Singlet Pairing Research Articles

Odd-frequency pairing effect on the superfluid density and the Pauli spin susceptibility in spatially nonuniform spin-singlet superconductors

A theoretical study is presented on the odd-frequency spin-singlet pairing that arises in nonuniform even-frequency superconductors as a consequence of broken translation symmetry. The effect of the odd-frequency pairing on the superfluid density and the spin susceptibility is analyzed by using the quasiclassical theory of superconductivity. It is shown that (1) the superfluid density is reduced by the formation of the odd-frequency singlet pairs and (2) the odd-frequency pairing increases the spin susceptibility even though its spin symmetry is singlet. The two unusual phenomena are related to each other through a generalized Yosida formula by taking into account both the even- and odd-frequency pairing effects.

Ginzburg–Landau Description of Twin Boundaries in Noncentrosymmetric Superconductors

We study theoretically a model for twin boundaries in superconductors with Rashba spin-orbit coupling, which can be relevant to both three-dimensional noncentrosymmetric tetragonal crystals and two-dimensional gated superconductors such as the LaAlO$_3$/SrTiO$_3$ interface. In both cases, the broken inversion symmetry allows for a coexistence of singlet and triplet pairing. Within the framework of a Ginzburg-Landau theory, we identify two $\mathbb{Z}_2$ symmetries that are broken via two consecutive second order phase transitions as the temperature is lowered. We show that a time-reversal symmetry breaking superconducting state nucleates near the twin boundary if singlet and triplet pairing amplitudes are of comparable magnitude. As a consequence, the tendency towards ferromagnetic order is locally increased along with the emergence of spontaneous supercurrents parallel to the twin boundary. Spin currents, which are present in the form of Andreev bound states, are found enhanced in the time-reversal broken phases.

Tuning between singlet, triplet, and mixed pairing states in an extended Hubbard chain

We study spin-half fermions in a one-dimensional extended Hubbard chain at low filling. We identify three triplet and one singlet pairing channels in the system, which are independently tunable as a function of nearest-neighbor charge and spin interactions. In a large-size system with translational invariance, we derive gap equations for the corresponding pairing gaps and obtain a Bogoliubov--de Gennes Hamiltonian with its nontrivial topology determined by the interplay of these gaps. In an open-end system with a fixed number of particles, we compute the exact many-body ground state and identify the dominant pairing revealed by the pair density matrix. Both cases show competition between the four pairing states, resulting in broad regions for each of them and relatively narrow regions for mixed-pairing states in the parameter space. Our results enable the possibility of tuning a nanowire between singlet and triplet pairing states without breaking time-reversal or $\text{SU}(2)$ symmetry, accompanied by a change in the system's topology.

Triplet pair correlations and nonmonotonic supercurrent decay with Cr thickness in Nb/Cr/Fe/Nb Josephson devices

Supercurrents carry charge but not spin in the vast majority of superconductors. This is because the charge carriers are Cooper pairs which are formed of electrons with antiparallel spins (singlet pairs). It is now established that if singlet pairs propagate through a superconductor interface with an inhomogeneous ferromagnet, triplet pair correlations form so the supercurrents can acquire a net spin component. Although the spins at sputter-deposited Fe/Cr interfaces can be frustrated due to surface roughness and interdiffusion, an antiferromagnetic spin density wave (SDW) state can still form in Cr close to the interface. Here, we show evidence for triplet pair correlations in Josephson junctions with Cr/Fe and Cr/Fe/Cr barriers. Although the exact mechanism of pair conversion is unknown, we propose a simple model in which a SDW state in Cr and frustrated spins at the Cr/Fe interfaces serve as spin-mixers for generating triplet supercurrents and so provide a potential means to generating large superconducting spin current densities.

Microscopic theory of the optical properties of colloidal graphene quantum dots

We present a microscopic theory of electronic and optical properties of colloidal graphene quantum dots (CGQDs). The single-particle properties are described in the tight-binding model based on the ${p}_{z}$ carbon orbitals. Electron-electron screened Coulomb direct, exchange, and scattering matrix elements are calculated using Slater ${p}_{z}$ orbitals. The many-body ground state and excited states are constructed as a linear combination of a finite number of excitations from the Hartree-Fock (HF) ground state (GS) by exact diagonalization techniques. HF ground states corresponding to semiconductor, Mott-insulator, and spin-polarized phases are obtained as a function of the strength of the screened interaction versus the tunneling matrix element. In the semiconducting phase of a triangular CGQD, the top of the valence band and the bottom of the conduction band are found to be degenerate due to rotational symmetry. The singlet and triplet exciton spectra from the HF GS are obtained by solving the Bethe-Salpeter equation. The low-energy exciton spectrum is predicted to consist of two bright-singlet exciton states corresponding to two circular polarizations of light and a lower-energy band of two dark singlets and 12 dark triplets. The robustness of the bright degenerate singlet pair against correlations in the many-body state is demonstrated as well as the breaking of the degeneracy by the lowering of symmetry of the CGQD. The band-gap renormalization, electron-hole attraction, fine structure, oscillator strength, and polarization of the exciton are analyzed as a function of the size, shape, screening, and symmetry of the CGQD. The theoretical results are compared with experimental absorption spectra.

Annihilation of Colliding Bogoliubov Quasiparticles Reveals their Majorana Nature

The single-particle excitations of a superconductor are coherent superpositions of electrons and holes near the Fermi level, called Bogoliubov quasiparticles. They are Majorana fermions, meaning that pairs of quasiparticles can annihilate. We calculate the annihilation probability at a beam splitter for chiral quantum Hall edge states, obtaining a 1±cosϕ dependence on the phase difference ϕ of the superconductors from which the excitations originated (with the ± sign distinguishing singlet and triplet pairing). This provides for a nonlocal measurement of the superconducting phase in the absence of any supercurrent.

Ferromagnetism and Borromean Binding in Three-Fermion Clusters

A three-particle spin-12 fermion problem with on-site repulsion and nearest-neighbor attraction is solved on the two-dimensional square lattice by discretizing a Schrödinger equation in momentum space. Energies of bound complexes (trions) and their binding conditions are obtained. For total spin S=1/2, a wide region of trion instability toward decaying into a stable singlet pair plus a free fermion is identified. The instability is attributed to the formation of a wave function node upon addition of the third fermion. In the S=3/2 sector, trions are found to form in the absence of bound pairs indicating Borromean binding. In the strong coupling limit the system transitions from an S=1/2 ground state to a ferromagnetic S=3/2 ground state in agreement with the Nagaoka theorem for a four-site plaquette.

Higgs phenomenology in the two-singlet model

We study the phenomenology of the Standard Model (SM) Higgs sector extended by two singlet scalars. The model predicts two CP-even scalars $h_{1,2}$ which are a mixture of doublet and singlet components as well as a pure singlet scalar $S_{0}$ which is a dark matter candidate. We show that the model can satisfy the relic density and direct detection constraints as well as all the recent ATLAS and CMS measurements. We also discuss the effect of the extra Higgs bosons on the different Higgs triple couplings $h_{i}h_{j}h_{k}$, $i,j,k=1,2$. A particular attention is given to the triple self-coupling of the SM-like Higgs where we found that the one loop corrections can reach $150\%$ is some cases. We also discuss some production mechanisms for $h_{1}$ and $h_{2}$ at the LHC as well as at the future International Linear Collider. It is found that the production cross section of a pair of SM-like Higgs bosons could be much larger than the corresponding one in the SM and would reveal physics beyond the SM if observable. We also show that in this model the branching ratio of the SM-like Higgs decaying to two singlet scalars could be of the order of $20\%$, therefore the production of the SM Higgs followed by its decay to a pair of singlets would be an important source of production of singlet scalars.

Odd parity pairing and nodeless antiphases±in iron-based superconductors

We discuss the sign change of superconducting order parameters in both real and reciprocal spaces when the odd parity spin singlet pairing proposed recently in\cite{huoddparity} is allowed. We show that in this case an nodeless anti-phase $s^\pm$ can be generated. In a 2-Fe Brilliouin zone (BZ), sign change exists between two hole pockets and between two electron pockets. In a 1-Fe BZ which includes two 2-Fe BZs, the sign change is between two 2-Fe BZs, which leads to a d-wave type sign distribution on the electron pockets, namely, an anti-phase $s^\pm$ state with no symmetry protected gapless node on the electron pockets. This sign change character consistently explains experimental results related to sign change properties measured on both iron-pnictides and iron-chalcogenides.

Spin susceptibility in superconducting LiFeAs studied by polarized neutron diffraction

The local spin susceptibility in superconducting LiFeAs was studied by polarized neutron diffraction as a function of temperature. In the superconducting phase the spin susceptibility is clearly suppressed and it can be well described by the Yosida function suggesting a singlet pairing to occur at low temperature. The spin susceptibility in the normal state and its suppression in the superconducting phase are fully comparable to observations in Co-doped BaFe${}_{2}$As${}_{2}$.

The Role of Central Microtubules in the Beating of Eukaryotic Flagella, Revealed by High-Speed Holographic Microscopy

Understanding the mechanics of the eukaryotic flagellum is a key challenge in biophysics. As well as being of scientific interest, there are clear therapeutic applications, not least in reproductive medicine. The axoneme lies at the heart of the flagellum, and its structure is known: nine microtubule doublets surround a central pair of microtubule singlets. The role of the central pair in this canonical ‘9+2’ arrangement has been the subject of speculation for some time, though they are known to assist in regulating the flagellar beat. Our group has developed high-speed holographic microscopy that allows us to numerically refocus a digital image off-line. By generating a stack of refocused images from each frame in a video, we obtain scans of the sample volume at the frame rate of our video camera. Effectively, this allows us to image 500-1000 volumes per second. By analyzing this volumetric data, we can measure the waveform of a eukaryotic flagellum to within 200 nm in three dimensions, and with millisecond time resolution. We have previously used this method to measure the waveform of a naturally occurring, isolated flagellum: the microgamete of the rodent malaria parasite Plasmodium berghei. In order to assess the role of the central pair, we take advantage of a newly-available mutant strain that is lacking one or both central microtubules. By comparing the three-dimensional shape and movement observed in mutant flagella to that in the wild-type, we can get some insight into how the central pair helps to regulate the beating action.

Robustness of Spin-Triplet Pairing and Singlet–Triplet Pairing Crossover in Superconductor/Ferromagnet Hybrids

We have investigated the proximity effect in superconductor/ferromagnet junctions in a systematic manner to discuss the relationship between the zero-energy peak (ZEP) of the local density of states (LDOS) and spin-triplet odd-frequency pairing. By exactly solving the nonlinear Usadel equations, we have found that the ZEP is realized in a wide range of geometrical and material parameters in the case of the noncollinear magnetization. This strongly suggests the robustness of the ZEP induced by spin-triplet odd-frequency pairing in such systems. We also found that the crossover from singlet pairing to triplet pairing can be detected by measuring the F layer thickness dependence of the ZEP height. Furthermore, we show how to observe signatures of spin-triplet odd-frequency pairing and the pairing crossover by LDOS measurement. Our results provide a direct way to experimentally detect signatures of the odd-frequency pairing state.

Early morphogenesis of ciliated cells in human oral cavity

Ciliated cells were found in the epithelium of the oral cavity of human embryos and fetuses starting from the seventh week of prenatal development. At the early stages of prenatal development (until the 13th week), cells with cilia cover most of the dorsal surface of the tongue and the soft palate, whereas they are found only near the gland ducts in the circumvallate and foliate lingual papillae after 17 weeks of development. The ultrastructure of the axoneme of cilia corresponds to the structure of motile cilia and is represented by nine microtubule doublets that surround the central pair of microtubule singlets. An immunohistochemical study performed on weeks 10-12 of development identified nerve endings associated with the ciliated cells. Until the 14th week of development, the cytoplasm of ciliated cells is immunopositive for NSE. The spatial distribution of ciliated cells in the tongue epithelium until the 13th week of development is not related to the morphogenesis of lingual papillae, and their role in the human oral cavity during the first trimester of pregnancy is unclear and requires further study.

Triplet recombination of radical ion pairs: CIDNP effects and DFT calculations on 1,2-dicyanoethylene

Radical ion pairs generated by electron transfer from photo-excited aromatic hydrocarbons to maleo- and fumaronitrile (cis- and trans-1,2-dicyanoethylene, 1) undergo back electron transfer from singlet and triplet pairs. The pair energies relative to the reactant ground states and to the triplet state, respectively, determine the competition between the recombination pathways. Cross sections through the potential surfaces of the radical anion and the triplet state of 1 have been examined by density functional theory calculations. The radical anion surface has minima in which the carbon and nitrogen skeleton is essentially planar; the central C-C bond is lengthened (weakened), but the barrier to geometric isomerization is still sizeable (31.2 kcal mol(-1)). The triplet energy surface has a minimum at a bisected geometry (plus its enantiomer); rotation of the H-C-CN segments of the triplet yields a syn-periplanar and an anti-periplanar point 9.3 kcal mol(-1) and 8.2 kcal mol(-1) above the minimum, respectively.

Unconventional superconductivity in a two-dimensional repulsive gas of fermions with spin–orbit coupling

We investigate the superconducting instability of a two-dimensional repulsive Fermi gas with Rashba spin–orbit coupling αR. Using renormalization group approach, we find the superconducting transition temperature as a function of the dimensionless ratio Θ=12mαR2/EF where EF=0 when the smaller Fermi surface shrinks to a (Dirac) point. The general trend is that superconductivity is enhanced as Θ increases, but in an intermediate regime Θ∼0.1, a dome-like behavior appears. At a very small value of Θ, the angular momentum channel jz in which superconductivity occurs is quite high. With increasing Θ, jz decreases with a step of 2 down to jz=6, after which we find the sequence jz=6, 4, 6, 2, the last value of which continues to Θ→∞. In an extended range of Θ, the superconducting gap predominantly resides on the large Fermi surface, while Josephson coupling induces a much smaller gap on the small Fermi surface. Below the superconducting transition temperature, we apply mean field theory to derive the self-consistent equations and find the condensation energies. The state with the lowest condensation energy is an unconventional superconducting state which breaks time-reversal symmetry, and in which singlet and triplet pairings are mixed. In general, these states are topologically nontrivial, and the Chern number of the state with total angular momentum jz is C=2jz.

Decaying asymmetric dark matter relaxes the AMS-Fermi tension

The first result of AMS-02 confirms the positron fraction excessobserved by PAMELA, but the spectrum is somewhat softer than that ofPAMELA. In the dark matter (DM) interpretation it brings a tensionbetween AMS-02 and Fermi-LAT, which reported an excess of theelectron plus positron flux. In this work we point out that theasymmetric cosmic ray from asymmetric dark matter (ADM) decayrelaxes the tension. It is found that in the case of two-body decaya bosonic ADM around 2.4 TeV and decaying into μ−τ+ cansignificantly improve the fits. Based on the R−parity-violatingsupersymmetry with operators LLEc, we propose a minimal model torealize that ADM. The model introduces only a pair of singlets(X,X̄) with a tiny coupling LHuX, which makes the ADM sharethe lepton asymmetry and decay into μ−τ+ along the operatorLLEc.

Theory of superfluid states with singlet and triplet types of pairing in nuclear matter

This paper presents the results of investigation of the superfluid states in a two-component Fermi liquid within the framework of the Fermi liquid approach. Particular attention is paid to the superfluid states in nuclear matter which are characterized by the superposition of singlet and triplet types of pairing in spin and isospin spaces. The fundamental principles of the Fermi liquid approach are formulated and further used in the study of superfluidity in nuclear matter with the superposition of singlet and triplet types of pairing. The system of self-consistency equations is derived and its solutions are presented. The conditions of existence of the considered states are determined. These conditions impose certain constraints on the interaction potential and particle density in the system. It is shown that the states with a complete set of nonzero order parameters are realized only in a narrow density range, the width and position of which on the density scale depend on the actual parametrization of the Skyrme potential employed. We considered 18 different parameterizations and indicated for which of them the studied types of superfluid states may appear. The problem of stability of the states with the superposition of singlet and triplet pairing is studied. It is shown that the lowest value of the thermodynamic potential corresponds to purely triplet states. Then, in the order of increasing, follow the thermodynamic potentials of purely singlet states and mixed singlet-triplet states. Separately, we consider the case of unitary states, for which the solutions of the self-consistency equations are also analyzed. It is shown that the density range in which such states can be realized is different from that corresponding to the nonunitary states. The problem of existence of the unitary superfluid states with the superposition of singlet and triplet superfluidity is considered in the case of asymmetrical nuclear matter. It is shown that the appearance of asymmetry in nuclear matter breaks the unitarity of superfluid states in nuclear matter with regard to isospin.

Time-Resolved Magnetic Field Effects Distinguish Loose Ion Pairs from Exciplexes

We describe the experimental investigation of time-resolved magnetic field effects in exciplex-forming organic donor–acceptor systems. In these systems, the photoexcited acceptor state is predominantly deactivated by bimolecular electron transfer reactions (yielding radical ion pairs) or by direct exciplex formation. The delayed fluorescence emitted by the exciplex is magnetosensitive if the reaction pathway involves loose radical ion pair states. This magnetic field effect results from the coherent interconversion between the electronic singlet and triplet radical ion pair states as described by the radical pair mechanism. By monitoring the changes in the exciplex luminescence intensity when applying external magnetic fields, details of the reaction mechanism can be elucidated. In this work we present results obtained with the fluorophore-quencher pair 9,10-dimethylanthracene/N,N-dimethylaniline (DMA) in solvents of systematically varied permittivity. A simple theoretical model is introduced that allows discriminating the initial state of quenching, viz., the loose ion pair and the exciplex, based on the time-resolved magnetic field effect. The approach is validated by applying it to the isotopologous fluorophore-quencher pairs pyrene/DMA and pyrene-d10/DMA. We detect that both the exciplex and the radical ion pair are formed during the initial quenching stage. Upon increasing the solvent polarity, the relative importance of the distant electron transfer quenching increases. However, even in comparably polar media, the exciplex pathway remains remarkably significant. We discuss our results in relation to recent findings on the involvement of exciplexes in photoinduced electron transfer reactions.

Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap

We propose the density-functional theory for one-dimensional harmonically trapped spin-1 bosons in the ground state with repulsive density-density interaction and anti-ferromagnetic spin-exchange interaction. The density distributions of spin singlet paired bosons and polarized bosons with different total polarization for various interaction parameters are obtained by solving the Kohn-Sham equations which are derived based on the local density approximation and the Bethe ansatz exact results for homogeneous system. Non-monotonicity of the central densities is attributed to the competition between the density interaction and spin-exchange. The results reveal the phase separation of the paired and polarized bosons, the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction. We give the R-P phase diagram at strong interaction and find the critical polarization, which paves the way to direct observe the exotic singlet pairing in spinor gas experimentally.

Entanglement spectrum and entangled modes of randomXXspin chains

We study in this work the ground state entanglement properties of finite XX spin-1/2 chains with random couplings, using Jordan-Wigner transformation. We divide the system into two parts and study reduced density matrices (RDMs) of its subsystems. Due to the free-fermion nature of the problem, the RDMs take the form of that of a free fermion thermal ensemble. Finding spectrum of the corresponding entanglement Hamiltonian and corresponding eigenvectors, and comparing them with real space renormalization group (RSRG) treatment, we establish the validity of the RSRG approach for entanglement in the limit of strong disorder, but also find its limitations when disorder is weak. In the latter case our work provides a way to visualize the "effective spins" that form long distance singlet pairs.