Triplet Component Research Articles

Influence of a Feshbach resonance on the photoassociation of LiCs

We analyze the formation of ultracold 7Li133Cs molecules in the rovibrational ground state through photoassociation into the B1Π state, which has recently been reported (Deiglmayr et al 2008 Phys. Rev. Lett. 101 133004). Absolute rate constants for photoassociation at large detunings from the atomic asymptote are determined and are found to be surprisingly large. The photoassociation process is modeled using a full coupled-channel calculation for the continuum state, taking all relevant hyperfine states into account. The enhancement of the photoassociation rate is found to be caused by an ‘echo’ of the triplet component in the singlet component of the scattering wave function at the inner turning point of the lowest triplet a3Σ+ potential. This perturbation can be ascribed to the existence of a broad Feshbach resonance at low scattering energies. Our results elucidate the important role of couplings in the scattering wave function for the formation of deeply bound ground state molecules via photoassociation.

Competition between triplet, singlet and FFLO states in organic superconductors (TMTSF)2X under magnetic field

We study the competition between triplet f-wave, singlet d-wave, and the FFLO state in a model for (TMTSF)2X using random phase approximation. The result suggests the possibility of the singlet→FFLO→triplet transition upon increasing the magnetic field. We also show that the triplet component mixing increases in the FFLO state with increasing the magnetic field, and the off-site repulsions increase the mixing rate. The results seem to suggest that the large triplet mixing results in an enhanced tendency toward the FFLO state over the usual pairing state.

Cooper pairs with broken time-reversal, parity, and spin-rotational symmetries in singlet type-II superconductors

We show that singlet superconductivity in the Abrikosov vortex phase is absolutely unstable with respect to the appearance of a chiral triplet component of a superconducting order parameter. This chiral component, p_x + i p_y, breaks time-reversal, parity, and spin rotational symmetries of the internal order parameter, responsible for a relative motion of two electrons in the Cooper pair. We demonstrate that the symmetry breaking Pauli paramagnetic effects can be tuned by a magnetic field strength and direction and can be made of the order of unity in organic and high-temperature layered superconductors.

Electrical Transport Study of Patterned Lateral Niobium-Permalloy Junctions

In order to investigate the interplay between magnetic domain walls and superconductivity we study the electrical transport property of lateral Nb-permalloy-Nb junctions where the permalloy thickness is varied from 50 to 90 nm. Magnetic force microscopy images confirm the presence of domain walls in the ferromagnetic portion between the two superconducting electrodes for samples with permalloy thickness of 60, 70 and 90 nm. Below superconducting transition temperature, the zero bias conductance (ZBC) for these samples shows a sharp reduction in the magnetic field range of 0 to 0.15 T and after that it stays almost at a constant level until a high field is applied. The phenomenon is attributed to domain wall assisted crossed Andreev reflection (CAR) and/or long range triplet component (LRTC) of superconductivity. On the contrary, the decreasing trend of ZBC at low field is absent for the sample with 50 nm thick NiFe which indicates that the conductance contribution from CAR and/or LRTC is absent in this sample. This is presumably due the fact that the permalloy in the gap region for this sample is in a single domain state. A quantitative analysis for conductance contribution from domain wall assisted CAR is provided.

Competition between triplet, singlet, and FFLO states in organic superconductors (TMTSF)2X under magnetic field

We study the competition between triplet f-wave, singlet d-wave, and the FFLO state in a model for (TMTSF)2X using random phase approximation. The result suggests the possibility of singlet →FFLO→triplet transition upon increasing the magnetic field. The singlet →FFLO→triplet transition can appear in a large parameter regime on the space of the magnetic field and the off-site repulsions which induce the coexistence with 2kF charge and 2kF spin fluctuations, although decreasing the off-site repulsions suppresses the spin triplet f-wave pairing. We also show that the triplet component mixing increases in the FFLO state with increasing the magnetic field, and the off-site repulsions increase the mixing rate. The results seem to suggest that the large triplet mixing results in an enhanced tendency toward the FFLO state over the usual pairing state.

Odd triplet superconductivity in a superconductor/ferromagnet structure with a narrow domain wall

We study proximity effect in superconductor/ferromagnet (SF) structure with a narrow domain wall (DW) at the SF interface. The width of the domain wall is assumed to be larger than the Fermi wavelength but smaller than other characteristic lengths (for example, the ``magnetic'' length). The transmission coefficient is supposed to be small so that we deal with a weak proximity effect. Solving the linearized Eilenberger equation, we find analytical expressions for quasiclassical Green's functions. These functions describe the short-range (SR) condensate components, singlet and triplet, with zero projection of the total spin on the quantization $z$ axis, induced in ferromagnet (F) due to the proximity effect as well as long-range odd triplet component (LRTC) with a nonzero projection of the total spin of Cooper pairs on the $z$ axis. The amplitude of the LRTC essentially depends on the product $h\ensuremath{\tau}$ and increases with increasing the exchange energy $h$ ($\ensuremath{\tau}$ is the elastic-scattering time). We calculate the Josephson current in superconductor/ferromagnet/superconductor junction with a thickness of the F layer much greater than the penetration length of the SR components. The Josephson critical current caused by the LRTC may be both positive and negative depending on chirality of the magnetic structure in F. The density of states (DOS) in a diffusive SF bilayer is also analyzed. It is shown that the contributions of the SR and LR components to the DOS in F have a different dependence on the thickness $d$ of the F layer (nonmonotonous and monotonous).

Signature of superconducting states in cubic crystal without inversion symmetry

The effects of the absence of inversion symmetry on superconducting states are investigated theoretically. In particular, we focus on the noncentrosymmetric compounds that have the cubic symmetry $O$ like ${\mathrm{Li}}_{2}{\mathrm{Pt}}_{3}\mathrm{B}$. An appropriate and isotropic spin-orbital interaction is added in the Hamiltonian, and it acts like a magnetic monopole in the momentum space. The consequent pairing wave function has an additional triplet component in the pseudospin space, and a Zeeman magnetic field $\mathbf{B}$ can induce a collinear supercurrent $\mathbf{J}$ with a coefficient $\ensuremath{\kappa}(T)$. The effects of anisotropy embedded in the cubic symmetry and the nodal superconducting gap function on $\ensuremath{\kappa}(T)$ are also considered. From the macroscopic perspectives, the pair of mutually induced $\mathbf{J}$ and magnetization $\mathbf{M}$ can affect the distribution of magnetic field in such noncentrosymmetric superconductors, which is studied through solving the Maxwell equation in the Meissner geometry as well as the case of a single vortex line. In both cases, magnetic fields perpendicular to the external ones emerge as a signature of the broken symmetry.

Triplet pairing and upper critical field in the mixed state ofd-wave superconductors

We show that an additional triplet component of the order parameter is generated in the vortex phase of the $d$-wave superconductor. Spatial variations of the triplet component are analyzed for a strong spin-orbit coupling. Corrections to the London equation and an unusual temperature dependence of the upper critical field ${H}_{c2}(T)$ are obtained in the case of the weak spin-orbit coupling.

Spin orbit scattering effect on long-range odd frequency triplet pairing in ferromagnet/superconductor bilayers

A formulation of triplet proximity effect in a ferromagnet/superconductor bilayer based on the de Gennes correlation function method is presented by extending the Takahashi–Tachiki theory. The inhomogeneous in-plane spiral magnetic order is employed in this approach the superconducting order parameter is a conventional spin singlet s-wave pairing, and the induced triplet pair amplitude arises as a result of the broken time-reversal invariance due to the presence of the rotating exchange field. A new type of triplet condensate still possesses the s-wave state but the symmetry requires an odd frequency parity. We find that the inhomogeneous exchange interaction leads to the appearance of the long-range odd frequency triplet pair amplitude, and the inclusion of the spin orbit scattering affects both short-range and long-range triplet components. The superconducting critical temperature of the diffusive ferromagnet/superconductor sandwiches is determined from the secular equation of the linearized gap equation in order to investigate the behavior of the induced triplet pairing. It is found that the induced long-range triplet component exists which arises from the modulation of the in-plane pair amplitudes in the transverse direction. Moreover, the possibility of the cryptoferromagnetic state is demonstrated in favor of superconductivity and this may explain a possible origin of the magnetically dead layer.

Odd triplet superconductivity in superconductor ferromagnet structures: a survey

We review the main features of odd triplet superconductivity in superconductor-ferromagnet (S/F) structures. We discuss the different types of superconducting condensate that can be experimentally observed and pay special attention to the triplet component induced in a ferromagnet which is in contact with a superconductor. The triplet component is an even function of the momentum and an odd function of the frequency and leads to novel phenomena.

Enhanced triplet superconductivity in noncentrosymmetric systems

We study pairing symmetry of noncentrosymmetric superconductors based on the extended Hubbard model on the square lattice near half-filling, using the random phase approximation. We show that $d+f$-wave pairing is favored and the triplet $f$-wave state is enhanced by Rashba-type spin-orbit coupling originating from the broken inversion symmetry. The enhanced triplet superconductivity stems from the increase of the effective interaction for the triplet pairing and the reduction of the spin susceptibility caused by the Rashba-type spin-orbit coupling which lead to the increase of the triplet component and the destruction of the singlet one, respectively.

He-like Ar xvii triplet observed by RESIK

We present the observations of He-like Ar triplet lines obtained by RESIK spectrometer aboard CORONAS-F. Interpretation of intensity ratios between triplet lines of lower Z elements is known to provide useful diagnostics of plasma conditions within the emitting source. Here, we investigate whether triplet line ratios are useful for interpretation of higher Z element spectra. A high sensitivity, low background and precise absolute calibration of RESIK allow to consider in addition also the continuum contribution. This provides a way to determine the Ar absolute abundance from the observed triplet component ratios. The method is presented and the results are shown for two selected flares. Derived values of Ar absolute abundance for these flares are found to be similar: 2.6 × 10 −6 and 2.9 × 10 −6. They fall in the range between presently accepted Ar photospheric and coronal abundances.

Josephson effect due to the long-range odd-frequency triplet superconductivity inSFSjunctions with Néel domain walls

We consider a SFS Josephson junction made of two superconductors S and a multidomain ferromagnet F with an in-plane magnetization. We assume that the neighboring domains of the ferromagnet are separated by Neel domain walls. An odd-frequency triplet long-range component of superconducting correlations arises in the domain walls and spreads into the domains over a long distance of the order $\xi_T = \sqrt{D / 2 \pi T}$, where $D$ is the diffusion coefficient (dirty limit is implied). We calculate the contribution of this component to the Josephson current in the situation when conventional short-range components exponentially decay over the thickness of the F layer and can be neglected. In the limit when the thickness of the F layer is much smaller than the penetration length of the long-range component, we find that the junction is in the $\pi$ state. We also analyze a correction to the density of states due to the long-range triplet component.

Superconducting critical temperature and singlet and triplet pair functions of superconductor/normal-metal/ferromagnet trilayers

We calculate the superconducting critical temperature ${T}_{c}$, the singlet pair function ${\ensuremath{\Psi}}^{+}(x)$, and triplet pair function ${\ensuremath{\Psi}}^{\ensuremath{-}}(x)$ of superconductor/normal-metal/ferromagnet $(S∕N∕F)$ trilayers using the linearized Usadel equation near ${T}_{c}$. The Green's function method developed by Fominov et al. for the $S∕F$ bilayers is extended to the $S∕N∕F$ trilayer systems. The $S$ of the trilayers is taken to be an $s$-wave singlet pairing superconductor, and the $S∕N$ and $N∕F$ interfaces are modeled in terms of the interface resistances parametrized, respectively, by ${\ensuremath{\gamma}}_{b}^{SN}$ and ${\ensuremath{\gamma}}_{b}^{NF}$. We present the ${T}_{c}$, ${\ensuremath{\Psi}}^{+}(x)$, and ${\ensuremath{\Psi}}^{\ensuremath{-}}(x)$ for typical ${\ensuremath{\gamma}}_{b}^{SN}$, ${\ensuremath{\gamma}}_{b}^{NF}$, and the exchange energy ${E}_{\mathit{ex}}$: (a) For a small (large) ${\ensuremath{\gamma}}_{b}^{NF}$, ${T}_{c}$ of $S∕N∕F$ trilayers, as ${d}_{N}$ is increased, increases (decreases) on the length scale of $N$ coherence length ${\ensuremath{\xi}}_{N}$ with a discontinuity at ${d}_{N}=0$ due to a boundary condition mismatch. (b) ${T}_{c}({d}_{F})$ shows a nonmonotonic behavior like $S∕F$ bilayers with a weakened shallow dip. (c) The odd frequency triplet component ${\ensuremath{\Psi}}^{\ensuremath{-}}(x)$, induced by ${E}_{\mathit{ex}}$ and proximity effects, has a maximum near the $N∕F$ interface and decreases on the length scale ${\ensuremath{\xi}}_{\mathit{ex}}$ in $F$. It also penetrates into $N$ and $S$ regions on the length scale ${\ensuremath{\xi}}_{N}$ and ${\ensuremath{\xi}}_{S}$, respectively. Based on these results we make comments on the experimental observation of the odd triplet components and the recent ${T}_{c}$ measurements in $\mathrm{Nb}∕\mathrm{Au}∕\mathrm{Co}\mathrm{Fe}$ trilayer systems.

Nonuniform Mixed-Parity Superfluid State in Fermi Gases

We study the effects of dipole interaction on the superfluidity in a homogeneous Fermi gas with population imbalance. We show that the Larkin-Ovchinnikov-Fulde-Ferrell phase is replaced by another nonuniform superfluid phase, in which the order parameter has a nonzero triplet component induced by the dipole interaction.

Thymine-substituted nitronyl nitroxide biradical as a triplet ( S = 1) component for bio-inspired molecule-based magnets

As a novel crystal engineering approach to organic molecule-based magnets, we have proposed a strategy of bio-inspired molecular assemblage based on intermolecular hydrogen bonding. Complementary hydrogen bonding between nucleobases as found in DNA is a promising non-covalent interaction for controlling the molecular arrangement of open-shell building block molecules. The hydrogen bonding of complementary nucleobases substituted with radical entities of different spin quantum numbers S, e.g., S = 1 and S = 1/2, gives rise to a heteromolecular aggregation of the S = 1 and S = 1/2 entities, leading to organic ferrimagnetics. In this study, we have designed and synthesized a thymine-substituted nitronyl nitroxide biradical ( 1) as a triplet ( S = 1) component for the bio-inspired ferrimagnetic system. The molecular ground state of 1 has been found to be triplet ( S = 1) with a singlet–triplet energy gap of 2 J/ k B = 21.4 K from magnetic susceptibility measurements. It has been found from X-ray structure analyses that the molecules form hydrogen-bonded aggregates in the crystalline solid state, in which the thymine moiety plays a primary role in the molecular packing. The ground-state triplet biradical serves as an S = 1 building block for bio-inspired molecule-based magnets with hydrogen-bonded nucleobase pairings.

Diagonal perturbative triple corrections to the general‐model‐space state‐universal coupled‐cluster method: Are they warranted and useful?

The recently developed general‐model‐space (GMS) state‐universal (SU) coupled‐cluster (CC) approach, together with its version corrected for triples via a single‐reference (SR) CCSD(T)‐type correction of the diagonal elements of the effective Hamiltonian, is applied to several molecular electronic structure problems in order to assess their performance and the role of triples. These results are compared with an alternative handling of higher‐than‐pair clusters via the externally corrected SU CCSD method, denoted (M,N)‐CCSD, which employs N wave functions of the M‐reference CISD as an external source for N‐reference SU CCSD. These methods are applied to the problem of bond breaking in the ground and excited states of the F2 and HF molecules, where the high‐spin triplet component is also handled via the SR CCSD method. We further examine the vertical excitation energies of water and the basic spectroscopic constants (equilibrium geometries, harmonic frequencies, and excitation energies) for several low‐lying states of oxygen. The results are encouraging and are discussed from the viewpoint of the applicability and usefulness of perturbative‐type triple corrections.

Superconducting Phase Coherent Electron Transport in Proximity Conical Ferromagnets

We report superconducting phase-periodic conductance oscillations in ferromagnetic wires with interfaces to conventional superconductors. The ferromagnetic wires were made of Ho, a conical ferromagnet. The distance between the interfaces was much larger than the singlet superconducting penetration depth. We explain the observed oscillations as due to the long-range penetration of an unusual helical triplet component of the order parameter that is generated at the superconductor/ferromagnet interfaces and maintained by the intrinsic rotating magnetization of Ho.

Type-IV Superconductivity: Can Superconductivity be more Exotic than Unconventional?

Abrikosov vortex phase in s-wave layered superconductor in a parallel magnetic field is shown to be absolutely unstable with respect to the appearance of a triplet component which breaks inversion (parity) and spin-rotational symmetries of Cooper pairs. Symmetry breaking paramagnetic effects are demonstrated to be of the order of unity if the orbital upper critical field, Hc2 (0), is of the order of Clogston paramagnetic limiting field, Hp. We suggest a generic phase diagram of such type-IV superconductor, which is singlet one at H=0 and in the Meissner phase and characterized by mixed singlet-triplet order parameter with broken symmetries of Copper pairs in vortex phase. A possibility to observe type-IV superconductivity in clean organic, high-Tc, and MgB2 superconductors is discussed.

Analytical Result on Electronic States around a Vortex Core in a Noncentrosymmetric Superconductor

We analytically study electronic bound states around a single vortex core in a noncentrosymmetric superconductor such as ${\rm CePt_3Si}$ without mirror symmetry about the $ab$ plane. Considering a mixed spin-singlet-triplet Cooper pairing model, we obtain a formula about the local density of states (LDOS) around a vortex core in any directions of magnetic fields. The LDOS under a magnetic field perpendicular to the c axis are quite different from those of typical s-wave or d-wave superconductors. From the ellipticity of the spatial pattern of the LDOS around a vortex core, one can estimate experimentally the pairing symmetry of ${\rm CePt_3Si}$ such as the position of the gap nodes and the ratio of the singlet component to the triplet component in order parameter.