Weyl Fermions and broken symmetry phases of laterally confined3He films.

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,Lz=(N/2)ℏ, forN/2Cooper pairs. The power law suppression of the angular momentum,Lz(T)≃(N/2)ℏ[1-23(πT/Δ)2]for0⩽T≪Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry atDc2∼16ξ0. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement lengthD→Dc2. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral 'polar phase' atDc1∼9ξ0, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

Impurity-Induced Anomalous Thermal Hall Effect in Chiral Superconductors.

Chiral superconductors exhibit novel transport properties that depend on the topology of the order parameter, topology of the Fermi surface, the spectrum of bulk and edge Fermionic excitations, and the structure of the impurity potential. In the case of electronic heat transport, impurities induce an anomalous (zero-field) thermal Hall conductivity that is easily orders of magnitude larger than the quantized edge contribution. The effect originates from branch-conversion scattering of Bogoliubov quasiparticles by the chiral order parameter, induced by potential scattering. The former transfers angular momentum between the condensate and the excitations that transport heat. The anomalous thermal Hall conductivity is shown to depend to the structure of the electron-impurity potential, as well as the winding number ν of the chiral order parameter Δ(p)=|Δ(p)|e^{iνϕ_{p[over ^]}}. The results provide quantitative formulas for interpreting heat transport experiments seeking to identify broken T and P symmetries, as well as the topology of the order parameter for chiral superconductors.

Chiral Higgs Mode in Nematic Superconductors.

Nematic superconductivity with spontaneously broken rotation symmetry has recently been reported in doped topological insulators, M_{x}Bi_{2}Se_{3} (M=Cu, Sr, Nb). Here we show that the electromagnetic (EM) response of these compounds provides a spectroscopy for bosonic excitations that reflect the pairing channel and the broken symmetries of the ground state. Using quasiclassical Keldysh theory, we find two characteristic bosonic modes in nematic superconductors: the nematicity mode and the chiral Higgs mode. The former corresponds to the vibrations of the nematic order parameter associated with broken crystal symmetry, while the latter represents the excitation of chiral Cooper pairs. The chiral Higgs mode softens at a critical doping, signaling a dynamical instability of the nematic state towards a new chiral ground state with broken time reversal and mirror symmetry. Evolution of the bosonic spectrum is directly captured by EM power absorption spectra. We also discuss contributions to the bosonic spectrum from subdominant pairing channels to the EM response.

Spontaneous Helical Order of a Chiral p-Wave Superfluid Confined in Nanoscale Channels.

Strong interactions that favor chiral p-wave pairing, combined with strong pair breaking by confining boundaries, are shown to lead to new equilibrium states with different broken symmetries. Based on a strong-coupling extension of the Ginzburg-Landau theory that accurately accounts for the thermodynamics and phase diagram of the bulk phases of superfluid ^{3}He, we predict new phases of superfluid ^{3}He for confined geometries that spontaneously break rotational and translational symmetry in combination with parity and time-reversal symmetry. One of the newly predicted phases exhibits a unique combination of chiral and helical order that is energetically stable in cylindrical channels of radius approaching the Cooper pair coherence length, e.g., R∼100 nm. Precise numerical minimization of the free energy yields a broad region of stability of the helical phase as a function of pressure and temperature, in addition to three translationally invariant phases with distinct broken spin and orbital rotation symmetries. The helical phase is stable at both high and low pressures and favored by boundaries with strong pair breaking. We present calculations of transverse NMR frequency shifts as functions of rf pulse tipping angle, magnetic field orientation, and temperature as signatures of these broken symmetry phases.

Dose frequency of prostaglandin F2α administration to dairy cows exposed to presynchronization and either 5- or 7-day Ovsynch program durations: Ovulatory and luteolytic risks.

We hypothesized (1) that neither duration of the Ovsynch program nor dose frequency of PGF2α would change the proportion of cows with complete luteolysis (progesterone <0.4 ng/mL 72 h after PGF2α) and (2) that the additional GnRH treatment administered as part of a presynchronization program would not alter the proportion of anovulatory cows starting the timed artificial insemination (AI) program compared with an alternative shorter presynch program including only 1 GnRH treatment. Lactating Holstein cows (n = 406) were milked 3 times daily and enrolled in a 2 × 2 × 2 factorial experiment consisting of 8 treatments before the first postpartum AI. Treatments were used to test ovulatory, luteal, and luteolytic outcomes to 3 main effects: (1) 2 GnRH-PGF2α presynchronization programs (PG-3-G vs. Double Ovsynch), (2) 2 Ovsynch program durations [5 d: GnRH (GnRH-1)-5 d-PGF2α-24 h-PGF2α-32 h-GnRH (GnRH-2)-16 h-timed AI; 7 d: GnRH-1-7 d-PGF2α-56 h-GnRH-2-16 h-timed AI], and (3) 2 PGF2α dose frequency treatments (2 × 25 mg) 24 h apart versus 1 dose (1 × 50 mg) of PGF2α administered 72 h before timed AI. The presynchronization treatments of PG-3-G and Double Ovsynch had no effect on the proportion of cows with luteal function at the onset of the Ovsynch treatments (87.9 vs. 86.2%). Although ovulatory responses were similar after GnRH-1 (>60%), Double Ovsynch cows tended to have greater ovulatory responses than PG-3-G after GnRH-2 (95.3 vs. 90.6%). The 2 × 25-mg doses of PGF2α and the 1 × 50-mg dose induced luteolysis in both Ovsynch treatment durations, but the 1 × 50-mg dose was less effective in the 5-d program. More pregnancy per AI (P/AI; 49.2%) tended to occur in the PG-3-G cows in the 7-d program compared with the other treatment combinations (range: 32.4-37.4%; Ovsynch × presynch interaction). In addition, an Ovsynch × PGF2α dose frequency interaction resulted in cows receiving the 1 × 50-mg dose in the 7-d program having the greatest P/AI (46.1%) and cows receiving the 1 × 50-mg dose in the 5-d program having the least P/AI (30.6%). We conclude that complete luteolysis was less effective in the 5-d program when the 1 × 50-mg dose was applied, but both PGF2α dose frequencies (1 × 50 mg and 2 × 25 mg 24 h apart) effectively induced complete luteolysis in the 7-d program. Treatments producing complete luteolysis tended to be related to subsequent pregnancy outcomes.

Andreev bound states and their signatures.

Many of the properties of superconductors related to quantum coherence are revealed when the superconducting state is forced to vary in space in response to an external magnetic field, a proximity contact, an interface to a ferromagnet or to impurities embedded in the superconductor. Among the earliest examples is Andreev reflection of an electron into a retro-reflected hole at a normal-superconducting interface. In regions of strong inhomogeneity, multiple Andreev reflection leads to the formation of sub-gap states, Andreev bound states, with excitation energies below the superconducting gap. These states play a central role in our understanding of inhomogeneous superconductors. The discoveries of unconventional superconductivity in many classes of materials, advances in fabrication of superconducting/ferromagnetic hybrids and nanostructures for confining superfluid 3 He, combined with theoretical developments in topological quantum matter have dramatically expanded the significance of branch conversion scattering and Andreev bound state formation. This collection of articles highlights developments in inhomogeneous superconductivity, unconventional superconductivity and topological phases of superfluid 3 He, in which Andreev scattering and bound states underpin much of the physics of these systems. This article provides an introduction to the basic physics of Andreev scattering, bound-state formation and their signatures. The goal is both an introduction for interested readers who are not already experts in the field, and to highlight examples in which branch conversion scattering and Andreev bound states provide unique signatures in the transport properties of superconductors.This article is part of the theme issue 'Andreev bound states'.

Additional small dose of prostaglandin F2α at timed artificial insemination failed to improve pregnancy risk of lactating dairy cows.

Two experiments were performed to test the hypothesis that administering PGF2α concurrent with timed artificial insemination (AI) in lactating dairy cows would enhance pregnancy per AI (P/AI). In experiment 1, lactating Holstein cows (n = 289) in one herd were enrolled after a non-pregnancy diagnosis (30-36 d after AI) to synchronize subsequent ovulation before AI. Cows were assigned randomly to receive (im) 10 mg of PGF2α concurrent with timed AI (Day 0; treatment) or no injection (control). Blood samples were collected on Days -3, 0, and 13 to determine serum concentrations of progesterone. Ovaries were scanned via transrectal ultrasonography to determine follicle diameters (Day -3), subsequent ovulation risk (Day 13), and total volume of luteal tissue (Day 13). Diagnosis of pregnancy occurred on Days 32 and 80 after AI. Ovulation risk post-AI exceeded 90% and did not differ between treatments. In addition, PGF2α treatment only numerically increased progesterone (5.7 ±â€¯0.3 vs. 6.2 ±â€¯0.3 ng/mL) or luteal tissue volume (8.9 ±â€¯0.4 vs. 9.8 ±â€¯0.5 ng/mL) on Day 13 by 8.8% (P = .206) or 10.1% (P = .134) in control and treated cows, respectively. Pregnancy per AI at Days 32 (P = .50) and 80 (P = .33) did not differ between treatments. Cows with progesterone >0.5 ng/mL at timed AI had reduced (P < .001) ovulation risk but risk was unaffected by treatment. In experiment 2, lactating dairy cows (n = 1828) in two commercial dairy herds were enrolled at time of insemination (Day 0), and assigned randomly to treatment or control as described in experiment 1. Initial (Days 32-35) and confirmed (Days 63-68) pregnancy diagnosis revealed no differences in P/AI or pregnancy loss. Pregnancy diagnosis on Days 32-35 produced percentage increases in P/AI for primiparous compared with multiparous cows (20.8%; P = .002), for first-service compared with repeat-service cows (26%; P = .001), and cows in one herd compared with the second herd (36%; P < .001). Pregnancy loss was greater (P = .001) for cows inseminated at first (10.0%) vs. later services (5.3%) but was unaffected by treatment. Cows treated with PGF2α in one herd produced more twins than control cows (11.7 vs. 3.2%), whereas no treatment difference was detected in the second herd (5.6 vs. 5.6%), respectively. We conclude that im treatment of lactating dairy cows with 10 mg of PGF2α concurrent with timed AI did not improve P/AI or embryo survival, but increased twinning in one herd.

Increasing estrus expression in the lactating dairy cow.

Using an activity monitoring system (AMS) equipped with an accelerometer, 2 experiments were conducted to test the hypotheses that (1) enhancing progesterone before inducing luteolysis or (2) exposing cows to estradiol cypionate (ECP) or testosterone propionate (TP) after luteolysis would increase occurrence and intensity of estrus. Our goal was to determine if more cows could be detected in estrus by an AMS compared with other estrus-detection aids. In experiment 1, cows (n=154) were fitted with both an AMS collar and a pressure-sensitive, rump-mounted device (HeatWatch; HW) and assigned to 3 treatments: (1) no CL + progesterone insert (CIDR) for 5d, (2) CL only, or (3) CL + 2 CIDR inserts for 5d to achieve a range in concentrations of progesterone. Prostaglandin F2α was administered to all cows upon CIDR insert removal or its equivalent. Progesterone concentration up to 72h posttreatment was greatest in CL + 2 CIDR, followed by CL only, and no CL + CIDR cows. Estrus occurred 14 to 28h earlier in no CL + CIDR compared with CL-bearing cows. Estrus intensity was greater for CL + 2 CIDR than for CL-only cows. The AMS and HW detected 70 and 59% of cows defined to be in estrus, respectively. In experiment 2, cows (n=203) were equipped with both an AMS and a friction-activated, rump-mounted patch (Estrotect patch) and assigned to receive 1mg of ECP, 2mg of TP, or control 24h after PGF2α. Concentrations of estradiol 24 and 48h after treatment were greater in ECP cows compared with controls. Estrus expression detected by AMS or patches in cows defined to be in estrus tended to be greater or was greater for ECP compared with controls, respectively. Compared with controls and in response to TP or ECP, estrus occurred 8 to 18h earlier and was of greater intensity for ECP cows, respectively. The AMS and patches determined 73 and 76% of cows defined to be in estrus, respectively. Of cows exposed to the AMS, HW, or patches, 70, 61, and 75%, respectively, were detected in estrus and more than 93% of these subsequently ovulated. In contrast, of the residual cows not detected in estrus, 62 to 77% ovulated in the absence of detected estrus. Only ECP was successful in inducing more expression and intensity of estrus, and proportions of cows detected in estrus exceeded 80%. Given the large proportion of cows equipped with AMS collars ovulating in the absence of estrus, further research is warranted to determine if more pregnancies can be achieved by inseminating those cows not detected in estrus at an appropriate time when PGF2α is administered to induce luteolysis.

Anomalous attenuation of transverse sound in 3He.

We present the first measurements of the attenuation of transverse sound in superfluid 3He-B. We use fixed path length interferometry combined with the magnetoacoustic Faraday effect to vary the effective path length by a factor of 2, resulting in absolute values of the attenuation. We find that attenuation is significantly larger than expected from the theoretical dispersion relation, in contrast with the phase velocity of transverse sound. We suggest that the anomalous attenuation can be explained by surface Andreev bound states.

Dynamics of spin transport in voltage-biased Josephson junctions.

We investigate spin transport in voltage-biased spin-active Josephson junctions. The interplay of spin filtering, spin mixing, and multiple Andreev reflection leads to nonlinear voltage dependence of the dc and ac spin current. We compute the voltage characteristics of the spin current (IS) for superconductor-ferromagnet-superconductor Josephson junctions. The subharmonic gap structure of IS(V) is shown to be sensitive to the degree of spin mixing generated by the ferromagnetic interface, and exhibits a pronounced even-odd effect associated with spin transport during multiple Andreev reflection processes. For strong spin mixing both the magnitude and the direction of the dc spin current can be sensitively controlled by the bias voltage.

Crystalline order in superfluid (3)He films.

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).

Specific heat of disordered superfluid 3He.

The specific heat of superfluid 3He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk 3He. The magnitude of the discontinuity is also suppressed. This disorder effect can be understood from the Ginzburg-Landau theory which takes into account elastic quasiparticle scattering suppressing both the transition temperature and the amplitude of the order parameter. We infer that the limiting temperature dependence of the specific heat is linear at low temperatures in the disordered superfluid state, consistent with predictions of gapless excitations everywhere on the Fermi surface.

Phase modulated thermal conductance of Josephson weak links.

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference (phi) of the superconducting leads. Branch-conversion processes, low-energy Andreev bound states near the contact, and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature, and disorder, on the conductance, are reported. For high-transmission weak links, D-->1, the formation of an Andreev bound state leads to suppression of the density of states for the continuum excitations, and thus, to a reduction in the conductance for phi approximately pi. For low-transmission (D<<1) barriers resonant scattering leads to an increase in the thermal conductance as T drops below T(c) (for phase differences near phi=pi).