydrides under high pressure & On magnetic field screening and expulsion in hydride superconductors
Transport measurements are presented on thin-film superconducting spin-valve systems, where the controlled non-collinear arrangement of two ferromagnetic Co layers can be used to influence the superconducting state of Nb. We observe a very clear oscillation of the superconducting transition temperature with the relative orientation of the two ferromagnetic layers. Our measurements allow us to distinguish between the competing influences of domain averaging, stray dipolar fields and the formation of superconducting spin triplets. Domain averaging is shown to lead to a weak enhancement of transi…
Symmetry of the crystal lattice can be a determining factor for the structure of Cooper pairs in unconventional superconductors. In this study we extend the discussion of superconductivity in non-centrosymmetric materials to the case when inversion symmetry is missing locally, but is present on a global level. Concretely, we investigate the staggered non-centrosymmetricity within a regular sublattice structure, in some analogy to the discussion of superconductivity in antiferromagnetic systems. Three crystal structures are analyzed in detail as illustrative examples for the extended classifica…
Josephson junctions with a ferromagnetic metal weak link reveal a very strong decrease of the critical current compared to a normal metal weak link. We demonstrate that in the ballistic regime the presence of a small region with a non-collinear magnetization near the center of a ferromagnetic weak link restores the critical current inherent to the normal metal. The above effect can be stimulated by additional electrical bias of the magnetic gate which induces a local electron depletion of ferromagnetic barrier. The underlying physics of the effect is the interference phenomena due to the magne…
Electrons in a multielectron bubble in helium form a spherical, two-dimensional system coupled to the ripplons at the bubble surface. The electron-ripplon coupling, known to lead to polaronic effects, is shown to give rise also to Cooper pairing. A Bardeen-Cooper-Schrieffer (BCS) Hamiltonian arises from the analysis of the electron-ripplon interaction in the bubble, and values of the coupling strength are obtained for different bubble configurations. The BCS Hamiltonian on the sphere is analysed using the Richardson method. We find that although the typical ripplon energies are smaller than th…
To identify the microscopic mechanism of heavy-fermion Cooper pairing is an unresolved challenge in quantum matter studies; it may also relate closely to finding the pairing mechanism of high temperature superconductivity. Magnetically mediated Cooper pairing has long been the conjectured basis of heavy-fermion superconductivity but no direct verification of this hypothesis was achievable. Here, we use a novel approach based on precision measurements of the heavy-fermion band structure using quasiparticle interference (QPI) imaging, to reveal quantitatively the momentum-space (k-space) structu…
A new theory for Cooper pair formation and superconductivity is derived from quantum statistical mechanics. It is shown that zero momentum Cooper pairs have non-local permutations and behave as effective bosons with an internal weight close to unity when bound by a primary minimum in the potential of mean force. For a short-ranged, shallow, and highly curved minimum there is no thermodynamic barrier to condensation. The size of the condensing Cooper pairs found here is orders of magnitude smaller than those found in BCS theory. The new statistical theory is applicable to high temperature super…
Bulk superconductivity (SC) has recently been observed in the Al-Zn-Mg quasicrystal (QC). To settle several fundamental issues of the SC on the QC, we use an attractive Hubbard model to perform a systematic study on the Penrose lattice. The first issue is the Cooper instability of the QC, i.e., no Fermi surface under an infinitesimal attractive interaction. Starting from the two-electron problem outside the filled Fermi-sea, we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of state is nonzero at the Fermi level, which prov…
Superfluidity and superconductivity are genuine many-body manifestations of quantum coherence. For finite-size systems the associated pairing gap fluctuates as a function of size or shape. We provide a parameter free theoretical description of pairing fluctuations in mesoscopic systems characterized by order/chaos dynamics. The theory accurately describes experimental observations of nuclear superfluidity (regular system), predicts universal fluctuations of superconductivity in small chaotic metallic grains, and provides a global analysis in ultracold Fermi gases.
A consistent microscopic theory of pseudogap phenomena and novel Bose-liquid superconductivity (superfluidity) is presented, based on the fact that in high-$T_c$ cuprates and related systems the energy $\varepsilon_A$ of the effective attraction between fermions is comparable with their Fermi energy $\varepsilon_F$ and the bosonic Cooper pairs are formed above $T_c$ and then a part of such Cooper pairs condense into a Bose superfluid at $T_c$. High-$T_c$ cuprates and other systems with low Fermi energies ($\varepsilon_F\sim\varepsilon_A$) are bosonic superconductors/superfluids and exhibit pse…
We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter $r_s \leq 2$. We confirm that superconductivity naturally emerges from purely repulsive interactions described by the Kukkonen-Overhauser vertex function. By employing the implicit renormalization approach we reveal that even in the small-$r_s$ limit, the dominant mechanism behind Cooper instability is based on dynamic screening of the Coulomb interaction--accurately captured by the random phase approximation, whereas the Kohn-Luttinger contribution is negligibly s…
Scanning tunneling spectroscopies in the subKelvin temperature range were performed on superconducting Silicon epilayers doped with Boron in the atomic percent range. The resulting local differential conductance behaved as expected for a homogeneous superconductor, with an energy gap dispersion below +/- 10%. The spectral shape, the amplitude and temperature dependence of the superconductivity gap follow the BCS model, bringing further support to the hypothesis of a hole pairing mechanism mediated by phonons in the weak coupling limit.
Superconductivity forms out of the condensation of Cooper pairs of electrons. The mechanism by which Cooper pairs are created in non-conventional superconductors is often elusive because experimental signatures that connect a specific pairing mechanism to the properties of superconducting state are rare. The recently discovered superconducting oxide-insulator/KTaO$_3$ interface may offer clues about its origins. Here we observe distinct dependences of the superconducting transition temperature Tc on carrier density n$_{2D}$ for electron gases formed at KTaO$_3$ (111), (001) and (110) interface…
Vortex phase in a singlet superconductor in the absence of impurities is shown to be absolutely unstable with respect to the appearance of a triplet component which breaks both inversion and time-reversal symmetries of Cooper pairs. Symmetry breaking paramagnetic effects are demonstrated to be of the order of unity if the orbital upper critical field, Hc2(0), is of the order of Clogston paramagnetic limiting field, Hp. We suggest a generic phase diagram of such type-IV superconductor, which is singlet one at H=0 and characterized by mixed singlet-triplet order parameter with broken time-revers…
Recent experiments on Nb-doped SrTiO$_3$ have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen-Cooper-Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and related studies, we show that the Cooper pairing mediated by a single soft transverse-optical phonon is the most natural mechanism for such a superconducting dome given experimental constraints, and present the microscopic theory for this pairing mechanism. Furthermore, we show that this mechanism is consistent with the $T^2$ resistivity in the normal state. Las…
We use radio-frequency reflectometry to measure quasiparticle tunneling rates in the single-Cooper-pair-transistor. Devices with and without quasiparticle traps in proximity to the island are studied. A $10^2$ to $10^3$-fold reduction in the quasiparticle tunneling rate onto the island is observed in the case of quasiparticle traps. In the quasiparticle trap samples we also measure a commensurate decrease in quasiparticle tunneling rate off the island.
We establish universal behavior in temperature dependencies of some observables in $(s+id)$-wave BCS superconductivity in the presence of a weak $s$ wave. There also could appear a second second-order phase transition. As temperature is lowered past the usual critical temperature $T_c$, a less ordered superconducting phase is created in $d$ wave, which changes to a more ordered phase in $(s+id)$ wave at $T_{c1}$ ($< T_c$). The presence of two phase transitions manifest in two jumps in specific heat at $T_c$ and $T_{c1}$. The temperature dependencies of susceptibility, penetration depth, and th…
We have found the mechanism of the electron Cooper pair formation via the electron interaction by means of the spin-electron acoustic waves. This mechanism takes place in metals with rather high spin polarization, like ferromagnetic, ferrimagnetic and antiferromagnetic materials. The spin-electron acoustic wave mechanism leads to transition temperatures 100 times higher than the transition temperature allowed by the electron-phonon interaction. Therefore, spin-electron acoustic waves give the explanation for the high-temperature superconductivity. We find that the transition temperature has st…
We study a possible superconductivity in quasiperiodic systems, by portraying the issue within the attractive Hubbard model on a Penrose lattice. Applying a real-space dynamical mean-field theory to the model consisting of 4181 sites, we find a superconducting phase at low temperatures. Reflecting the nonperiodicity of the Penrose lattice, the superconducting state exhibits an inhomogeneity. According to the type of the inhomogeneity, the superconducting phase is categorized into three different regions which cross over each other. Among them, the weak-coupling region exhibits spatially extend…
In monolayer transition metal dichalcogenides (TMDs), electrons in opposite $K$ valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originated from in-plane mirror symmetry breaking pins the electron spins in out-of-plane directions, and results in the newly discovered Ising superconducting states with strongly enhanced upper critical fields. In this work, we show that the Ising SOC generates equal-spin triplet Cooper pairs with spin polarization in the in-plane directions. Importantly, the spin-triplet Cooper…
Time-reversal symmetry breaking (TRSB) with a Bardeen-Cooper-Schrieffer (BCS) -like superconductivity occurs in a small, but growing number of noncentrosymmetric (NCS) materials, although the mechanism is poorly understood. We present heat capacity, magnetization, resistivity, and muon spin resonance/relaxation ($μ$SR) measurements on polycrystalline samples of NCS La$_{7}$Pd$_{3}$. Transverse-field $μ$SR and heat capacity data show La$_{7}$Pd$_{3}$ is a type-II superconductor with a BCS-like gap structure, while zero-field $μ$SR results provide evidence of TRSB. We discuss the implications of…
Ni-substitution effects on the superconductivity and Cu-spin correlation have been investigated in La2-xSrxCu1-yNiyO4 from the electrical resistivity and muon spin relaxation measurements, taking into account the hole trapping by Ni recently suggested. It has been found that the Ni-substitution suppresses the superconductivity, induces the localization of holes and develops the Cu-spin correlation to the same degree as the Zn substitution. These suggest that Ni with a trapped hole tends to give rise to potential scattering of holes in the CuO2 plane to the same degree as Zn, being discussed in…
In conventional superconductors, phonons glue two electrons with opposite spins to form Cooper pairs and condensation of these pairs leads to the superconductivity. Identifying the underlying mechanism of the high temperature superconductivity in cuprates is among the most important problems in physics. Even quarter of a century after the first report of high temperature superconductor by Bednorz and Muller in 1986, there is still no general consensus on the pairing mechanism of superconductivity in these materials. So far, many theories have been developed to explain the exotic properties of …
If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps Δ_i(k) should appear on the different electronic bands i. Here we introduce intra-band Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of Δ_i(k) in such materials, focusing on LiFeAs. We identify the three hole-like bands assigned previously as γ, α_2 and α_1, and we determine the anisotropy, magnitude and relative orientations of their Δ_i(k). These measurements …
The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above $T_c$, pre-existing but fluctuating Cooper pairs give rise to the unconventional {\it pseudogap} (PG) state, well-characterized by experiment. At the critical temperature, the pair-pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below $T_c$, both the condensation energy and the pair-pair interaction $β$ are proportional to the condensate density $N_{oc}(T)$, whereas the usual Fermi-level spectral gap $Δ_p$ is independe…
Recent discoveries of superconductivity in hydrogen-rich compounds stabilized by high pressures have shown that a critical temperature of superconductivity Tc can reach near room temperature values. The current studies focus on the search for new superconductors with higher Tcs to understand the ultimate limit of conventional superconductivity, and high-Tc superconductors at lower pressures. However, high pressure conditions put serious limitations on experimental studies. Electrical transport measurements have long been the primary experimental technique for reliable detection of superconduct…
We develop a concise self-consistent perturbation expansion for superconductivity where all the pair processes are naturally incorporated without drawing "anomalous" Feynman diagrams. This simplification results from introducing an interaction vertex that is symmetric in the particle-hole indices besides the ordinary space-spin coordinates. The formalism automatically satisfies conservation laws, includes the Luttinger-Ward theory as the normal-state limit, and reproduces the Bardeen-Cooper-Schrieffer theory as the lowest-order approximation. It enables us to study the thermodynamic, single-pa…
Topological superconductor is a very interesting and frontier topic in condensed matter physics1. Despite the tremendous efforts in exploring the topological superconductivity, its presence is however still under heavy debates. The Dirac electrons are supposed to exist in a thin layer of the surface of a topological insulator. Due to the finite spin-orbital coupling, these electrons will have a spin-momentum locking effect. In this case, the superfluid with the spin singlet Cooper pairing is not completely comforted by the Dirac electrons. It thus remains unclear whether and how the Dirac elec…
Many-body transport has emerged as an efficient tool for understanding interaction effects in quantum materials with a multi-band electronic structure. This paper proposes a formula for the two-particle transmission coefficient for Cooper-pair transport between multi-band normal and superconducting materials. The approach employs a tight-binding nonequilibrium Green's function technique, allowing a direct calculation of the two-particle current, without invoking the paradigm of Andreev reflection. As an application of the theory, we demonstrate a low-field linear magnetoresistance effect for s…
High temperature superconducting materials have been known since the pioneering work of Bednorz and Mueller in 1986. While the microscopic mechanism responsible for high Tc superconductivity is still debated, most materials showing high Tc contain highly electronic polarizable ions, suggesting that the mechanism driving high Tc superconductivity can be related to the ion electronic polarizability in high Tc materials. Here we show that a free charge carrier polarizes the ions surrounding it and the total electrical potential generated by the charge carrier itself and the polarized ions becomes…
Chiral skyrmionic superconductivity from doping a Chern Ferromagnet
Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论物理中心）；Department of Physics and National High Magnetic Field Laboratory, Florida State University（佛罗里达州立大学物理系及国家高磁场实验室）；Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部T-4和CNLS）；Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室集成纳米技术中心）
Dipole interaction in the triplet superconductivity is studied. If the Cooper pairs are formed by the electrons at $\mib{r}$ and $\mib{r}+(\pm\frac{a}{2},\pm\frac{a}{2},\pm\frac{c}{2})$ in the body centered tetragonal lattice, (in this case the line nodes run horizontally on the cylindrical Fermi surface), the dipole energy is low when the ${\mib{d}}$-vector is perpendicular to the direction of the angular momentum of the Cooper pairs ($\mib{l}$-vector). This result is in contrast with the dipole energies in the ABM state of superfluid $^3$He, where $\mib{d}$-vector is forced to be parallel or…
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Conventional Cooper pairing arises from attractive interaction of electrons in the metallic bands. Recent experiment on Co-doped LiFeAs shows superconductivity in the insulating valence band, which is evolved from a metallic hole band upon doping. Here we examine this phenomenon by studying superconductivity in a three-orbital Hamiltonian relevant to the doped LiFeAs. We show explicitly that Cooper pairing of the insulating hole band requires a finite pairing interaction strength. For strong coupling, the superconductivity in the hole band is robust against the sink of the hole band below the …
