Strength Of Pairing Interaction Research Articles

Bounds on the superconducting transition temperature

I summarize recent progress on obtaining rigorous upper bounds on superconducting transition temperature [Formula: see text] in two dimensions independent of pairing mechanism or interaction strength. These results are derived by finding a general upper bound for the superfluid stiffness for a multi-band system with arbitrary interactions, with the only assumption that the external vector potential couples to the kinetic energy and not to the interactions. This bound is then combined with the universal relation between the superfluid stiffness and the Berezinskii–Kosterlitz–Thouless [Formula: see text] in 2D. For parabolic dispersion, one obtains the simple result that [Formula: see text], which has been tested in recent experiments. More generally, the bounds are expressed in terms of the optical spectral weight and lead to stringent constraints for the [Formula: see text] of low-density, strongly correlated superconductors. Results for [Formula: see text] bounds for models of flat-band superconductors, where the kinetic energy vanishes and the vector potential must couple to interactions, are briefly summarized. Upper bounds on [Formula: see text] in 3D remains an open problem, and I describe how questions of universality underlie the challenges in 3D.

Origin of gamma surface asymmetries in body-centered cubic refractory high entropy alloys

In this study, we develop an understanding of the effect of high stacking fault elements in the γ-surfaces and twinnability of NbMoTaW refractory High Entropy Alloy (HEA) using first-principles density functional theory calculations. γ-surfaces developed low energy pathways leading to asymmetries by controlling the concentration of high stacking fault energy elements in the HEA. This effect was correlated to the strength of specific solid-state pair interactions using the projected crystal orbital Hamilton population analysis, and they were found to be weak except for W-Mo and W-Ta. Since the interactions involving Tungsten are stronger than the other interactions, stacking fault and twin formation are less likely to happen near tungsten-rich portions of the alloy. This suggests the formation of tungsten-deficient twin boundaries in NbMoTaW which will further improve the ductility of the system. Stable twin fault energy as low as 522 mJ/m2 is reported for the equimolar random atomic configurations of the HEA system. The ratio between twin boundary migration energy and the difference in unstable stacking fault energies (γTBMΔus) was found to be as low as 0.13 suggesting deformation twinning can happen in the HEA system. Vibrational analysis of the alloy system has indicated that tungsten and tantalum contribute to the acoustic phonon frequencies of the HEA. Fundamental insights from this study will help in engineering high entropy alloys with high strength and ductility.

Impact of the pairing interaction on fission of U isotopes

The role of pairing interactions on the scission configurations, the total kinetic energy, and the mass distributions in U isotopes is investigated using the deformed mean-field plus standard pairing model. The total kinetic energy and the mass distributions of $^{232--238}\mathrm{U}$ isotopes obtained using the shape-dependent probability distribution expressed by the Wigner function reproduces the experimental data remarkably well. The model calculations show that the scission region is sensitive to the variation of the pairing interaction strength, particularly for the asymmetric and symmetric scission points. The apparent changes in the peak-to-valley ratio in mass distribution by varying the pairing interaction strength confirm that the pairing interaction plays an important role in achieving the scission process for $^{236}\mathrm{U}$ under the present model. These results also suggest that the pairing interaction strength in the current work should increase with the elongation of the nucleus to yield better fission products. Through numerical analysis, we provide possible microscopic pictures of spontaneous fission around the scission configurations in the exactly solvable pairing model.

Shedding light on the physical nature of ion pair interactions involving carba-closo-dodecaborate anions. Insights from computation.

closo-Carboranes are structures that have been studied for many decades due to their vast applicability in medicine, catalysis, and energy storage. In order to go deeper into the physics behind the interactions of oppositely charged ions, which have potential applications in electrical energy storage and conversion devices, the present work aims to shed light on the physical nature of the interactions involving (R-CB11H11-, R = H, F, CH3, CF3) and Mq+ = Li+, Na+, Mg2+, Zn2+ ions. The bonding situations are evaluated in light of both canonical Kohn-Sham energy decomposition, EDA-NOCV, and local energy decomposition, LED, analyses. Electron and hole transports are also evaluated through charge transfer integrals. The findings reveal that such complexes present not only more significant electrostatic, but also non-negligible orbital contributions. Both energy decomposition analyses EDA-NOCV and DLPNO-LED confirm that the strength of ionic pair interactions (R-CB11H11- ↔ Mq+) is much more dependent on the nature of the cation employed than on the substituent R used. The results also reveal that charge transfers are not significant in such interacting systems.

Superconductor-Insulator Transition in a Non-Fermi Liquid.

We present a model of a strongly correlated system with a non-Fermi liquid high temperature phase. Its ground state undergoes an insulator to superconductor quantum phase transition (QPT) as a function of a pairing interaction strength. Both the insulator and the superconductor are originating from the same interaction mechanism. The resistivity in the insulating phase exhibits the activation behavior with the activation energy, which goes to zero at the QPT. This leads to a wide quantum critical regime with an algebraic temperature dependence of the resistivity. Upon raising the temperature in the superconducting phase, the model exhibits a finite temperature phase transition to a Bose metal phase, which separates the superconductor from the non-Fermi liquid metal.

Topological superconductivity in a two-dimensional Weyl SSH model

We study the emergence of topological superconductivity in a two-dimensional Weyl system, composed of stacked Su-Schrieffer-Heeger (SSH) chains. A previous analysis of the model showed that the addition of an attractive Hubbard interaction between spinful electrons leads to a superconducting state that has an intricate pairing structure, but is topologically trivial. Here we consider a pairing interaction that couples spinless fermions on opposite sublattices within the same unit cell. We observe that this physically motivated, momentum-independent pairing interaction induces a topological superconducting state, characterized by a gap function with a nontrivial phase, as well as Majorana and Fermi arc edge states along the edge perpendicular to the direction of the SSH dimerization. In addition, we observe a transition as a function of pairing interaction strength and chemical potential, indicated by a change in the sign of the topological charge carried by each of the four Bogoliubov-Weyl nodes.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity.

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Studies related to changes in ionic strength due to addition of sodium chloride to an aqueous solution of cationic dye methylene blue (MB): Electronic spectra analysis for dimerization equilibria

It is well-known that methylene blue (MB),a cationic dye forms dimer and higher aggregates in aqueous solutions. For specific concentration range (1∙10−6–1∙10−4 M), a D⇌2M equilibria has been postulated and well characterized by visible electronic spectroscopy. The dye molecules can lead to formation of stacking (end on end and sandwich) type structures in solution phase stabilized by weak dispersion van der Waals forces and cation-anion-cation ion pairs and triplet interactions usually referred as hydrophobic interactions. Recent literature reports indicate that excess chemical potential of small hydrophobic particles and the strength of hydrophobic pair interactions appear to be linearly related. Our observations about precipitation of dye (MB) at higher concentrations of salt like sodium chloride (NaCl) made us to study the dimerization equilibria in detail since in the Corona health disaster; use of MB to diagnose the type of Covid variants helped Scientists in a great way. Salting-out of proteins is in general used to explain the specific protein aggregation behaviour observed in Huntington's disease. For model compound like tertiary butyl-alcohol, Geiger et al. reported enhancement of hydrophobic contacts which increase with increase in salt concentration. NaCl is an essential ingredient of biological fluids, of which concentration controls the various biological life governing processes. However, such information is non-existent for aqueous solutions of dyes.We therefore reported measured optical absorbance of aqueous solution containing NaCl (0.1–1.0 M) and dye at different concentrations (1∙10−6–1∙10−4 M) at 298 K spectrophotometrically, in the wavelength range of 550–700 nm. The spectrums are compared to those obtained for binary solutions of MB in water. Analysis of the spectral data yielded the dimer dissociation constant and individual characteristic monomer and dimer spectra. Further information about the geometry and twist angle between the dipoles of the MB molecules in the dimer species has been obtained. The results are analyzed for the monomer-dimer equilibria and salting-out effect as well applications of mass action model and exciton theories are discussed.

Fermi arcs and pseudogap phase in a minimal microscopic model of d -wave superconductivity

We show conclusively that a pseudogap state can arise at $T > T_c$, for reasonable pairing interaction strength, from order parameter fluctuations in a two dimensional minimal model of $d$-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest neighbor interaction and establish our result using a combination of cluster based Monte Carlo for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\sim 160 \times 160$ allows two major conclusions: (i)~at $T < T_c$, despite the presence of thermal phase fluctuations the superconductor has only nodal Fermi points while all non nodal points on the normal state Fermi surface show a two peak spectral function with a dip at $\omega =0$, and (ii)~for $T > T_c$ the Fermi points develops into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature $T^* > T_c$. We show the variation of $T_c$ and $T^*$ with coupling strength and provide detailed spectral results at a coupling where $T^* \sim 1.5T_c$.

Impact of pairing interactions on fission in the deformed mean-field plus standard pairing model

The role of pairing interactions on fission barriers and static fission paths in Th, U and Pu isotopes is investigated by using the deformed mean-field plus standard pairing model. It is found that pairing interaction plays different roles in different stages of the fission process. The first and second saddle point of the fission process are sensitive to the pairing interaction strength, while the ground-state and prescission points are mainly driven by nuclear deformation. It is also demonstrated that pairing interactions play a crucial role in the region of the inner and outer barriers. The barrier heights obtained by using the present model are found to reproduce the experimental data remarkably well and yield better results than those obtained by using the BCS approximation, thus indicating the importance of exact solutions of pairing interactions. Through numerical analysis, we provide possible microscopic pictures of spontaneous fission in the current pairing model.

Nuclear charge-exchange excitations based on a relativistic density-dependent point-coupling model

Spin-isospin transitions in nuclei away from the valley of stability are essential for the description of astrophysically relevant weak interaction processes. While they remain mainly beyond the reach of experiment, theoretical modeling provides important insight into their properties. In order to describe the spin-isospin response, the proton-neutron relativistic quasiparticle random phase approximation is formulated using the relativistic density-dependent point coupling interaction, and separable pairing interaction in both the $T=1$ and $T=0$ pairing channels. By implementing recently established DD-PCX interaction with improved isovector properties relevant for the description of nuclei with neutron-to-proton number asymmetry, the isobaric analog resonances (IAR) and Gamow-Teller resonances (GTR) have been investigated. In contrast to other models that usually underestimate the IAR excitation energies in Sn isotope chain, the present model accurately reproduces the experimental data, while the GTR properties depend on the isoscalar pairing interaction strength. This framework provides not only an improved description of the spin-isospin response in nuclei, but it also allows future large-scale calculations of charge-exchange excitations and weak interaction processes in stellar environment.

Strength of the isoscalar pairing interaction determined by a relation between double-charge change and double-pair transfer for double- β decay

A new method has been proposed to determine the strength of the isoscalar proton-neutron pairing interaction applicable to many nuclei. The principle is the equivalence between the double charge change and the double transfer of like-particle pair, and a constraint is derived to the effective interactions used in approximations. This method was applied to the quasiparticle random-phase approximation for determining that interaction strength. In this paper, detail of this method is explained thoroughly, and applications are made to nuclei of several instances of the double-$\beta$ decays. The systematics of the strengths determined for those nuclei is understood in terms of a midshell effect. The effect of the new interaction strength is examined in two examples of the Gamow-Teller strength function with comparisons with the experimental data. The nuclear matrix elements of the neutrinoless double-$\beta$ decay are also calculated.

Strength of pairing interaction for hyperons in multistrangeness hypernuclei

Pairing correlations play a very important role in atomic nuclei. Although several effective pairing interactions have been used in mean field calculations for nucleons, little is known about effective pairing interactions for hyperons. Based on the quark model, we propose a relationship between effective pairing interactions for hyperons and for nucleons; e.g., for Λs, the strength of the pairing interaction is 4/9 of that for nucleons. A separable pairing force of finite range which has been widely applied to describing pairing correlations in normal nuclei is used to investigate pairing effects in multi-Λ Ca, Sn and Pb hypernuclei.

Exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits

The exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits, which is an extension of the widely used standard (two-body) pairing model, is derived based on the Bethe–Richardson–Gaudin approach. The Bethe–Richardson–Gaudin equations in determining eigenstates and the corresponding eigen-energies of the model are provided and exemplified with up to three-pair interactions. With a suitable parameterization of the overall multi-pair interaction strengths, the model with one adjustable parameter and valence nucleons confined in the $$1d_{5/2}$$ and $$0g_{7/2}$$ orbits is applied to fit binding energies of $$^{102{\text {--}}112}$$Sn. It is shown that the ground-state occupation probabilities of nucleon pairs calculated from this model and those from the standard pairing model are almost the same with perfect ground-state overlap of the two models. A noticeable feature of the multi-pair interactions is that the even–odd staggering of pairing interaction strength appearing in the standard pairing model due to the Pauli-blocking is suppressed. As the result, the pairing interaction strength of the model only depends on the number of valence nucleon pairs in the system.

Aggregation Patterns in Low- and High-Charge Anions Define Opposite Solubility Trends.

Molecular dynamics simulations in aqueous solution reveal the existence of two distinct patterns of aggregation in low and high charge density Lindqvist-type polyoxometalates (POMs). Our results indicate the presence of contact and solvent-shared ion pairs and specific and preferential interactions of alkalis with POMs. Highly charged POMs are capable of breaking apart the Li+ and Cs+ solvation shell, thus enhancing the formation of long-lived alkali-POM contact ion pairs, where alkalis act as an electrostatic "glue" forming large oligomers. Stronger ion pair interactions for Li+ than for Cs+ promote lower solubility for Li+ than for Cs+, evoking anomalous solubility trends. Lower charge density POMs are not capable of disrupting the Li+ solvation shell and only solvent-shared ion pairs are formed, whereas for Cs+, contact ion pairs exist. The large number of oxygen atoms in the POM surface enhances the hydrogen bonds between POM and water, thus promoting aggregation. In this case, aggregation follows normal solubility trends. Thus, aggregation depends on the strength of ion pair interactions, the capacity of POM to disrupt alkali's solvation shell, and the contact surface area between the solvent and POM.

Postquench gap dynamics of two-band superconductors

Recent experimental progress in the fields of cold quantum gases and ultrafast optical spectroscopy of quantum materials allows to controllably induce and probe non-adiabatic dynamics of superconductors and superfluids. The time-evolution of the gap function before relaxation with the lattice is determined by the superposition of coherently evolving individual Cooper pairs within the manifold of the Bardeen-Cooper-Schrieffer (BCS) wavefunction. While dynamics following an abrupt quench of the pairing interaction strength in the single-band BCS model has been exactly solved due to the integrability of the model, the dynamics of post-quench multi-band superconductors remain under scrutiny. Here, we develop a generalization of the Volkov-Kogan Laplace-space perturbative method that allows us to determine the non-adiabatic gap dynamics of two-band fully gapped superconductors for a wide range of quench amplitudes. Our approach expands the long-time dynamics around the steady-state asymptotic value of the gap, which is self-consistently determined, rather than around the equilibrium value of the gap. We explicitly demonstrate that this method recovers the exact solution of the long-time gap dynamics in the single-band case and perfectly agrees with a numerical solution of the two-band model. We discover that dephasing of Cooper pairs from different bands leads to faster collisionless relaxation of the gap oscillation with a power-law of $t^{-3/2}$ instead of the well-known $t^{-1/2}$ behavior found in the single-band case. Furthermore, the gap oscillations display beating patterns arising from the existence of two different asymptotic gap values. Our results have important implications to a variety of two-band superconductors driven out of equilibrium, such as iron-based superconductors, MgB$_{2}$, and SrTiO$_{3}$.

Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double- β and β decays

We have proposed in a series of previous articles a method to determine the effective axial-vector current coupling and the strength of the isoscalar proton-neutron pairing interaction for calculating the nuclear matrix elements of the neutrinoless double-$\ensuremath{\beta}$ ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay by the quasiparticle random-phase approximation (QRPA). The combination of these two parameters has had an uncertainty in the QRPA approach, but now this uncertainty is removed by introducing a mathematical identity derived under the closure approximation to the nuclear matrix element of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay. In this article, we apply our method to the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decays of $^{136}\mathrm{Xe}$ and $^{130}\mathrm{Te}$ and show the nuclear matrix elements and reduced half-lives. Our calculation is tested first by a self-check method using the two-neutrino double-$\ensuremath{\beta}$ decay, and this test ensures the application of our method to $^{136}\mathrm{Xe}$. It turns out, however, that our method is not successful in $^{130}\mathrm{Te}$. Further tests are made for our calculation, and satisfactory results are obtained for $^{136}\mathrm{Xe}$.

Bounds on the Superconducting Transition Temperature: Applications to Twisted Bilayer Graphene and Cold Atoms

Understanding the material parameters that control the superconducting transition temperature $T_c$ is a problem of fundamental importance. In many novel superconductors, phase fluctuations determine $T_c$, rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multi-band systems, valid in any dimension. This in turn leads to an upper bound on $T_c$ in two dimensions (2D), which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrow-band systems, where mean field theory fails. For a simple parabolic band in 2D with Fermi energy $E_F$, we find that $k_BT_c \leq E_F/8$, an exact result that has direct implications for the 2D BCS-BEC crossover in ultra-cold Fermi gases. Applying our multi-band bound to magic-angle twisted bilayer graphene (MA-TBG), we find that band structure results constrain the maximum $T_c$ to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on $T_c$ in 3D.

Fate of superconductivity in disordered Dirac and semi-Dirac semimetals

The influence of weak disorder on the superconductivity in ordinary metals can be formally described by the Abrikosov-Gorkov diagrammatic approach. The vertex correction is ignored in this approach because an inequality kF l ≫ 1, where kF is the Fermi momentum and l mean free path, is satisfied in ordinary metals with a large Fermi surface. In a Dirac semimetal that has discrete Fermi points, this inequality may break down even for arbitrarily weak disorder since , and thus the vertex correction could be important. We incorporate the vertex correction into the self-consistent equations of the superconducting gap and the disorder scattering rate, and then apply the generalized approach to study how s-wave superconductivity is affected by random chemical potential in two- and three-dimensional Dirac semimetals, as well as two-dimensional semi-Dirac semimetal. In the clean limit, superconductivity is formed only when the pairing interaction strength is greater than some critical value in these materials. Adding random chemical potential to the system promotes superconductivity by generating a finite fermionic density of states at the Fermi level. In three-dimensional Dirac semimetal, the critical attraction strength is reduced by weak disorder, but remains finite. In the other two cases, superconductivity is induced by arbitrarily weak attraction. Including the vertex correction does not change these qualitative results, and actually could further promote superconductivity in the weak-attraction regime. Bilayer graphene is quite special in that its zero-energy density of states is nonzero despite the existence of Fermi points. Due to this peculiar property, superconductivity is always slightly suppressed by random chemical potential, and the impact of vertex correction is nearly negligible.

Ground-state shape evolution in Er and Yb isotopes

The ground-state shape (phase) evolution in Er and Yb isotopes is manifested in the axially deformed Nilsson mean-field plus extended pairing model. The energy ratio R02+/21+, the odd-even mass differences, the ground-state occupation probabilities of valence nucleon pairs with different angular momenta and the information entropy are calculated. It is shown from these quantities as functions of the quadrupole deformation parameter and the overall pairing interaction strength that the ground-state shape (phase) evolution is mainly driven by the pairing interaction and less affected by the quadrupole deformation, which thus provides a possible origin of the ground-state shape (phase) evolution of these isotopes.