The BCS Critical Temperature at High Density

We investigate the BCS critical temperature $$T_c$$ T c in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of $$T_c$$ T c at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.

Pressure-dependent topological superconductivity on the surface of FeTe0.5Se0.5

FeTe1-xSex is a family of iron-based superconductors with its critical temperature (Tc) dependent on the composition of Se. A well-known Tc is 14.5 K for x = 0.45, which exhibits an s-wave superconducting gap between the topological superconducting surfaces states. Exchange interaction between the electrons has been proposed as the mechanism behind the formation of Cooper pairs for the sample of FeTe0.5Se0.5. In this article we provide further proof that exchange interaction, and hence the associated Tc, depends on the applied pressure on FeTe0.5Se0.5. Using density functional calculations for electrons and phonons and the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity, we found that Tc and superconducting gap for FeTe0.5Se0.5 soars under increasing compression, consistent with the results of experiment.

Elastic behavior, pressure-induced doping and superconducting transition temperature of GdBa2Cu3O7-x

Doping superconductors are known to vary the superconducting transition temperature TC depending on the degree of holes or electrons introduced in a system. In this study, we report how pressure-induced hole doping influences the TC of GdBa2Cu3O7-x superconducting perovskite. The study was carried out in the framework of density functional theory (DFT) using the Quantum espresso code. Ultrasoft pseudopotential with generalized gradient approximation (GGA) and local density approximation (LDA) functional was used to calculate the ground state energy using the plane waves (PW). The stability criterion was satisfied from the calculated elastic constants. The BCS theory and the Mc Millan’s equation was used to calculate the TC of the material at different conditions of pressure. The underdoped regime where the holes were less than those at optimal doping was found to be below 20 GPa of doping pressure. Optimal doping where the material achieved the highest TC (max) ~ 20 GPa of the doping pressure. Beyond the pressure of ~20 GPa was the over doping regime where a decrease in TC was recorded. The highest calculated TC (max) was ~141.16 K. The results suggest that pressure of ~20 GPa gave rise to the highest TC in the study.

High Temperature Superconductors Through the Van Hove Singularity

<p>The antibonding VHS of the high temperature superconductor Bi-2212 appears in the extreme overdoped regime, a part of the cuprate phase diagram little studied to date. Observation of this VHS motivated taking a fresh look at the cuprates using fundamentals of electronics as the foundation for understanding the physics involved in the superconductivity of these materials. In the study of the high temperature superconductors it appears important questions have been overlooked, notably the possible contribution of the gapped state and whether these materials are better considered as doped semiconductors rather than as 'poor' metals. We also find the question of the contribution of oxygen, a substance with a strong magnetic signature, to data of the oxygen-doped cuprates has been neglected. Comparison with non-oxygen doping is supportive of the view the oxygen dopant contributes noticeably to magnetic data. Through magnetic susceptibility measurements the antibonding VHS location, predicted by use of Fermi liquid theory, is well confirmed in polycrystals of the lead-doped cuprate Bi-2212. It was found that the peak in the DOS at the VHS produces no corresponding local peak in the critical temperature versus doping. Instead, the VHS appears associated with the disappearance of the superconductivity, rather than with the maximum critical temperature. We find the metal-insulator transition plays an important role. There are two of these in the cuprates, a horizontal doping dependent one and a vertical temperature dependent one. They affect each other. Noting the consequences of doping an insulator until a metallic state is reached enables a connection to be made between doping and pressure. Three requirements are identified for superconductivity to occur: 1. screening 2. pairing 3. charge mobility Each requirement may be separately satisfied in a manner whereby each can vary differently as a function of the same variable. The superconductivity of the cuprates is found to arise out of an underlying non-metallic state. As such, BCS theory, being formulated to explain superconductivity arising from metallic conduction, cannot be directly applicable. However, although HTS materials are a rich repository of both novel and familiar solid state physics, evidence does not appear to support the notion that superconductivity in the cuprates is caused by "exotic" physics. We also find cause for optimism regarding the development of new or improved superconducting materials.</p>

High Temperature Superconductors Through the Van Hove Singularity

<p>The antibonding VHS of the high temperature superconductor Bi-2212 appears in the extreme overdoped regime, a part of the cuprate phase diagram little studied to date. Observation of this VHS motivated taking a fresh look at the cuprates using fundamentals of electronics as the foundation for understanding the physics involved in the superconductivity of these materials. In the study of the high temperature superconductors it appears important questions have been overlooked, notably the possible contribution of the gapped state and whether these materials are better considered as doped semiconductors rather than as 'poor' metals. We also find the question of the contribution of oxygen, a substance with a strong magnetic signature, to data of the oxygen-doped cuprates has been neglected. Comparison with non-oxygen doping is supportive of the view the oxygen dopant contributes noticeably to magnetic data. Through magnetic susceptibility measurements the antibonding VHS location, predicted by use of Fermi liquid theory, is well confirmed in polycrystals of the lead-doped cuprate Bi-2212. It was found that the peak in the DOS at the VHS produces no corresponding local peak in the critical temperature versus doping. Instead, the VHS appears associated with the disappearance of the superconductivity, rather than with the maximum critical temperature. We find the metal-insulator transition plays an important role. There are two of these in the cuprates, a horizontal doping dependent one and a vertical temperature dependent one. They affect each other. Noting the consequences of doping an insulator until a metallic state is reached enables a connection to be made between doping and pressure. Three requirements are identified for superconductivity to occur: 1. screening 2. pairing 3. charge mobility Each requirement may be separately satisfied in a manner whereby each can vary differently as a function of the same variable. The superconductivity of the cuprates is found to arise out of an underlying non-metallic state. As such, BCS theory, being formulated to explain superconductivity arising from metallic conduction, cannot be directly applicable. However, although HTS materials are a rich repository of both novel and familiar solid state physics, evidence does not appear to support the notion that superconductivity in the cuprates is caused by "exotic" physics. We also find cause for optimism regarding the development of new or improved superconducting materials.</p>

Phase fluctuations in conventional superconductors

Within the Bardeen-Cooper-Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness, J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductors J is normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors, J can drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.

Possible superconductivity from incoherent carriers in overdoped cuprates

There is now compelling evidence that the normal state of superconducting overdoped cuprates is a strange metal comprising two distinct charge sectors, one governed by coherent quasiparticle excitations, the other seemingly incoherent and characterized by non-quasiparticle (Planckian) dissipation. The zero-temperature superfluid density n_s(0)ns(0) of overdoped cuprates exhibits an anomalous depletion with increased hole doping pp, falling to zero at the edge of the superconducting dome. Over the same doping range, the effective zero-temperature Hall number n_{\rm H}(0) transitions from pp to 1 + pp. By taking into account the presence of these two charge sectors, we demonstrate that in the overdoped cuprates Tl_22Ba_22CuO_{6+\delta}6+δ and La_{2-x}2−xSr_xxCuO_44, the growth in n_s(0)ns(0) as pp is decreased from the overdoped side may be compensated by the loss of carriers in the coherent sector. Such a correspondence is contrary to expectations from conventional BCS theory and implies that superconductivity in overdoped cuprates emerges uniquely from the sector that exhibits incoherent transport in the normal state.

Thermodynamic Properties of the Superconducting State in Metallic Hydrogen: Electronic Correlations, Non-conventional Electron-Phonon Couplings and the Anharmonic Effects

Thermodynamical properties of the superconducting state in metallic hydrogen were determined on the basis of the model of two compressed hydrogen planes. We took into account both the on-site and the inter-site electronic correlations (U and K), as well as the relevant non-conventional electron-phonon coupling functions (gU and gK). We proved, within the Eliashberg formalism, that the maximum value of the critical temperature of transition into the superconducting state is about 200 K for the harmonic approximation, and about 84 K for the Morse anharmonic approximation. Omission of the electronic correlations results in a considerable overstatement of the TC value. On the other hand, the TC value is remarkably understated if the non-conventional interactions are disregarded. Other thermodynamic quantities, such as the order parameter, the jump in the specific heat value, the thermodynamic critical field, and the upper critical field, take the values for which the non-dimensional ratios RΔ, RC, RH and RH2 do not differ substantially from the predictions of the BCS theory.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the 1S0 neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.