Pair-breaking Processes Research Articles

Model-independent determination of the gap function of nearly localized superconductors

The gap function $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ carries essential information on both, the pairing glue as well as the pair-breaking processes in a superconductor. Unfortunately, in nearly localized superconductors with a nonconstant density of states in the normal state, the standard procedure for extraction of $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ cannot be applied. Here we introduce a model-independent method that makes it possible to extract $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ also in this case. The feasibility of the procedure is demonstrated on the tunneling data for the disordered thin films of TiN. We find an unconventional feature of $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ which suggests that the electrons in TiN are coupled to a very soft pair-breaking mode.

Upper Limit on the QCD Axion Mass from Isolated Neutron Star Cooling.

The quantum chromodynamics (QCD) axion may modify the cooling rates of neutron stars (NSs). The axions are produced within the NS cores from nucleon bremsstrahlung and, when the nucleons are in superfluid states, Cooper pair breaking and formation processes. We show that four of the nearby isolated magnificent seven NSs along with PSR J0659 are prime candidates for axion cooling studies because they are coeval, with ages of a few hundred thousand years known from kinematic considerations, and they have well-measured surface luminosities. We compare these data to dedicated NS cooling simulations incorporating axions, profiling over uncertainties related to the equation of state, NS masses, surface compositions, and superfluidity. Our calculations of the axion and neutrino emissivities include high-density suppression factors that also affect SN 1987A and previous NS cooling limits on axions. We find no evidence for axions in the isolated NS data, and within the context of the Kim-Shifman-Vainshtein-Zakharov QCD axion model, we constrain m_{a}≲16 meV at 95% confidence level. An improved understanding of NS cooling and nucleon superfluidity could further improve these limits or lead to the discovery of the axion at weaker couplings.

Microwave response of superconductors that obey local electrodynamics

Surface impedance of type-II superconductors is determined by their local optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$. Standard BCS-like theoretical descriptions of $\ensuremath{\sigma}(\ensuremath{\omega})$, due to Mattis and Bardeen [Phys. Rev. 111, 412 (1958)] or Zimmermann et al. [Physica C 183, 99 (1991)], do not take pair-breaking processes into account. Therefore they do not provide a quantitative explanation of the microwave response, and in particular, they cannot predict the magnitude of the coherence peak. Here, based on the recently developed concept of Dynes superconductors, which does take also the pair-breaking scattering into account, we provide a simple but complete description of the microwave response of type-II superconductors, concentrating on the unexpected properties of clean superconductors which are often used as cavity materials.

Microscopic origin of the Dynes parameterΓof theLaAlO3–SrTiO3interface superconductor

The superconducting density of states of the two-dimensional electron system at the ${\mathrm{LaAlO}}_{3}--{\mathrm{SrTiO}}_{3}$ interface exhibits broad quasiparticle peaks that are well described by the Dynes parameter $\mathrm{\ensuremath{\Gamma}}$. We measured $\mathrm{\ensuremath{\Gamma}}$ in a wide range of temperatures and gate voltages using tunneling spectroscopy. $\mathrm{\ensuremath{\Gamma}}$ exhibits a ${T}^{q}$ temperature dependence, with $q=2.2\ifmmode\pm\else\textpm\fi{}0.2$. We discuss several interpretations of $\mathrm{\ensuremath{\Gamma}}$ and conclude that $\mathrm{\ensuremath{\Gamma}}$ is an intrinsic parameter of the superconducting state that quantifies the effect of the pair-breaking processes in the superconductor. The strong temperature dependence at low temperatures rules out inelastic electron scattering and magnetic scattering as the origin of the pair breaking. We find that $\mathrm{\ensuremath{\Gamma}}$ can be explained by interband scattering and by scattering in a superconductor with nodes in the order parameter.

Pauli-limit upper critical field of high-temperature superconductor La1.84Sr0.16CuO4

The upper critical field of a cuprate high-temperature superconductor, La1.84Sr0.16CuO4, was investigated by high-frequency self-resonant contactless electrical conductivity measurements in magnetic fields up to 102 T. An irreversible transition was observed at 85 T (T = 4.2 K), defined as the upper critical field. The temperature-dependent upper critical field was argued on the basis of the Werthamer-Helfand-Hohenberg theory. The Pauli-limiting pair-breaking process with a small contribution of the spin-orbit coupling explained the first-order phase transition exhibiting a hysteresis observed at low temperatures.

Effect of hydrostatic pressure on the superconducting properties of quasi-1D superconductor K2Cr3As3

K2Cr3As3 is a newly discovered quasi-1D superconductor with a Tc = 6.1 K and an upper critical field µ0Hc2(0) ≈ 40 T three times larger than the Pauli paramagnetic limit µ0Hp that is suggestive of a spin-triplet Cooper pairing. In this paper, we have investigated the effects of hydrostatic pressure on its Tc and µ0Hc2 by measuring the ac magnetic susceptibility χ'(T) under magnetic fields at various hydrostatic pressures up to 7.5 GPa. The major findings include: (1) Tc is suppressed gradually to below 2 K at 7.5 GPa; (2) the estimated µ0Hc2(0) decreases dramatically to below µ0Hp above ~2 GPa and becomes slight lower than the orbital limiting field estimated from the initial slope of upper critical field via = −0.73TcdHc2/ in the clean limit; (3) the estimated Maki parameter α = √2/Hp drops from 4 at ambient pressure to well below 1 at P > 2 GPa, suggesting the crossover from Pauli paramagnetic limiting to orbital limiting in the pair breaking process upon increasing pressure. These observations suggested that the application of hydrostatic pressure could drive K2Cr3As3 away from the ferromagnetic instability and lead to a breakdown of the spin-triplet pairing channel. We have also made a side-by-side comparison and discussed the distinct effects of chemical and physical pressures on the superconducting properties of K2Cr3As3.

Electromagnetic properties of impure superconductors with pair-breaking processes

Recently a generic model has been proposed for the single-particle properties of gapless superconductors with simultaneously present pair-conserving and pair-breaking impurity scattering (the so-called Dynes superconductors). Here we calculate the optical conductivity of the Dynes superconductors. Our approach is applicable for all disorder strengths from the clean up to the dirty limit and for all relative ratios of the two types of scattering, nevertheless the complexity of our description is equivalent to that of the widely used Mattis-Bardeen theory. We identify two optical fingerprints of the Dynes superconductors: (i) the presence of two absorption edges and (ii) a finite absorption at vanishing frequencies even at the lowest temperatures. We demonstrate that the recent anomalous optical data on thin MoN films can be reasonably fitted by our theory.

Consistent two-lifetime model for spectral functions of superconductors

Recently it has been found that models with at least two lifetimes have to be considered when analyzing the angle resolved photoemission data in the nodal region of the cuprates [T. Kondo et al., Nat. Commun. 6, 7699 (2015)]. In this paper we compare two such models. First we show that the phenomenological model used by Kondo et al. violates the sum rule for the occupation number. Next we consider the recently proposed model of the so-called Dynes superconductors, wherein the two lifetimes measure the strengths of pair-conserving and pair-breaking processes. We demonstrate that the model of the Dynes superconductors is fully consistent with known exact results and we study in detail the resulting spectral functions. Finally, we show that the spectral functions in the nodal region of the cuprates can be fitted well by the model of the Dynes superconductors.

The response of the polarized Fermi mixture to an artificial vector potential: The interaction strength and imbalance chemical potential effects

We consider a polarized Fermi mixture (with normal-superfluid phase separation), subjected to artificial vector potential. We concentrate on the BCS regime with various interaction strengths and numerically obtain the polarisability of the system. We obtain the functional dependence of the polarisability of the system on frequency and the relevant physical parameters, namely the interaction strength, the mass ratio, the average and imbalance chemical potentials. Also, we find the special frequency (ωs), for which the rate of the response of system to the potential is changed and the cut-off frequency (ωcutoff), for which the response starts to become infinity. We investigate the behavior of the curves of polarisability versus proper physical parameters for ω<ωs and ωs<ω<ωcutoff at a nonzero temperature and interpret the existence of special and cut-off frequencies via the propagator concept (of particles or holes). Also, we offer the explanation of the minimum energy required for the occurrence of the pair-breaking process and the existence of the cut-off frequency, which is different with respect to the conventional superfluid Fermi gas, and is related to the relevant physical parameters. Finally, the system's response can be controlled by relevant physical parameters, such as interaction strength.

Magnetar superconductivity versus magnetism: Neutrino cooling processes

We describe the microphysics, phenomenology, and astrophysical implication of a $B$-field induced unpairing effect that may occur in magnetars, if the local $B$ field in the core of a magnetar exceeds a critical value ${H}_{c2}$. Using the Ginzburg-Landau theory of superconductivity, we derive the ${H}_{c2}$ field for proton condensate taking into the correction $(\ensuremath{\le}30%)$ which arises from its coupling to the background neutron condensate. The density dependence of pairing of proton condensate implies that ${H}_{c2}$ is maximal at the crust-core interface and decreases towards the center of the star. As a consequence, magnetar cores with homogenous constant fields will be partially superconducting for ``medium-field'' magnetars $({10}^{15}\ensuremath{\le}B\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{G})$ whereas ``strong-field'' magnetars $(B&gt;5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{G})$ will be void of superconductivity. The neutrino emissivity of a magnetar's core changes in a twofold manner: (i) the $B$-field assisted direct Urca process is enhanced by orders of magnitude, because of the unpairing effect in regions where $B\ensuremath{\ge}{H}_{c2}$; (ii) the Cooper-pair breaking processes on protons vanish in these regions and the overall emissivity by the pair-breaking processes is reduced by a factor of only a few.

Selected problems in astrophysics of compact objects

I review three problems in astrophysics of compacts stars: (i) the phase diagram of warm pair-correlated nuclear matter at sub-saturation densities at finite isospin asymmtery; (ii) the Standard Model neutrino emission from superfluid phases in neutron stars within the Landau theory of Fermi (superfluid) liquids; (iii) the beyond Standard Model physics of axionic cooling of compact stars by the Cooper pair-breaking processes.

Neutrino emissivity of anisotropic neutron superfluids

We examine the influence of the anisotropy of the superfluid energy gap and residual Fermi-liquid interactions in the triplet-correlated neutron liquid onto neutrino energy losses through neutral weak currents. The neutrino-pair emission caused by the pair breaking and formation processes and by the spin-wave decays is considered for the case of the $^{3}P_{2}$ pairing in the state with $m_{j}=0$. The simple analytical formulae are obtained. A comparison with the previous results of the average-angle approach shows that the gap anisotropy leads to quenching of the neutrino emissivity caused by the pair recombination processes on about 15% and to substantial suppression of the spin-wave decays. Residual particle-hole interactions increase the energy losses in both the channels on about 5%.

Axions from cooling compact stars: Pair-breaking processes

Once formed in a supernova explosion, a neutron star cools rapidly via neutrino emission during the first 10^4-10^5 yr of its life-time. Here we compute the axion emission rate from baryonic components of a star at temperatures below their respective critical temperatures T_c for normal-superfluid phase transition. The axion production is driven by a charge neutral weak process, associated with Cooper pair breaking and recombination. The requirement that the axion cooling does not overshadow the neutrino cooling puts a lower bound on the axion decay constant f_a > 6 10^9 T_{c9}^{-1} GeV, with T_{c9} = T_c/10^9 K. This translates into a upper bound on the axion mass m_a < 10^{-3} T_{c9} eV.

Microscopic study of nuclear level densities and thermodynamical properties in 170,171,172Yb

The nuclear level density and entropy were extracted for 170,171,172Yb isotopes within microscopic theory, which includes nuclear pairing interaction. The calculations were based on the modified harmonic oscillator according the Nilsson potential for deformed nuclei. From the level densities, thermodynamical quantities such as temperature and entropy have been deduced. The entropies of the neutron hole and particle are estimated from the entropy difference between the odd-mass and even–even nuclei. The critical temperature of the pair-breaking process is found to be Tc ∼ 0.4–0.5 MeV. The results were compared with experimental data obtained by the Oslo group.

The origin and non-quasiparticle nature of Fermi arcs in Bi2Sr2CaCu2O8+δ

A Fermi arc is a disconnected segment of a Fermi surface observed in the pseudogap phase of cuprate superconductors. This simple description belies the fundamental inconsistency in the physics of Fermi arcs, specifically that such segments violate the topological integrity of the band. Efforts to resolve this contradiction of experiment and theory have focused on connecting the ends of the Fermi arc back on itself to form a pocket, with limited and controversial success. Here we show the Fermi arc, while composed of real spectral weight, lacks the quasiparticles to be a true Fermi surface. To reach this conclusion we developed a new photoemission-based technique that directly probes the interplay of pair-forming and pair-breaking processes with unprecedented precision. We find the spectral weight composing the Fermi arc is shifted from the gap edge to the Fermi energy by pair-breaking processes. While real, this weight does not form a true Fermi surface, because the quasiparticles, though significantly broadened, remain at the gap edge. This non-quasiparticle weight may account for much of the unexplained behavior of the pseudogap phase of the cuprates.

Spin excitonic and diffusive modes in superfluid Fermi liquids

The role of the particle-particle $p$-wave spin interaction in Fermi liquids with an $s$-wave pairing is studied. Depending on the sign of the interaction, there arises either a new exciton collective mode below the pair-breaking threshold or a diffusive excitation mode above the threshold. The Landau parameters that control the interaction strength are evaluated for various systems: dilute fermion gases, a degenerate electron liquid, metals, atomic nuclei, and neutron matter. The interaction removes also the square-root singularity in the phase space of pair-breaking processes. How these effects influence the neutrino emissivity in neutron Cooper-pair recombinations in neutron stars is shown.

Superfluid nucleon matter in and out of equilibrium and weak interactions

The Larkin-Migdal approach to a cold superfluid Fermi liquid is generalized for a non-equilibrium system. The Schwinger-Keldysh diagram technique is applied. The developed formalism is applicable to the pairing in the states with arbitrary angular momenta. We consider the white body radiation problem by calculating probabilities of different direct reactions from a piece of a fermion superfluid. The closed diagram technique is formulated in terms of the full Green's functions for systems with the pairing correlation. The cutting rules are used to classify the diagrams representing one-nucleon, two-nucleon, etc. processes in the matter. The important role of multi-piece diagrams for the vector-current conservation is demonstrated. In the case of equilibrated systems, dealing with dressed Green's functions, we demonstrate correspondence between calculations in the Schwinger-Kadanoff-Baym-Keldysh formalism and the ordinary Matsubara technique. As an example we consider neutrino radiation from the neutron pair breaking and formation processes in case of a singlet pairing. Necessary correlation effects are included. The in-medium renormalization of normal and anomalous vertices is performed.

Quantum Incompressibility of a Falling Rydberg Atom, and a Gravitationally-Induced Charge Separation Effect in Superconducting Systems

Freely falling point-like objects converge toward the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum mechanical object such as a hydrogen atom prepared in a high principal-quantum-number state, i.e. a circular Rydberg atom, is predicted to fall more slowly than a classical point-like object, when both objects are dropped from the same height above the Earth’s surface. This indicates that, apart from transitions between quantum states, the atom exhibits a kind of quantum mechanical incompressibility during free fall in inhomogeneous, tidal gravitational fields like those of the Earth.A superconducting ring-like system with a persistent current circulating around it behaves like the circular Rydberg atom during free fall. Like the electronic wavefunction of the freely falling atom, the Cooper-pair wavefunction is quantum mechanically incompressible. The ions in the lattice of the superconductor, however, are not incompressible, since they do not possess a globally coherent quantum phase. The resulting difference during free fall in the response of the nonlocalizable Cooper pairs of electrons and the localizable ions to inhomogeneous gravitational fields is predicted to lead to a charge separation effect, which in turn leads to a large Coulomb force that opposes the convergence caused by the tidal gravitational force on the superconducting system.A “Cavendish-like” experiment is proposed for observing the charge separation effect induced by inhomogeneous gravitational fields in a superconducting circuit. The charge separation effect is determined to be limited by a pair-breaking process that occurs when low frequency gravitational perturbations are present.

Experimental Observation of the Crystallization of a Paired Holon State

An excitation at 201 meV is observed in the doped-hole ladder cuprate Sr14Cu24O41, using ultraviolet resonance Raman scattering with incident light at 3.7 eV polarized along the rungs. The excitation is of charge nature, with a temperature independent excitation energy, and can be understood via an intraladder pair-breaking process. The intensity tracks closely the order parameter of the charge density wave in the ladder CDW(L), but persists above its transition temperature T(CDW(L)), indicating a strong local pairing above the T(CDW(L)). The 201 meV excitation vanishes in La6Ca8Cu24O(41+δ), and La5Ca9Cu24O41 which are samples with no holes in the ladders. Our results suggest that the doped holes in the ladder are composite bosons consisting of paired holons that order below T(CDW).

Neutral weak currents in nucleon superfluid Fermi liquids: Larkin-Migdal and Leggett approaches

Neutrino emission in the processes of breaking and formation of nucleon Cooper pairs is calculated in the framework of the Larkin-Migdal and Leggett approaches to the description of superfluid Fermi liquids at finite temperatures. We explain peculiarities of both approaches and explicitly demonstrate that they lead to the same expression for the emissivity in pair breaking and formation processes.