Classical BCS Research Articles

Gapless Neutron Superfluidity Can Explain the Late Time Cooling of Transiently Accreting Neutron Stars.

The current interpretation of the observed late time cooling of transiently accreting neutron stars in low-mass x-ray binaries during quiescence requires the suppression of neutron superfluidity in their crust at variance with recent abinitio many-body calculations of dense matter. Focusing on the two emblematic sources KS 1731-260 and MXB 1659-29, we show that their thermal evolution can be naturally explained by considering the existence of a neutron superflow driven by the pinning of quantized vortices. Under such circumstances, we find that the neutron superfluid can be in a gapless state in which the specific heat is dramatically increased compared to that in the classical BCS state assumed so far, thus delaying the thermal relaxation of the crust. We perform neutron-star cooling simulations taking into account gapless superfluidity, and we obtain excellent fits to the data, thus reconciling astrophysical observations with microscopic theories. The imprint of gapless superfluidity on other observable phenomena is briefly discussed.

Disorder effects in NbTiN superconducting resonators

Disordered superconducting materials like NbTiN possess a high kinetic inductance fraction and an adjustable critical temperature, making them a good choice for low-temperature detectors. Their energy gap (Δ), critical temperature (T c), and quasiparticle density of states (QDOS) distribution, however, deviate from the classical BCS theory due to the disorder effects. The Usadel equation, which takes account of elastic scattering, non-elastic scattering, and electro–phonon coupling, can be applied to explain and describe these deviations. This paper presents numerical simulations of the disorder effects based on the Usadel equation to investigate their effects on the Δ, T c, QDOS distribution, and complex conductivity of the NbTiN film. Furthermore, NbTiN superconducting resonators with coplanar waveguide (CPW) structures are fabricated and characterized at different temperatures to validate our numerical simulations. The pair-breaking parameter α and the critical temperature in the pure state TcP of our NbTiN film are determined from the experimental results and numerical simulations. This study has significant implications for the development of low-temperature detectors made of disordered superconducting materials.

Pressure-Stabilized Ir3– in a Superconducting Potassium Iridide

The first charge-separated iridide (Ir3–) in an extended solid was identified at elevated pressure when combined with potassium. According to an unbiased structure searching method that combines first-principles calculations with particle swarm optimization algorithms, K3Ir in the Cu3Ti-type structure shows a favorable formation enthalpy (ΔH) compared to the elements and is dynamically stable above 10 GPa. This novel semiconductor (Eg ≈ 1.6 eV) has sufficient orbital separation to allow complete charge transfer from K to Ir, and Bader charge analysis supports the formation of a formally anionic Ir3–. Further, electron doping of K3Ir through Pt substitution makes the system metallic, and electron–phonon coupling calculations indicate that K3(Ir0.875Pt0.125) falls in the strong-coupling regime, with a predicted superconducting transition temperature (Tc) of ∼27 K at 20 GPa. These results suggest that systems containing elements isoelectronic with classical BCS superconductors such as mercury might have an i...

Redefining Budd-Chiari syndrome: A systematic review.

To re-examine whether hepatic vein thrombosis (HVT) (classical Budd-Chiari syndrome) and hepatic vena cava-Budd Chiari syndrome (HVC-BCS) are the same disorder. A systematic review of observational studies conducted in adult subjects with primary BCS, hepatic vein outflow tract obstruction, membranous obstruction of the inferior vena cava (IVC), obliterative hepatocavopathy, or HVT during the period of January 2000 until February 2015 was conducted using the following databases: Cochrane Library, CINAHL, MEDLINE, PubMed and Scopus. Of 1299 articles identified, 26 were included in this study. Classical BCS is more common in women with a pure hepatic vein obstruction (49%-74%). HVC-BCS is more common in men with the obstruction often located in both the inferior vena cava and hepatic veins (14%-84%). Classical BCS presents with acute abdominal pain, ascites, and hepatomegaly. HVC-BCS presents with chronic abdominal pain and abdominal wall varices. Myeloproliferative neoplasms (MPN) are the most common etiology of classical BCS (16%-62%) with the JAK2V617-F mutation found in 26%-52%. In HVC-BCS, MPN are found in 4%-5%, and the JAK2V617-F mutation in 2%-5%. Classical BCS responds well to medical management alone and 1(st) line management of HVC-BCS involves percutaneous recanalization, with few managed with medical management alone. Systematic review of recent data suggests that classical BCS and HVC-BCS may be two clinically different disorders that involve the disruption of hepatic venous outflow.

High-pressure superconductivity in yttrium: The strong-coupling approach

Abstract In the framework of the Eliashberg formalism, the properties of the superconducting state inducing in yttrium for the pressure at p 1 ≡ 26 GPa and p 2 ≡ 31 GPa ( [ T C ] p 1 = 7.9 K and [ T C ] p 2 = 9.27 K ) have been determined. It has been proven that the value of the Coulomb pseudopotential is high and increases with the increasing pressure: [ μ ⋆ ] p 1 = 0.181 and [ μ ⋆ ] p 2 = 0.251 . Next, the order parameter ( Δ ( T ) ) , the thermodynamic critical field ( H C ( T ) ) , the specific heat in the superconducting state ( C S ( T ) ) , and the specific heat in the normal state ( C N ( T ) ) have been calculated. It has been proven that the values of the dimensionless parameters R Δ ≡ 2 Δ ( 0 ) k B T C , R C ≡ C S ( T C ) − C N ( T C ) C N ( T C ) , and R H ≡ T C C N ( T C ) H C 2 ( 0 ) significantly deviate from the predictions of the classical BCS theory: R Δ ∈ { 3.97 , 4.13 } , R C ∈ { 2.16 , 2.41 } , and R H ∈ { 0.153 , 0.152 } . The electron effective mass is high for both pressures [ m e ⋆ ] p 1 T = T C = 2.16 m e and [ m e ⋆ ] p 2 T = T C = 2.64 m e , where the symbol me denotes the electron band mass.

The phonon-mediated superconductivity in [formula omitted] sheet

The values of the thermodynamic parameters of the superconducting state induced by the electron–phonon interaction in the B2C sheet have been determined. It has been found that the critical temperature (TC) can change in the range from 20.4K to 13K for the Coulomb pseudopotential (μ⋆) ranging from 0.1 to 0.2. Generalization of the results for the atomic layer demonstrated that the maximum value of TC is equal to 25K. Next for the B2C sheet, the order parameter (Δ), the thermodynamic critical field (HC), and the specific heat for the superconducting (CS) state and the normal (CN) state have been calculated. The obtained results show that the dimensionless thermodynamic ratios, RΔ≡2Δ(0)/kBTC, RH≡TCCN(TC)/HC2(0), and RC≡(CS(TC)−CN(TC))/CN(TC), deviate from the predictions of the classical BCS theory. In particular RΔ(μ⋆)∈〈3.87,3.79〉, RH(μ⋆)∈〈0.155,0.157〉, and RC(μ⋆)∈〈1.67,1.62〉. The numerical calculations have been conducted in the framework of the Eliashberg formalism.

Description of the superconducting state in the high‐pressure fcc phase of platinum‐hydride

AbstractThe thermodynamic parameters of the superconducting state in PtH at the pressure 76GPa have been examined. The calculations have been carried out in the framework of the Eliashberg formalism. It has been found that the critical temperature () changes in the range from to K, depending on the assumed value of the Coulomb pseudopotential: . The other thermodynamic quantities differ significantly from the predictions of the classical BCS theory. In particular: (i) the parameter reaches the values from to , where denotes the low‐temperature order parameter. (ii) The ratio of the specific heat jump () to the specific heat in the normal state () takes the values from to . (iii) Finally, , where is the low‐temperature thermodynamic critical field.

On the critical temperature and the energy gap in dense [formula omitted]([formula omitted])2 at 250 GPa

The critical temperature (TC) and the energy gap (2Δ(T)) for the superconductor SiH4(H2)2 at 250GPa have been calculated. The wide range of the Coulomb pseudopotential's values has been considered: μ⋆∈〈0.1,0.3〉. It has been stated that TC decreases together with the increase of μ⋆ from 129.83K to 81.40K. The low-temperature energy gap (T∼0 K) decreases together with the increase of the Coulomb pseudopotential from 50.96meV to 30.12meV. The high values of 2Δ(0) mean that the dimensionless ratio RΔ≡2Δ(0)/kBTC significantly exceeds the value predicted by the classical BCS theory. In the considered case: RΔ∈〈4.55,4.29〉. Due to the unusual dependence of the critical temperature and the energy gap on μ⋆, the analytical expressions for TC(μ⋆) and Δ(μ⋆) have been given.

Classical r-matrices and integrable BCS models with many types of fermions

Based on generalized Gaudin models and Lie algebras so(2m), we construct two integrable cases of the pairing BCS Hamiltonians containing m types of ‘spinless’ fermions. They are the so-called s-type and px + ipy-type BCS Hamiltonians. In the particular case of the Lie algebra so(8), the constructed models can be viewed as N = Z proton–neutron integrable models. We find the spectrum of the constructed Hamiltonians in terms of solutions of Bethe-type equations.

Nonperturbative quantum dynamics of the order parameter in the BCS pairing model

We consider quantum dynamics of the order parameter in the discrete pairing model (Richardson model) in thermodynamic equilibrium. The integrable Richardson Hamiltonian is represented as a direct sum of Hamiltonians acting in different Hilbert spaces of single-particle and paired/empty states. This allows us to factorize the full thermodynamic partition function into a combination of simple terms associated with real spins on singly-occupied states and the partition function of the quantum XY-model for Anderson pseudospins associated with the paired/empty states. Using coherent-state path-integral, we calculate the effects of superconducting phase fluctuations exactly. The contribution of superconducting amplitude fluctuations to the partition function in the broken-symmetry phase is shown to follow from the Bogoliubov-de Gennes equations in imaginary time. These equations in turn allow several interesting mappings, e.g., they are shown to be in a one-to-one correspondence with the one-dimensional Schr\"odinger equation in supersymmetric Quantum Mechanics. However, the most practically useful approach to calculate functional determinants is found to be via an analytical continuation of the quantum order parameter to real time, \Delta(\tau -> it), such that the problem maps onto that of a driven two-level system. The contribution of a particular dynamic order parameter to the partition function is shown to correspond to the sum of the Berry phase and dynamic phase accumulated by the pseudospin. We also examine a family of exact solutions for two-level-system dynamics on a class of elliptic functions and suggest a compact expression to estimate the functional determinants on such trajectories. The possibility of having quantum soliton solutions co-existing with classical BCS mean-field is discussed.

Specific heat of superconducting MgCNi3 single crystals

The ac microcalorimetry measurements with light emitting diode used as a heater has been performed on high quality MgCNi3 single crystals with Tc of 6.9 K. The measurements have been realized in the temperature range down to 0.7 K and magnetic fields up to 8 T. All the measurements show sharp and well defined specific heat anomaly at the transition. The low-temperature electronic specific heat in superconducting state shows a classical exponential decrease confirming an s-wave pairing. Analysis of the data in the framework of classical BCS theory points to the moderate coupling in this material. The upper critical field Hc2 has also been derived from specific heat measurements in different magnetic fields. The temperature dependence of Hc2 is discussed.

Linear and nonlinear low-frequency electrodynamics of surface superconducting states in an yttrium hexaboride single crystal

We report on the low-frequency dynamics of surface superconducting states in yttrium hexaboride single crystal. Tunneling and dc magnetization experiments demonstrate that ${\text{YB}}_{6}$ is a classical type-II BCS superconductor with a slightly suppressed order parameter near the surface. The ac response at frequencies 10--1500 Hz has been measured for fields ${H}_{0}$ parallel to the crystal surface. We found that for ${H}_{0}>{H}_{c2}$ the dc magnetic moment completely disappeared, while the ac response exhibited the presence of surface superconductivity. Increasing ${H}_{0}$ above ${H}_{c2}$ revealed the loss maximum in a field between ${H}_{c2}$ and ${H}_{c3}$ with a magnitude considerably larger than in mixed or normal states. In some dc fields the frequency dependence of the real part of the susceptibility is reminiscent of a spin-glass system. At the same time the imaginary component exhibits frequency dispersion which is not a typical feature of the classical spin-glass response. Analysis of the experimental data with the Kramers--Kronig relations showed the possible existence of the loss peak at very low frequencies. It was found that the amplitude of the third harmonic was not a cubic function of the ac amplitude (as it follows from the perturbation theory) even at very low excitation levels. It was shown that the critical state model cannot adequately describe the existing experimental data. The proposed model of a slow relaxing of the order parameter allows one to understand the origin of partial shielding and losses for ${H}_{0}>{H}_{c2}$.

BCS-LIKE APPROXIMATION IN A TWO-BAND MODEL FOR SUPERCONDUCTIVITY IN MgB2

The BCS limit of a two-band model for superconductivity in MgB 2 is discussed and the temperature dependence of the gap functions is calculated together with their values at T = 0. We have studied the effect of interband coupling on the order parameters and critical temperature. The validity of the approximation was investigated by direct comparison with more accurate Eliashberg calculation and it was found that the BCS-like model is appropriate for temperatures up to T ~ 10 K . The two-band superconductivity in MgB 2 has been extensively studied in the literature, in Eliashberg or weak-coupling calculations, as well as in ab initio evaluations of electron–phonon interaction. Here we find from an analytical calculation the well known result that the ratio 2Δ/Tc is no longer universal in the multiband model, in contrast with the classical single-band BCS model.

MgB2: an old material, a new superconductor. An extensive scanning tunneling spectroscopy study

We have performed an extensive scanning tunneling spectroscopy study on different MgB2 samples. In the standard N–I–S geometry on powders, we observed spectra characterized by pronounced double gap structures that can be modeled by supposing two independent tunneling channels, with gap magnitudes Δσ=7.0±0.5meV and Δπ=3.0±0.4meV, i.e., well above and well below the classical BCS limit. In the conductance characteristics of oriented thin films, the presence of the small gap Δπ was predominant and only in few cases a weaker structure appeared around Δσ=7.0meV. Recent results on as-grown c-axis oriented single crystals yielded only small gap confirming the 3D π-band nature of this feature, that survives in magnetic field higher than 5T.

MgB 2: an old material, a new superconductor. An extensive scanning tunneling spectroscopy study

We have performed an extensive scanning tunneling spectroscopy study on different MgB 2 samples. In the standard N–I–S geometry on powders, we observed spectra characterized by pronounced double gap structures that can be modeled by supposing two independent tunneling channels, with gap magnitudes Δ σ=7.0±0.5 meV and Δ π=3.0±0.4 meV , i.e., well above and well below the classical BCS limit. In the conductance characteristics of oriented thin films, the presence of the small gap Δ π was predominant and only in few cases a weaker structure appeared around Δ σ=7.0 meV . Recent results on as-grown c-axis oriented single crystals yielded only small gap confirming the 3D π-band nature of this feature, that survives in magnetic field higher than 5 T .

The physics of inhomogeneous striped superconductors

We present a minimal model of a doped Mott insulator that simultaneously supports antiferromagnetic stripes and d-wave superconductivity. At the unrestricted mean-field level, the various phases of the cuprates, including weak and strong pseudogap phases, and two different types of superconductivity in the underdoped and the overdoped regimes, find a natural interpretation. We argue that on the underdoped side, the superconductor is intrinsically inhomogeneous — striped nanoscale coexistence of superconductivity and magnetism — and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. On the overdoped side, the state is overall homogeneous and the superconductivity is of the classical BCS type.

Ground State and Thermodynamic Properties of an Induced-Pairing Model

We study the phase diagrams and thermodynamic properties of a system of coexisting wide-band current carriers (c-particles) and narrow-band electrons (d-electrons) which can form local pairs. There are two distinct mechanisms of superconductivity in the model considered: (i) the intersubsystem charge exchange, which leads to the superconducting state involving both types of electrons and (ii) the pair hopping interaction of d-electrons, leading to the superconducting state of d-particles only. In contrast to previous works on the subject, we assume an arbitrary value of on-site density interaction of d-electrons U, which allows us to study the effects of reduced d-pair binding energy. Within the approach in which the U term is exactly treated we determine the evolution of superconducting properties as a function of interactions and relative position of the bands. In a definite range of parameters the system shows features which are intermediate between those of a local pair superconductor and those of a classical BCS model. The increasing on-site Coulomb repulsion U competing with the intersubsystem charge exchange and the pair hopping interaction reduces the superconducting critical temperature. Moreover, it can induce a change of the superconducting transition into the first order one. Above a critical value of U, dependent on concentration of electrons and other interactions, the superconducting state cannot be stable at any temperature.

Electronic Band Structure Calculations of theMNX(M=Zr, Ti;X=Cl, Br, I) System and Its Superconducting Member, Li-Dopedβ-ZrNCl

Electronic band structure calculations have been performed forβ-ZrNCl,β-ZrNBr,α-ZrNBr,α-ZrNI, andα-TiNX(X=Cl, Br, I) using the extended Hückel method. These calculations reveal thatn-dopedβ-ZrNCl has a single narrow band at the Fermi level which is stabilized by overlap of 4dz2orbitals on zirconium with respect to the remainder of the conduction band states. This band shows only a small degree of dispersion and can essentially be described as a localized Zr–Zr bond when the carrier concentrations are low. The calculated band structure is consistent with the experimental observations of activated carrier transport, and an indirect optical band gap inβ-ZrNCl andβ-ZrNBr. A simple picture is presented which describes a mechanism for strong electron-phonon coupling in theβ-ZrNXstructure, suggesting thatβ-LixZrNCl is a classical BCS superconductor. This localized 4dz2band at the Fermi level is absent in the electronic band structures ofα-ZrNXandα-TiNXcompounds. The dispersion relations for these compounds show a direct optical band gap, as observed experimentally. The absence of significant metal–metal bonding inα-MNXcompounds implies thatn-doping will be more difficult to achieve in compounds adopting this structure. The relative stability ofα- andβ-polymorphs is also discussed.

Superconducting instability in the Holstein-Hubbard model: A numerical renormalization-group study

We have studied the d-wave pairing-instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation exchange approximation which treats both Coulomb and electron-phonon (EP) interaction diagrammatically on an equal footing. A generalized numerical renormalization group technique has been developed to solve the resulting self-consistent field equations. The $d$-wave superconducting phase diagram shows an optimal T_c at electron concentration <n> ~ 0.9 for the purely electronic Hubbard system. The EP interaction suppresses the d-wave T_c which drops to zero when the phonon-mediated on-site attraction $U_p$ becomes comparable to the on-site Coulomb repulsion $U$. The isotope exponent $\alpha$ is negative in this model and small compared to the classical BCS value $\alpha_{BCS} = 1/2$ or compared to typical observed values in non-optimally doped cuprate superconductors.

Remarks on Superconductivity

These notes try and compare the situation in the new superconductors, and especially the oxide ones, to those where the classical BCS approach holds.