BCS Critical Temperature Research Articles

Boundary superconductivity in the BCS Model

We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg–Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity.

Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials

We theoretically investigate how the Berry curvature, which arises in multiband structures when the electrons can be described by an effective single-band Hamiltonian, affects the superconducting properties of two-dimensional electronic systems. Generically, the Berry curvature is coupled to electric fields beyond those created by the periodic crystal potential. A potential source of such electric fields, which vary slowly on the lattice scale, is the mutual interaction between the electrons. We show that the Berry curvature provides additional terms in the Hamiltonian describing interacting electrons within a single band. When these terms are taken into account in the framework of the usual BCS weak-coupling treatment of a generic attractive interaction that allows for the formation of Cooper pairs, the coupling constant is modified. In pure singlet and triplet superconductors, we find that the Berry curvature generally lowers the coupling constant and thus the superconducting gap and the critical temperature as a function of doping. From an experimental point of view, a measured deviation from the expected BCS critical temperature upon doping, e.g., in doped two-dimensional transition-metal dichalcogenides, may unveil the strength of the Berry curvature.

The BCS Critical Temperature at High Density

We investigate the BCS critical temperature 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 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.

The BCS critical temperature in a weak homogeneous magnetic field

We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.

The External Field Dependence of the BCS Critical Temperature

We consider the Bardeen-Cooper-Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg-Landau equation.

Experimental First Order Pairing Phase Transition in Atomic Nuclei

The natural log of experimental nuclear level densities at low energy is linear with energy. This can be interpreted in terms of a nearly 1st order phase transition from a superfluid to an ideal gas of quasi particles. The transition temperature coincides with the BCS critical temperature and yields gap parameters in good agreement with the values extracted from even- odd mass differences from rotational states. This converging evidence supports the relevance of the BCS theory to atomic nuclei.

BEC-BCS crossover in neutron matter with renormalization-group-based effective interactions

We study pure neutron matter in the BEC-BCS crossover regime using renormalization group based low-momentum interactions within the Nozi\`eres-Schmitt-Rink framework. This is an attempt to go beyond the mean field description for low-density matter. We work in the basis of so-called Weinberg eigenvectors where the operator $G_0V$ is diagonal, which proves to be an excellent choice that allows one to use non-local interactions in a very convenient way. We study the importance of correlations as a function of density. We notice that there is a significant reduction of the BCS critical temperature at low-densities as the neutron matter approaches the unitary limit.

Finite-temperature stability and dimensional crossover of exotic superfluidity in lattices

We investigate exotic paired states of spin-imbalanced Fermi gases in anisotropic lattices, tuning the dimension between one and three. We calculate the finite temperature phase diagram of the system using real-space dynamical mean-field theory in combination with the quantum Monte Carlo method. We find that regardless of the intermediate dimensions examined, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state survives to reach about one third of the BCS critical temperature of the spin-density balanced case. We show how the gapless nature of the state found is reflected in the local spectral function. While the FFLO state is found at a wide range of polarizations at low temperatures across the dimensional crossover, with increasing temperature we find out strongly dimensionality-dependent melting characteristics of shell structures related to harmonic confinement. Moreover, we show that intermediate dimension can help to stabilize an extremely uniform finite temperature FFLO state despite the presence of harmonic confinement.

Pairing in spherical nanograins

Conditions are ascertained when the pairing and other thermodynamic properties of spherical nanograins with numbers of delocalized electrons N < 10 5 can be investigated by using the Single Shell Model ( SSM) that gives the eigenvalues of the pairing Hamiltonian for a solitary shell. In the frame of SSM the exact canonical and grand canonical descriptions are employed first to analyze the absence of the abrupt superconducting-normal phase transition in finite systems in which an increase of the pairing and BCS critical temperature can be observed and secondly to study such new phenomena as the temperature re-entrance of the pairing in postcritical magnetic fields and also low temperature oscillations of the magnetic susceptibility and electronic heat capacity in an increasing uniform magnetic field.

The BCS Critical Temperature for Potentials with Negative Scattering Length

We prove that the critical temperature for the BCS gap equation is given by $${T_c = \mu \left( \frac 8\pi {\rm e}^{\gamma -2} + o(1) \right) {\rm e}^{\pi/(2\sqrt \mu a)}}$$ in the low density limit μ→ 0, with γ denoting Euler’s constant. The formula holds for a suitable class of interaction potentials with negative scattering length a in the absence of bound states.

On the Nature of Resistive Transition in Disordered Superconducting Nanowires

Hot-electron single-photon counters based on long superconducting nanowires are starting to become popular in optical and infrared technologies due to their ultimately high sensitivity and very high response speed. We investigate intrinsic fluctuations in long NbN nanowires in the temperature range of 4.2 K-20 K, i.e. above and below the superconducting transition. These fluctuations are responsible for fluctuation resistivity and also determine the noise in practical devices. Measurements of the fluctuation resistivity were performed at low current densities and also in external magnetic fields up to 5 T. Above the BCS critical temperature T <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_co</i> the resistivity is well described by the Aslamazov-Larkin (AL) theory for two-dimensional samples. Below T <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_co</i> the measured resistivity is in excellent agreement with the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory developed for one-dimensional superconductors. Despite that our nanowires of 100 nm width are two-dimensional with respect to the coherence length, our analysis shows that at relatively low current densities the one-dimensional LAMH mechanism based on thermally induced phase slip centers dominates over the two-dimensional mechanism related to unbinding of vortex-antivortex pairs below the Berezinskii-Kosterlitz-Thouless transition.

Percolation theory of the pseudogap state

A concept of the pseudogap state in high-${T}_{c}$ layered cuprates on the basis of percolation theory is proposed. Contrary to the self-consistent BCS critical temperature, which defines ${T}^{*}$, the upper boundary of the pseudogap state, the real critical temperature ${T}_{c}$ is defined as the percolation threshold, where the infinite cluster appears. This permits the exact formula for ${T}_{c}$ to be obtained as a function of doping and its ``domelike'' shape to be understood.

Ranges and limits of the electron-phonon coupling constant of superconductivity

A simplified study of the effect of including self energy and vertex corrections to the BCS critical temperature Tc expression is carried out her to identify the possible ranges and limits of the electron-phonon coupling constant λ in superconductivity. The results show that the inclusion of the self energy will reduce the BCS Tc to that of McMillan which is generally believed to yield unrealistic λ while the inclusion of vertex corrections produce a Tc that provides the realistic ranges and limits of λ in superconductivity. The implication of these results is then discussed. Nigerian Journal of Physics Vol. 16(2) 2004: 162-166

Self-consistent theory for molecular instabilities in a normal degenerate Fermi gas in the BEC-BCS crossover

We investigate within a self-consistent theory the molecular instabilities arising in the normal state of a homogeneous degenerate Fermi gas, covering the whole BEC-BCS crossover. These are the standard instability for molecular formation, the BCS instability which corresponds to the formation of Cooper pairs and the related Bose-Einstein instability. These instabilities manifest themselves in the properties of the particle-particle vertex, which we calculate in a ladder approximation. To find the critical temperatures corresponding to these various instabilities, we handle the properties of the interacting Fermi gas on the same footing as the instabilities by making use of the same vertex. This approximate treatment is shown to be quite satisfactory in a number of limiting situations where it agrees with known exact results. The results for the BCS critical temperature and for the BE condensation are found to be in fair agreement with earlier results. The threshold for formation of molecules at rest undergoes a sizeable shift toward the BEC side, due to quantum effects arising from the presence of the degenerate Fermi gas. This should make its experimental observation fairly easy. This shift remains important at least up to temperatures comparable to the Fermi energy of the gas.

Cooper pair coherence in a superfluid Fermi gasof atoms

We study the coherence properties of a trappedtwo-component gas of fermionic atoms below the BCScritical temperature. We propose an optical method toinvestigate the Cooper pair coherence across differentregions of the superfluid. Near-resonant laser light isused to induce transitions between the two coupledhyperfine states. The beam is split so that it probes twospatially separate regions of the gas. Absorption of thelight in this interferometric scheme depends on theCooper pair coherence between the two regions.

Pair transfer spectral function at finite temperature in nanometer-scale superconducting grains

The spectral function for Cooper pair transfer in small metallic superconductors is examined. By performing an exact calculation in a small system, it is shown that a clear evidence of pairing correlations persists in this quantity for temperatures well above the BCS critical temperature, as well as for sizes considerably below the BCS lower size limit for superconductivity. At the same time, however, signatures of the BCS phase transition in small systems remain evident. Differences between even and odd systems are as well analyzed. The number-parity-projected BCS and random-phase approximation treatments of the spectral function at finite temperature are also discussed and compared with the exact results. Their predictions for larger configuration spaces are also shown.

BCS theory for trapped ultracold fermions

We develop an extension of the well-known BCS-theory to systems with trapped fermions. The theory fully includes the quantized energy levels in the trap. The key ingredient is to model the attractive interaction between two atoms by a pseudo-potential which leads to a well defined scattering problem and consequently a BCS-theory free of divergences. We present numerical results for the BCS critical temperature and the temperature dependence of the gap. They are used as a test of existing semi-classical approximations.

Increase of the Kosterlitz-Thouless critical temperature by the external electric field

The shift of the Kosterlitz-Thouless critical temperature in a thin superconducting film due to an external electric field is calculated. It is shown that this shift is much larger than the shift of the superconducting BCS critical temperature and depends strongly on the polarity of the external electric field. It is shown that the resulting current-voltage characteristic in the electric field depends on the polarity of the electric field.

Increase of the Kosterlitz-Thouless critical temperature by the external electric field

The shift of the Kosterlitz-Thouless critical temperature in a thin superconducting film due to an external electric field is calculated. It is shown that this shift is much larger than the shift of the superconducting BCS critical temperature and depends strongly on the polarity of the external electric field. It is shown that the resulting current-voltage characteristic in the electric field depends on the polarity of the electric field.