Triplet Order Research Articles

Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: Collective modes and microscopic properties

The close interplay between superconductivity and antiferromagnetism in several quantum materials can lead to the appearance of an unusual thermodynamic state in which both orders coexist microscopically, despite their competing nature. A hallmark of this coexistence state is the emergence of a spin-triplet superconducting gap component, called $\pi$-triplet, which is spatially modulated by the antiferromagnetic wave-vector, reminiscent of a pair-density wave. In this paper, we investigate the impact of these $\pi$-triplet degrees of freedom on the phase diagram of a system with competing antiferromagnetic and superconducting orders. Although we focus on a microscopic two-band model that has been widely employed in studies of iron pnictides, most of our results follow from a Ginzburg-Landau analysis, and as such should be applicable to other systems of interest, such as cuprates and heavy fermions. The Ginzburg-Landau functional reveals not only that the $\pi$-triplet gap amplitude couples tri-linearly with the singlet gap amplitude and the staggered magnetization magnitude, but also that the $\pi$-triplet $d$-vector couples linearly with the magnetization direction. While in the mean field level this coupling forces the $d$-vector to align parallel or anti-parallel to the magnetization, in the fluctuation regime it promotes two additional collective modes - a Goldstone mode related to the precession of the $d$-vector around the magnetization and a massive mode, related to the relative angle between the two vectors, which is nearly degenerate with a Leggett-like mode associated with the phase difference between the singlet and triplet gaps. We also investigate the impact of magnetic fluctuations on the superconducting-antiferromagnetic phase diagram, showing that due to their coupling with the $\pi$-triplet order parameter, the coexistence region is enhanced.

Possible triplet superconducting order in a magnetic superconducting phase induced by paramagnetic pair breaking

Motivated by recent thermal conductivity measurements in the superconductor CeCoIn5, we theoretically examine a possible staggered spin-triplet superconducting order to be induced by the coupled spin-density-wave (SDW) and d-wave superconducting (SC) orders in the high field and low temperature (HFLT) SC phase peculiar to this material with strong paramagnetic pair-breaking (PPB). It is shown that one type of the $\pi$-triplet order is consistent with the thermal conductivity data and can naturally be incorporated in the picture that the Q-phase is a consequence of the strong PPB effect inducing the SDW order and the FFLO spatial modulation parallel to the applied magnetic field.

Theory of surface spectroscopy for noncentrosymmetric superconductors

We study noncentrosymmetric superconductors with the tetrahedral $T_d$, tetragonal $C_{4v}$, and cubic point group $O$. The order parameter is computed self-consistently in the bulk and near a surface for several different singlet to triplet order parameter ratios. It is shown that a second phase transition below $T_c$ is possible for certain parameter values. In order to determine the surface orientation's effect on the order parameter suppression, the latter is calculated for a range of different surface orientations. For selected self-consistent order parameter profiles the surface density of states is calculated showing intricate structure of the Andreev bound states (ABS) as well as spin polarization. The topology's effect on the surface states and the tunnel conductance is thoroughly investigated, and a topological phase diagram is constructed for open and closed Fermi surfaces showing a sharp transition between the two for the cubic point group $O$.

Early neonatal lamb mortality: postmortem findings

An investigation of stillbirth and early neonatal lamb mortality was conducted in sheep flocks in Norway. Knowledge of actual causes of death are important to aid the interpretation of results obtained during studies assessing the risk factors for lamb mortality, and when tailoring preventive measures at the flock, ewe and individual lamb level. This paper reports on the postmortem findings in 270 liveborn lambs that died during the first 5 days after birth. The lambs were from 17 flocks in six counties. A total of 27% died within 3 h after birth, 41% within 24 h and 80% within 2 days. Most lambs (62%) were from triplet or higher order litters. In 81% of twin and larger litters, only one lamb died. The most frequently identified cause of neonatal death was infectious disease (n=97, 36%); 48% (n=47) of these died from septicaemia, 25% (n=24) from pneumonia, 22% (n=21) from gastrointestinal infections and 5% (n=5) from other infections. Escherichia coli accounted for 65% of the septicaemic cases, and were the most common causal agent obtained from all cases of infection (41%). In total, 14% of neonatal deaths resulted from infection by this bacterium. Traumatic lesions were the primary cause of death in 20% (n=53) of the lambs. A total of 46% of these died within 3 h after birth and 66% within 24 h. Severe congenital malformations were found in 10% (n=27) of the lambs, whereas starvation with no concurrent lesions was the cause of death in 6% (n=17). In 16% (n=43) of the lambs, no specific cause of death was identified, lambs from triplet and higher order litters being overrepresented among these cases. In this study, the main causes of neonatal lamb mortality were infection and traumatic lesions. Most neonatal deaths occurred shortly after birth, suggesting that events related to lambing and the immediate post-lambing period are critical for lamb survival.

Abrikosov vortices in SF bilayers

We study the spatial distribution of supercurrent circulated around an Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the dirty limit regime and circular cell approximation for the vortex lattice, we derive the conditions when the Usadel equations the F layer can be solved analytically. Using the obtained solutions, we demonstrate the possibility of reversal of direction of proximity induced supercurrents around the vortex in the F layer compared to that in the S-layer. The direction of currents can be controlled either by varying transparency of the SF interface or by changing an exchange field in a ferromagnet. We argue that the origin of this effect is due the phase shift between singlet and triplet order parameter components induced in the F-layer. Possible ways of experimental detection of the predicted effect are discussed.

Anomalous superconducting proximity effect and coherent charge transport in semiconducting thin film with spin-orbit interaction

We present a microscopic theory of the superconducting proximity effect in a semiconducting thin film with a spin-orbit interaction in an external magnetic field. We demonstrate that an effective 1D Hamiltonian which describes induced superconductivity in NSO in contact with a usual s-wave superconductor possesses not only a spin-singlet induced superconducting order parameter term, as commonly adopted, but also a spin triplet order parameter term. Using this new effective Hamiltonian we confirm previous results for a normal current across contacts of NSO with a normal metal and for a Josephson current with the same NSO with induced superconductivity, obtained previously in the framework of the phenomenological Hamiltonian without spin-triplet terms. However, a calculated current-phase relation across the transparent contact between NSO with induced superconductivity in magnetic field and a usual s-wave superconductor differs significantly from previous results. We suggest the experiment which can confirm our theoretical predictions.

Gapped tripletp-wave superconductivity in strong spin-orbit-coupled semiconductor quantum wells in proximity tos-wave superconductor

We show that the {\it gapped} triplet superconductivity, i.e., a triplet superconductor with triplet order parameter, can be realized in strong spin-orbit-coupled quantum wells in proximity to $s$-wave superconductor. It is revealed that with the singlet order parameter induced from the superconducting proximity effect, in quantum wells, not only can the triplet pairings arise due to the spin-orbit coupling, but also the triplet order parameter can be induced due to the repulsive effective electron-electron interaction, including the electron-electron Coulomb and electron-phonon interactions. This is a natural extension of the work of de Gennes, in which the repulsive-interaction-induced singlet order parameter arises in the normal metal in proximity to $s$-wave superconductor [Rev. Mod. Phys. {\bf 36}, 225 (1964)]. Specifically, we derive the effective Bogoliubov-de Gennes equation, in which the self-energies due to the effective electron-electron interactions contribute to the singlet and triplet order parameters. It is further shown that for the singlet order parameter, it is efficiently suppressed due to this self-energy renormalization; whereas for the triplet order parameter, it is the $p$-wave ($p_x\pm ip_y$) one with the ${\bf d}$-vector parallel to the effective magnetic field due to the spin-orbit coupling. Finally, we perform the numerical calculation in InSb (100) quantum wells. Specifically, we reveal that the Coulomb interaction is much more important than the electron-phonon interaction at low temperature. Moreover, it shows that with proper electron density, the minimum of the renormalized singlet and the maximum of the induced triplet order parameters are comparable, and hence can be experimentally distinguished.

Control of magnetism in singlet-triplet superconducting heterostructures

We analyze the magnetization at the interface between singlet and triplet superconductors and show that its direction and dependence on the phase difference across the junction are strongly tied to the structure of the triplet order parameter as well as to the pairing interactions. We consider equal spin helical, opposite spin chiral, and mixed symmetry pairing on the triplet side and show that the magnetization vanishes at $\phi=0$ only in the first case, follows approximately a $\cos\phi$ behavior for the second, and shows higher harmonics for the last configuration. We trace the origin of the magnetization to the magnetic structure of the Andreev bound states near the interface, and provide a symmetry-based explanation of the results. Our findings can be used to control the magnetization in superconducting heterostructures and to test symmetries of spin-triplet superconductors.

Comparative analysis of perinatal outcome of spontaneous pregnancy reduction and multifetal pregnancy reduction in triplet pregnancies conceived after assisted reproductive technique.

INTRODUCTION:With the advent of assisted reproductive treatment options, the incidence of multiple pregnancies has increased. Although the need for elective single embryo transfer is emphasized time and again, its uniform applicability in practice is yet a distant goal. In view of the fact that triplet and higher order pregnancies are associated with significant fetomaternal complications, the fetal reduction is a commonly used option in such cases. This retrospective study aims to compare the perinatal outcome in patients with triplet gestation who have undergone spontaneous fetal reduction (SFR) as against those in whom multifetal pregnancy reduction (MFPR) was done.MATERIALS AND METHODS:In the present study, eighty patients with triplet gestation at 6 weeks were considered. The patients underwent SFR or MFPR at or before 12–13 weeks and were divided into two groups (34 and 46), respectively.RESULTS:Our study found no statistical difference in perinatal outcome between the SFR and MFPR groups in terms of average gestational age at delivery, abortion rate, preterm delivery rate, and birth weight. The study shows that the risk of aborting all fetuses after SFR is three times (odds ratio [OR] = 3.600, 95% confidence interval [CI] = 0.2794–46.388) that of MFPR in subsequent 2 weeks. There were more chances of loss of extra fetus in SFR (23.5%) group than MFPR group (8.7%) (OR = 3.889, 95% CI = 1.030–14.680). As neither group offers any significant benefit from preterm delivery, multiple pregnancies continue to be responsible for preterm delivery despite fetal reduction.CONCLUSION:There appears to be some advantages of MFPR in perinatal outcome when compared to SFR, especially if the latter happens at advanced gestation. Therefore, although it is advisable to wait for SFR to occur, in patients with triplet gestation at 11–12 weeks, MFPR is a viable option to be considered.

Domain walls in superconductors: Andreev bound states and tunneling features

Domain walls can be formed in superconductors with a discrete degeneracy of the ground state, for instance, due to the breaking of time reversal symmetry. We study all cases where the formation of domain walls is possible in a tetragonal superconductor with the point group ${D}_{4h}$. We discuss both triplet and mixed singlet order parameters. It is found that in all cases the domain walls support subgap Andreev bound states, whose energies strongly depend on the direction of semiclassical propagation. The bound state contribution to the density of quasiparticle states exhibits peculiar features, which can be observed in tunneling experiments.

Embryo transfer practices and multiple births resulting from assisted reproductive technology: an opportunity for prevention

To evaluate assisted reproductive technology (ART) ET practices in the United States and assess the impact of these practices on multiple births, which pose health risks for both mothers and infants. Retrospective cohort analysis using the National ART Surveillance System data. US fertility centers reporting to the National ART Surveillance System. Noncanceled ART cycles conducted in the United States in 2012. None. Multiple birth (birth of two or more infants, at least one of whom was live-born). Of 134,381 ART transfer cycles performed in 2012, 51,262 resulted in live births, of which 13,563 (26.5%) were multiple births: 13,123 twin and 440 triplet and higher order births. Almost half (46.1%) of these multiple births resulted from the following four cycle types: two fresh blastocyst transfers among favorable or average prognosis patients less than 35 years (1,931 and 1,341 multiple births, respectively), two fresh blastocyst transfers among donor-oocyte recipients (1,532 multiple births), and two frozen/thawed ETs among patients less than 35 years (1,452 multiple births). More than half of triplet or higher order births resulted from the transfer of two embryos (52.5% of births among fresh autologous transfers, 67.2% of births among donor-oocyte recipient transfers, and 42.9% among frozen/thawed autologous transfers). A substantial reduction of ART-related multiple (both twin and triplet or higher order) births in the United States could be achieved by single blastocyst transfers among favorable and average prognosis patients less than 35 years of age and donor-oocyte recipients.

456: Predicting preterm birth risks in asymptomatic triplet pregnancies using relative changes in second trimester cervical lengths

The rate of triplet and higher order pregnancy has increased by 500% over the past 30 years. Triplet pregnancies are at increased risk for almost all obstetric complications, the most common being preterm birth. Cervical length (CL) measurements in asymptomatic women with multiple gestations are commonly used to predict preterm birth. Our goal was to determine if the change in CL in the second trimester is a useful predictor of spontaneous preterm birth in asymptomatic triplet pregnancies.

Trends in the incidence and mortality of multiple births by socioeconomic deprivation and maternal age in England: population-based cohort study

ObjectiveTo investigate temporal trends in multiple birth rates and associated stillbirth and neonatal mortality by socioeconomic deprivation and maternal age in England.DesignPopulation cohort study.SettingEngland.ParticipantsAll live births and stillbirths (1 January...

Spin Josephson current in a ferromagnet/noncentrosymmetric superconductor junction

We investigate the equilibrium spin transport in a ferromagnet/noncentrosymmetric superconductor (FM/NCS) junction where the NCS has a dominant triplet order parameter and helical edge state. Based on the symmetry analysis and numerical calculation, we demonstrate that there is a nonzero spin supercurrent flowing in the junction, which stems from the exchange coupling between the FM magnetization and triplet Cooper-pair spin. It is also found that a transverse spin current other than the helical edge spin current is flowing along the interface of the junction, and its polarization is related to the longitudinal spin supercurrent. Besides, an equilibrium Hall current is also shown to flow along the junction’s interface due to the broken time-reversal symmetry from the FM.

Collective modes of the order parameter in a triplet superfluid neutron liquid

The complete spectrum of collective modes of the triplet order parameter in the superfluid neutron matter is examined in the BCS approximation below the pair-breaking threshold. The dispersion equations both for the unitary and nonunitary excitations are derived and solved in the limit of $q\rightarrow0$ by taking into account the anisotropy of the energy gap for the case of $P$-wave pairing. By our analysis, there is only one Goldstone mode which is associated with the broken gauge symmetry. We found no additional Goldstone modes associated with the broken rotational symmetry but found that the oscillations of the total angular momentum are qualitatively similar to the "normal-flapping" mode in the A-phase of superfluid Helium. There are also two collective modes associated with internal vibrations of the structure of the order parameter oscillating with $\omega(T=0) =1.20\Delta_{0}$ and $\omega(T=0) =0.61\Delta_{0}$.

Properties of Magnetic-Superconducting Proximity Systems

We discuss properties of proximity systems made of superconducting, ferromagnetic, and graphite nanoscale thin films. In superconducting-graphite proximity systems, we show how size quantization results in oscillations of the density of states with increasing graphite film thickness. In superconducting-ferromagnetic multilayers, we discuss the critical temperature variations of the proximity system as a function of ferromagnetic layer thickness and magnetic inhomogeneity. We also review the Josephson effect through a superconductor–ferromagnet–superconductor multilayer. In this context, we discuss the presence of a long-range odd-frequency triplet order parameter.

Interfacial spin Hall current in a Josephson junction with Rashba spin—orbit coupling

We theoretically investigate the spin transport properties of the Cooper pairs in a conventional Josephson junction with Rashba spin—orbit coupling considered in one of the superconducting leads. It is found that an angle-resolved spin supercurrent flows through the junction and a nonzero interfacial spin Hall current driven by the superconducting phase difference also appears at the interface. The physical origin of this is that the Rashba spin—orbit coupling can induce a triplet order parameter in the s-wave superconductor. The interfacial spin Hall current dependences on the system parameters are also discussed.

D-Wave-like nodal superconductivity in the organic conductor (TMTSF)2ClO4

We suggest theoretical explanation of the high upper critical magnetic field, perpendicular to conducting chains, Hc2b′, experimentally observed in the superconductor (TMTSF)2ClO4, in terms of singlet superconducting pairing. In particular, we compare the results of d-wave-like nodal, d-wave-like node-less, and s-wave scenarios of superconductivity. We show that, in d-wave-like nodal scenario, superconductivity can naturally exceed both the orbital upper critical magnetic field and Clogston–Shandrasekhar paramagnetic limit as well as reach experimental value, Hc2b′≃6T, in contrast to d-wave-like node-less and s-wave scenarios. In our opinion, the obtained results are strongly in favor of d-wave-like nodal superconductivity in (TMTSF)2ClO4, whereas, in a sister compound, (TMTSF)2PF6, we expect either the existence of triplet order parameter or the coexistence of triplet and singlet order parameters.

Josephson Hall current in a noncentrosymmetric superconductor/ferromagnet/superconductor junction

We theoretically study the transverse spin and charge transport in a 2D noncentrosymmetric superconductor (NCS)/ferromagnet (FM)/superconductor Josephson junction, in which the NCS has a dominant triplet order parameter and helical edge states. It is predicted that both equilibrium spin and charge Hall currents can flow transversely in the junction and are driven by the superconducting phase gradient. The physical origin of the Josephson Hall current is the broken time-reversal symmetry due to the FM and the mixing of the helical edge states. The Hall currents are sensitive to the FM magnetization direction, and the planar magnetization component is vitally important because it can lead to a spin flip effect that makes the Cooper pairs tunnel between unequal chiral edge states of the two NCSs.

Singlet versus triplet particle-hole condensates in quantum oscillations in cuprates

Quantum oscillations in a tilted magnetic field offer the possibility of distinguishing singlet versus triplet order parameters in the particle hole channel provided the measurements reflect a putative ``normal'' state of a density wave obtained by applying by high magnetic field at low temperatures. A theoretical analysis is given that compares spin density wave, a singlet $d$-density wave, and a triplet $d$-density wave. While the existence of a spin zero in the oscillation amplitude is a necessary consequence of a singlet order parameter, a triplet order parameter may or may not exhibit a spin zero, making it a quantitative issue that depends on the actual extremal orbits on the Fermi surface. Nonetheless, a theoretical analysis can shed light on the striking recent measurements in $\mathrm{YBa_{2}Cu_{3}O_{6+\delta}}$.