Superconducting Ground State Research Articles

Fidelity study of the superconducting phase diagram in the two-dimensional single-band Hubbard model

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the d-wave pair/spin/charge-density matrices. The calculations show a d-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion U and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping t'. We also demonstrate that negative t' plays an important role in facilitating d-wave superconductivity.

Linear magnetoresistivity in the ternaryAM2B2andA3Rh8B6phases (A=Ca, Sr;M=Rh, Ir)

We studied the magnetoresistivity of the AM2B2 and A3Rh8B6 (A = Ca, Sr; M = Rh, Ir) compounds within the ranges 1.8<=T<=300 K and 0<=H<=50 kOe. The zero-field resistivity {\rho}0(T) is metallic and follows closely the Bloch-Gr\"uneisen description. A positive, nonsaturating, and dominantly linear-in-H magnetoresistivity was observed in all samples, including the ones with a superconducting ground state. Such {\Delta}{\rho}T(H)/{\rho}T(0), reaching 1200% in favorable cases, was found to be much stronger for the AM2B2 compounds and to decrease with temperature as well as when Ca is replaced by Sr, or Rh is replaced by Ir. Finally, the general features of the observed magnetoresistivity will be discussed in terms of the Abrikosov model for the linear magnetoresistivity in inhomogeneous materials.

Strong coupling BCS superconductivity and holography

We attempt to give a holographic description of the microscopic theory of a BCS superconductor. Exploiting the analogy with chiral symmetry breaking in QCD we use the Sakai–Sugimoto model of two D8 branes in a D4 brane background with finite baryon number. In this case there is a new tachyonic instability which is plausibly the bulk analog of the Cooper pairing instability. We analyze the Yang–Mills approximation to the non-Abelian Dirac–Born–Infeld action. We give some exact solutions of the non-linear Yang–Mills equations in flat space and also give a stability analysis, showing that the instability disappears in the presence of an electric field. The holographic picture also suggests a dependence of T c on the number density which is different from the usual (weak coupling) BCS. The flat space solutions are then generalized to curved space numerically and also, in an approximate way, analytically. This configuration should then correspond to the ground state of the boundary superconducting (superfluid) ground state. We also give some preliminary results on Green functions computations in the Sakai–Sugimoto model without any chemical potential.

Exact superconducting ground states of the extended Anderson model

We obtain exact ground states of an extended periodic Anderson model (EPAM) with non-local hybridization and Coulomb repulsion between f and c electrons (Falicov–Kimball term) in one dimension. We show that for a range of parameter values these ground states exhibit composite hole pairing and superconductivity that originate from purely electronic interactions.

Phase diagram of pressure-induced superconductivity in EuFe2As2probed by high-pressure resistivity up to 3.2 GPa

We have constructed a pressure$-$temperature ($P-T$) phase diagram of $P$-induced superconductivity in EuFe$_2$As$_2$ single crystals, via resistivity ($\rho$) measurements up to 3.2 GPa. As hydrostatic pressure is applied, an antiferromagnetic (AF) transition attributed to the FeAs layers at $T_\mathrm{0}$ shifts to lower temperatures, and the corresponding resistive anomaly becomes undetectable for $P$ $\ge$ 2.5 GPa. This suggests that the critical pressure $P_\mathrm{c}$ where $T_\mathrm{0}$ becomes zero is about 2.5 GPa. We have found that the AF order of the Eu$^{2+}$ moments survives up to 3.2 GPa without significant changes in the AF ordering temperature $T_\mathrm{N}$. The superconducting (SC) ground state with a sharp transition to zero resistivity at $T_\mathrm{c}$ $\sim$ 30 K, indicative of bulk superconductivity, emerges in a pressure range from $P_\mathrm{c}$ $\sim$ 2.5 GPa to $\sim$ 3.0 GPa. At pressures close to but outside the SC phase, the $\rho(T)$ curve shows a partial SC transition (i.e., zero resistivity is not attained) followed by a reentrant-like hump at approximately $T_\mathrm{N}$ with decreasing temperature. When nonhydrostatic pressure with a uniaxial-like strain component is applied using a solid pressure medium, the partial superconductivity is continuously observed in a wide pressure range from 1.1 GPa to 3.2 GPa.

Determination of Gap Symmetry from Angle-DependentHc2Measurements onCeCu2Si2

The tetragonal heavy-fermion compound CeCu₂Si₂ exhibits a superconducting ground state (S type, T(c) = 0.67 K) close to a magnetic instability. Here, we present angle-resolved resistivity measurements of the upper critical field H(c2). In-plane rotation of S-type CeCu₂Si₂ single crystals reveals a fourfold oscillation of H(c2). An extended weak-coupling BCS model for a d-wave symmetry including strong Pauli-limiting effects confirms the aforementioned angular dependence and points towards d(xy) symmetry of the order parameter.

Interplay between magnetism, structure, and strong electron-phonon coupling in binary FeAs under pressure

Unlike the ferropnictide superconductors, which crystallize in a tetragonal crystal structure, binary FeAs forms in an orthorhombic crystal structure, where the local atomic environment resembles a highly distorted variant of the FeAs${}_{4}$ tetrahdedral building block of the ferropnictide superconductors. However, like the parent compounds of the ferropnictide superconductors, FeAs undergoes magnetic ordering at low temperatures, with no evidence favoring a superconducting ground state at ambient pressure. We employ pressure-dependent electrical transport and x-ray diffraction measurements using diamond anvil cells to characterize the magnetic state and the structure as a function of pressure. While the MnP-type structure of FeAs persists up to 25 GPa, compressing continuously with no evidence of structural transformations under pressure, features in the magnetotransport measurements associated with magnetism are not observed for pressures in excess of 11 GPa. Where observable, the features associated with magnetic order at ambient pressure show remarkably little pressure dependence, and transport measurements suggest that a dynamical structural instability coupled to the Fermi surface via a strong electron-phonon interaction may play an important role in enabling magnetism in FeAs.

KINETIC ENERGY DRIVEN SUPERCONDUCTIVITY, THE ORIGIN OF THE MEISSNER EFFECT, AND THE REDUCTIONIST FRONTIER

Is superconductivity associated with a lowering or an increase of the kinetic energy of the charge carriers? Conventional BCS theory predicts that the kinetic energy of carriers increases in the transition from the normal to the superconducting state. However, substantial experimental evidence obtained in recent years indicates that in at least some superconductors the opposite occurs. Motivated in part by these experiments many novel mechanisms of superconductivity have recently been proposed where the transition to superconductivity is associated with a lowering of the kinetic energy of the carriers. However none of these proposed unconventional mechanisms explores the fundamental reason for kinetic energy lowering nor its wider implications. Here I propose that kinetic energy lowering is at the root of the Meissner effect, the most fundamental property of superconductors. The physics can be understood at the level of a single electron atom: kinetic energy lowering and enhanced diamagnetic susceptibility are intimately connected. We propose that this connection extends to superconductors because they are, in a very real sense, "giant atoms". According to the theory of hole superconductivity, superconductors expel negative charge from their interior driven by kinetic energy lowering and in the process expel any magnetic field lines present in their interior. Associated with this we predict the existence of a macroscopic electric field in the interior of superconductors and the existence of macroscopic quantum zero-point motion in the form of a spin current in the ground state of superconductors (spin Meissner effect). In turn, the understanding of the role of kinetic energy lowering in superconductivity suggests a new way to understand the fundamental origin of kinetic energy lowering in quantum mechanics quite generally. This provides a new understanding of "quantum pressure", the stability of matter and the origin of fermion anticommutation relations, it leads to the prediction that spin currents exist in the ground state of aromatic ring molecules, and that the electron wavefunction is double-valued, requiring a reformulation of conventional quantum mechanics.

Phase diagram of superconductivity and antiferromagnetism in single crystals of Sr(Fe1−xCox)2As2and Sr1−yEuy(Fe0.88Co0.12)2As2

We report magnetic susceptibility, resistivity and heat capacity measurements on single crystals of the Sr(Fe1-xCox)2As2 and Sr1-yEuy(Fe0.88Co0.12)2As2 series. The optimal Co concentration for superconductivity in Sr(Fe1-xCox)2As2 is determined to be x ~ 0.12. Based on this we grew members of the Sr1-yEuy(Fe0.88Co0.12)2As2 series so as to examine the effects of well defined, local magnetic moments, on the superconducting state. We show that superconductivity is gradually suppressed by paramagnetic Eu2+ doping and coexists with antiferromagnetic ordering of Eu2+ as long as Tc > TN. For y >= 0.65, TN crosses Tc and the superconducting ground state (as manifested by zero resistivity) abruptly disappears with evidence for competition between superconductivity and local moment antiferromagnetism for y up to 0.72. It is speculated that the suppression of the antiferromagnetic fluctuations of Fe sublattice by coupling to the long range order of Eu2+ sublattice destroys bulk superconductivity when TN > Tc.

NON-UNIFORM CHIRAL AND 2SC COLOR SUPERCONDUCTING PHASES, TAKING INTO ACCOUNT THE NONZERO CURRENT QUARK MASS

We have shown that the possibility of the existence of the mixed phase of the non-uniform chiral (NCh) and the color superconducting (2SC) ground state depends significantly on the choice of the parameters and type of the regularization scheme. Our calculations indicate that irrespective of the choice of regularization type, in a moderate baryon density region, there is a local minimum of a system corresponding to the NCh/2SC related phase. In the 3d cutoff regularization scheme, the mixed region of the NCh and the 2SC phases exists for a broad set of NJL model parameters. However, in the Schwinger regularization scheme, if parameters are set to the vacuum values of fπ, mπ and [Formula: see text], then the mixed region of the NCh and the 2SC phases does not exist.

Specific heat andμSR study on the noncentrosymmetric superconductor LaRhSi3

We have investigated the superconducting properties of the noncentrosymmetric superconductor LaRhSi${}_{3}$ by performing magnetization, specific heat, electrical resistivity, and muon spin relaxation ($\ensuremath{\mu}$SR) measurements. LaRhSi${}_{3}$ crystallizes with the BaNiSn${}_{3}$-type tetragonal structure (space group $I4 \mathit{mm}$), as confirmed through our neutron diffraction study. Magnetic susceptibility, electrical resistivity and specific heat data reveal a sharp and well-defined superconducting transition at ${T}_{c}=2.16\ifmmode\pm\else\textpm\fi{}0.08$ K. The low-temperature specific heat data reveal that LaRhSi${}_{3}$ is a weakly coupled bulk BCS superconductor and has an $s$-wave singlet ground state with an isotropic energy gap of $~$0.3 meV, $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}=3.24$. The specific heat data measured in an applied magnetic field strongly indicate a type I behavior. Type I superconductivity in this compound is also inferred from the Ginzburg-Landau parameter, $\ensuremath{\kappa}=0.25$. Various superconducting parameters, including the electron-phonon coupling strength, penetration depth, and coherence length, characterize LaRhSi${}_{3}$ as a moderate dirty-limit superconductor. A detailed study of the magnetic field-temperature ($H\ensuremath{-}T$) phase diagram is presented and from a consideration of the free energy, the thermodynamic critical field, ${H}_{c0}$, is estimated to be $17.1\ifmmode\pm\else\textpm\fi{}0.1$ mT, which is in very good agreement with that estimated from the transverse field $\ensuremath{\mu}$SR measurement that gives ${H}_{c0}=17.2\ifmmode\pm\else\textpm\fi{}0.1$ mT. The transverse field $\ensuremath{\mu}$SR results are consistent with conventional type I superconductivity in this compound. Further, the zero field $\ensuremath{\mu}$SR results indicate that time-reversal symmetry is preserved when entering the superconducting state, also supporting a singlet pairing superconducting ground state in LaRhSi${}_{3}$.

50 Years of Fluxoid Quantization: 2e or Not 2e

The year 2011 is quite remarkable because it allows us to celebrate not only the centennial of the discovery of superconductivity by Heike Kamerlingh-Onnes (The superconductivity of Mercury, Comm. Phys. Lab. Univ. Leiden, vols. 122, 124, 1911), but also the half-centennial of the discovery of what is referred to as fluxoid quantization in superconductors by Robert Doll and Martin Nabauer (Phys. Rev. Lett. 7:51, 1961; Z. Phys. 169:526, 1962), and, independently, by Bascom S. Deaver Jr. and William Fairbank (Phys. Rev. Lett. 7:43, 1961; Ph.D. Thesis, Stanford University, 1962). The experimental proof of the quantization of magnetic flux (or more accurately fluxoid) in hollow superconducting cylinders actually supports two important theoretical concepts. The form of the fluxoid quantum, on the one hand, which contains twice the elementary charge, allows for the conclusion, that the superconducting ground state can be viewed as a condensate of electron pairs, as predicted by the BCS theory of superconductivity (Bardeen et al. in Phys. Rev. 106:162, 1957; Phys. Rev. 108:1175, 1957). It can be viewed, on the other hand, as a quantum phenomenon seen on macroscopic scales and thus supports the concept of the bosonic macroscopic wave function, here applied to the description of (quasi-bosonic) fermion pair condensates. This review is devoted to a discussion of the physics behind the Doll-Nabauer, Deaver-Fairbank discoveries and is intended to review historically the chain of events which motivated these talented experimentalists and which led to their independent discoveries at quite remote points of the earth.

Enhanced superconductivity by correlations between two Kondo impurities

We study the interplay between magnetic correlations of two Kondo impurities and superconducting singlet pairing. Performing a Schrieffer–Wolff transformation in the zero-bandwidth limit of the two-impurity Anderson model we obtain the Hamiltonian of two magnetic impurities and we add a superconducting term to the conduction electrons. The model allows us to study the effect of the magnetic correlation between the impurities on the superconducting ground state. At zero temperature, different superconducting ground states can be obtained depending on the magnitude of magnetic coupling between S1 and S2. For increasing coupling, the superconducting region is enlarged showing an interesting result: in the strong coupling limit, where the impurities are in a very strong ferromagnetic correlation state, half of the conduction electrons are decoupled from the local moments of the impurities and take advantage of the superconducting pairing lowering the ground state energy. On the contrary, when the coupling between S1and S2 decreases, the scenario of the two independent Kondo impurities in presence of superconductivity emerges and all the conduction electrons are involved in the pair breaking physics. At finite temperature, we obtain the phase diagram and we observe a region of parameters where the re-entrance phenomenon occurs.

Optical conductivity and superconductivity in LaSb2

We have measured the resistivity, optical conductivity, and magnetic susceptibility of LaSb2 to search for clues as to the cause of the extraordinarily large linear magnetoresistance and to explore the properties of the superconducting state. We find no evidence in the optical conductivity for the formation of a charge density wave state above 20 K despite the highly layered crystal structure. In addition, only small changes to the optical reflectivity with magnetic field are observed indicating that the MR is due to scattering rate, not charge density, variations with field. Although a superconducting ground state was previously reported below a critical temperature of 0.4 K, we observe, at ambient pressure, a fragile superconducting transition with an onset at 2.5 K. In crystalline samples, we find a high degree of variability with a minority of samples displaying a full Meissner fraction below 0.2 K and fluctuations apparent up to 2.5 K. The application of pressure stabilizes the superconducting transition and reduces the anisotropy of the superconducting phase.

Pressure and K doping induced superconductivity in BaFe2As2

We have measured electrical resistivity under pressure P and 75As NMR on single crystal and poly crystalline BaFe2As2 and (Ba1−xKx)Fe2As2 to elucidate mechanism of antiferromagnetic/superconducting phase transition in BaFe2As2. This system is an antiferromagnet, AF, with a transition temperature of 141 K, which shows superconductivity by applying P or by a carrier doping of K for Ba. From high P resistivity measurements, we understood that the transition was highly sensitive to the P homogeneity. Small uniaxial stress strongly suppresses AF order and stabilizes superconductivity at much lower pressure. 75As NMR study in (Ba1−xKx)Fe2As2 shows existence of large AF spin fluctuations in tetragonal phase having a superconducting ground state. The AF spin fluctuations decrease gradually with increasing K concentration.

SPIN SINGLET AND TRIPLET SUPERCONDUCTIVITY INDUCED BY CORRELATED HOPPING INTERACTIONS

In this article, we show that the Bardeen-Cooper-Schrieffer (BCS) formalism applied to a Hubbard model is capable to predict the s-, p- and d-wave superconductivity within a single theoretical scheme. This study is performed on a square lattice described by a generalized Hubbard Hamiltonian, in which correlated-hopping interactions are included in addition to the repulsive Coulombic one. Within the BCS formalism using a variable chemical potential, the superconducting ground states are determined by two coupled integral equations, whose integrand functions have main contributions around the Fermi surface. We observe the existence of a maximum critical temperature for s-, p- and d-wave superconducting channels that occur at the medium, low and high electron densities, respectively. Furthermore, the p- and d-wave superconducting specific heats show a power-law temperature dependence, instead of the exponential one for the s channel. Finally, the smallness of the anisotropic single-energy-excitation-gap minima is essential for the specific heat behavior, and this fact allows to understand the experimental data obtained from Sr2RuO4 and La2-xSrxCuO4 superconductors.

Towards a theory of superconductivity based on collective Cooper pairs

Superconductivity could be seen as a Bose–Einstein condensation (BEC) of Cooper pairs. However, the creation and annihilation operators of Cooper pairs do not satisfy the bosonic commutation relations and then, the mentioned viewpoint has a weakness in its foundation. In this work, we introduce the concept of collective Cooper pairs (CCP) as linear combinations of Cooper pairs and prove their bosonic nature at the dilute limit. This bosonic nature is given rise from their diffuse character on the Cooper pairs, which permits the accumulation of many collective pairs at a single quantum state. Moreover, the superconducting ground state proposed by Bardeen, Cooper and Schrieffer (BCS) can be written in terms of these collective Cooper pairs, which means that the BCS theory is consistent with a possible BEC theory of superconductivity based on collective Cooper pairs. Finally, we calculate the energy spectra and the BEC critical temperature of CCP.

Superconductivity in the repulsive Hubbard model: An asymptotically exact weak-coupling solution

We study the phase diagram of the Hubbard model in the limit where U, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for T$_c$, the superconducting transition temperature, in terms of the correlation functions of the non-interacting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing T$_c$ involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff $\Omega_0$. Then, the renormalization group (RG) flows of the resulting effective action are computed and T$_c$ is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that T$_c$ is independent of $\Omega_0$. Using this method, we find a variety of unconventional superconducting ground states in two and three dimensional lattice systems and present explicit results for T$_c$ and pairing symmetries as a function of the electron concentration.

Fate of the superconducting ground state on the Moyal plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is smaller compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt.

Polymorphism control of superconductivity and magnetism in Cs3C60 close to the Mott transition

The crystal structure of a solid controls the interactions between the electronically active units and thus its electronic properties. In the high-temperature superconducting copper oxides, only one spatial arrangement of the electronically active Cu(2+) units-a two-dimensional square lattice-is available to study the competition between the cooperative electronic states of magnetic order and superconductivity. Crystals of the spherical molecular C(60)(3-) anion support both superconductivity and magnetism but can consist of fundamentally distinct three-dimensional arrangements of the anions. Superconductivity in the A(3)C(60) (A = alkali metal) fullerides has been exclusively associated with face-centred cubic (f.c.c.) packing of C(60)(3-) (refs 2, 3), but recently the most expanded (and thus having the highest superconducting transition temperature, T(c); ref. 4) composition Cs(3)C(60) has been isolated as a body-centred cubic (b.c.c.) packing, which supports both superconductivity and magnetic order. Here we isolate the f.c.c. polymorph of Cs(3)C(60) to show how the spatial arrangement of the electronically active units controls the competing superconducting and magnetic electronic ground states. Unlike all the other f.c.c. A(3)C(60) fullerides, f.c.c. Cs(3)C(60) is not a superconductor but a magnetic insulator at ambient pressure, and becomes superconducting under pressure. The magnetic ordering occurs at an order of magnitude lower temperature in the geometrically frustrated f.c.c. polymorph (Néel temperature T(N) = 2.2 K) than in the b.c.c.-based packing (T(N) = 46 K). The different lattice packings of C(60)(3-) change T(c) from 38 K in b.c.c. Cs(3)C(60) to 35 K in f.c.c. Cs(3)C(60) (the highest found in the f.c.c. A(3)C(60) family). The existence of two superconducting packings of the same electronically active unit reveals that T(c) scales universally in a structure-independent dome-like relationship with proximity to the Mott metal-insulator transition, which is governed by the role of electron correlations characteristic of high-temperature superconducting materials other than fullerides.