P-wave States Research Articles

Vortical configurations in mesoscopic superconducting square loop with mixed pairing orders

Based on the microscopic Bogoliubov-de Gennes theory, we study vortical configurations in a mesoscopic superconducting square loop with mixed pairing orders. By choosing appropriate interaction strengths and chemical potential, the spin-triplet p-wave and subdominant spin-singlet d-wave pairing symmetries can be stabilized. In a small external magnetic field, unusual elliptical-like vortices in chiral p-wave orders as well as elongated vortices in the d-wave order tend to form in sample diagonals. For an enlarged flux, we find a two-quanta skyrmionic mode for the p-wave components, while the closed domain wall does not appear compared to the previous studies in superconducting systems with a pure p-wave state. Particularly, a novel multi-skyrmionic pattern containing four single-quanta skyrmions takes place with increasing flux. Such a single-quanta vortex structure consisting of two spatially separated half-quantum vortices is analogous to the nematic skyrmion with unit topological charge. In addition, several complex hybrid or multiple skyrmionic configurations are revealed in the strong flux range.

Study of $${\text{B}}_{{{\text{s}}2}}^{ * }$$(5840)0 and Bs1(5830)0 Mesons in the CMS Experiment

Using the data collected by the CMS experiment at the Large Hadron Collider in collisions of protons with a center-of-mass energy of 8 TeV, excited P-wave states $${\text{B}}_{{{\text{s}}2}}^{ * }{{(5840)}^{0}}$$ and Bs1(5830)0 of the $${\text{B}}_{{\text{s}}}^{0}$$ meson are studied. The decay $${\text{B}}_{{{\text{s}}2}}^{ * }{{(5840)}^{0}} \to {{{\text{B}}}^{0}}{\text{K}}_{{\text{s}}}^{0}$$ is observed for the first time, the first indication of the $${\text{B}}_{{{\text{s1}}}}^{ * }{{(5840)}^{0}} \to {\text{B}}_{{}}^{{ * 0}}{\text{K}}_{{\text{s}}}^{0}$$ decay existence is obtained, the probabilities of these decays with respect to the corresponding decays into B(*)+ $${\text{K}}_{{}}^{ - }$$ are measured. B0 and B+ ground states are reconstructed using $${{{\text{B}}}^{0}} \to {\text{J/}}\psi {{{\text{K}}}^{ + }}{{\pi }^{ - }}$$ and $${{{\text{B}}}^{ + }} \to {\text{J/}}\psi {{{\text{K}}}^{ + }}$$ decays. Masses of P-wave $${\text{B}}_{{\text{s}}}^{0}$$ mesons and the natural width of the $${\text{B}}_{{{\text{s}}2}}^{ * }{{(5840)}^{0}}$$ meson are measured; the mass difference $$M({\text{B}}{{{\text{*}}}^{0}}) - M({\text{B}}{{{\text{*}}}^{ + }})$$ between charged and neutral B* mesons is determined for the first time.

Dipole subtraction vs. phase space slicing in NLO NRQCD heavy-quarkonium production calculations

We compare two approaches to evaluate cross sections of heavy-quarkonium production at next-to-leading order in nonrelativistic QCD involving S- and P-wave Fock states: the customary approach based on phase space slicing and the approach based on dipole subtraction recently elaborated by us. We find reasonable agreement between the numerical results of the two implementations, but the dipole subtraction implementation outperforms the phase space slicing one both with regard to accuracy and speed.

Theory of the orbital moment in a superconductor

The chiral p-wave superconducting state is comprised of spin triplet Cooper pairs carrying a finite orbital angular momentum. For the case of a periodic lattice, calculating the net magnetisation arising from this orbital component presents a challenge as the circulation operator $\hat{\bf{r}} \times \hat{\bf{p}}$ is not well defined in the Bloch representation. This difficulty has been overcome in the normal state, for which a modern theory is firmly established. Here, we derive the extension of this normal state approach, generating a theory which is valid for a general superconducting state, and go on to perform model calculations for a chiral p-wave state in Sr$_2$RuO$_4$. The results suggest that the magnitude of the elusive edge current in Sr$_2$RuO$_4$ is finite, but lies below experimental resolution. This provides a possible solution to the long-standing controversy concerning the gap symmetry of the superconducting state in this material.

Chiral superconductivity in heavy-fermion metal UTe2.

Spin-triplet superconductors are condensates of electron pairs with spin 1 and an odd-parity wavefunction1. An interesting manifestation of triplet pairing is the chiral p-wave state, which is topologically non-trivial and provides a natural platform for realizing Majorana edge modes2,3. However, triplet pairing is rare in solid-state systems and has not been unambiguously identified in any bulk compound so far. Given that pairing is usually mediated by ferromagnetic spin fluctuations, uranium-based heavy-fermion systems containing f-electron elements, which can harbour both strong correlations and magnetism, are considered ideal candidates for realizing spin-triplet superconductivity4. Here we present scanning tunnelling microscopy studies of the recently discovered heavy-fermion superconductor UTe2, which has a superconducting transition temperature of 1.6 kelvin5. We find signatures of coexisting Kondo effect and superconductivity that show competing spatial modulations within one unit cell. Scanning tunnelling spectroscopy at step edges reveals signatures of chiral in-gap states, which have been predicted to exist at the boundaries of topological superconductors. Combined with existing data that indicate triplet pairing in UTe2, the presence of chiral states suggests that UTe2 is a strong candidate for chiral-triplet topological superconductivity.

Strong decays of the newly observed narrow Omega _b structures

Motivated by the newly observed narrow structures Omega _b(6316)^-, Omega _b(6330)^-, Omega _b(6340)^-, and Omega _b(6350)^- in the Xi _b^0 K^- mass spectrum, we investigate the strong decays of the low-lying Omega _b states within the ^3P_0 model systematically. According to their masses and decay widths, the observed Omega _b(6316)^-, Omega _b(6330)^-, Omega _b(6340)^-, and Omega _b(6350)^- resonances can be reasonably assigned as the lambda -mode Omega _b(1P) states with J^P=1/2^-, 3/2^-, 3/2^-, and 5/2^-. Meanwhile, the remaining P-wave state with J^P=1/2^- should have a rather broad width, which can hardly be observed by experiments. For the Omega _b(2S) and Omega _b(1D) states, our predictions show that these states have relatively narrow total widths and mainly decay into the Xi _b {bar{K}}, Xi _b^prime {bar{K}} and Xi _b^{prime *} {bar{K}} final states. These abundant theoretical predictions may be valuable for searching more excited Omega _b states in future experiments.

Hoyle-analog state in C13 studied with antisymmetrized molecular dynamics

The cluster states in $^{13}{\rm C}$ are investigated by antisymmetrized molecular dynamics. By investigating the spectroscopic factors, the cluster configurations of the excited states are discussed. It is found that the $1/2^+_2$ state is dominantly composed of the $^{12}{\rm C}(0^+_2)\otimes s_{1/2}$ configuration and can be regarded as a Hoyle analogue state. On the other hand, the p-wave states ($3/2^-$ and $1/2^-$) do not have such structure, because of the coupling with other configurations. The isoscalar monopole and dipole transition strengths from the ground to the excited states are also studied. It is shown that the excited $1/2^-$ states have strong isoscalar monopole transition strengths consistent with the observation. On the other hand, the excited $1/2^+$ states unexpectedly have weak isoscalar dipole transitions except for the $1/2^+_1$ state. It is discussed that the suppression of the dipole transition is attributed to the property of the dipole operator.

Spin-orbit coupling and spin-triplet pairing symmetry in Sr2RuO4

Spin-orbit coupling (SOC) plays a crucial role in determining the spin structure of an odd parity psedospin-triplet Cooper pairing state. Here, we present a thorough study of how SOC lifts the degeneracy among different p-wave pseudospin-triplet pairing states in a widely used microscopic model for $\mathrm{Sr_2 Ru O_4}$, combining a Ginzburg-Landau (GL) free energy expansion, a symmetry analysis of the model, and numerical weak-coupling renormalization group (RG) and random phase approximation (RPA) calculations. These analyses are then used to critically re-examine previous numerical results on the stability of chiral p-wave pairing. The symmetry analysis can serve as a guide for future studies, especially numerical calculations, on the pairing instability in $\mathrm{Sr_2 Ru O_4}$ and can be useful for studying other multi-band spin-triplet superconductors where SOC plays an important role.

The tetraquark states and the structure of X(2239) observed by the BESIII collaboration * * This project is supported by the National Natural Science Foundation of China (11705056, 11475192, U1832173, 11975245). This work is also supported by the Sino-German CRC 110 ”Symmetries and the Emergence of Structure in QCD” project by NSFC (11621131001) and the Key Research Program of Frontier

We investigate the mass spectrum of the tetraquark states in the relativized quark model. By solving the Schrödinger-like equation with the relativized potential, the masses of S- and P-wave tetraquarks are obtained. The screening effects are also taken into account. It is found that the resonant structure observed in the process by the BESIII collaboration can be assigned as a P-wave tetraquark state. Furthermore, the radiative transition and the strong decay behavior of this structure are also estimated, which can provide helpful information for future experimental searches.

Heavy quark spin multiplet structure of Pc-like pentaquarks as a P-wave hadronic molecular state

Abstract We study the heavy quark spin (HQS) multiplet structure of P-wave $Q\bar{Q}qqq$-type pentaquarks treated as molecules of a heavy meson and a heavy baryon. We define the light-cloud spin (LCS) basis decomposing the meson–baryon spin wave function into LCS and HQS parts. Introducing the LCS basis, we find HQS multiplets classified by the LCS: five HQS singlets, two HQS doublets, and three HQS triplets. We construct the one-pion exchange potential respecting the heavy quark spin and chiral symmetries to demonstrate which HQS multiplets are realized as a bound state. By solving the coupled channel Schrödinger equations, we study the heavy meson–baryon systems with $I=1/2$ and $J^P=(1/2^+, 3/2^+, 5/2^+, 7/2^+)$. The bound states which have the same LCS structure are degenerate at the heavy quark limit, and the degeneracy is resolved for finite mass. This HQS multiplet structure will be measured in future experiments.

Dipole subtraction at next-to-leading order in nonrelativistic-QCD factorization

We describe an implementation of a subtraction scheme in the nonrelativistic-QCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering S- and P-wave bound states. It is based on the dipole subtraction in the massless version by Catani and Seymour and its extension to massive quarks by Phaf and Weinzierl. Important additions include the treatment of heavy-quark bound states, in particular due to the more complicated infrared-divergence structure in the case of P-wave states.

Study of P-wave states at the CMS experiment

The observation of the decay and the evidence for the decay are presented. The analysis uses the data collected by the CMS experiment at the LHC in proton-proton collisions at . In addition, properties of the P-wave mesons are determined, as well as the mass differences M(B0) − M(B+) and M(B*0) − M(B*+), where the latter is measured for the first time.

P-wave superconductivity in iron-based superconductors

The possibility of p-wave pairing in superconductors has been proposed more than five decades ago, but has not yet been convincingly demonstrated. One difficulty is that some p-wave states are thermodynamically indistinguishable from s-wave, while others are very similar to d-wave states. Here we studied the self-field critical current of NdFeAs(O,F) thin films in order to extract absolute values of the London penetration depth, the superconducting energy gap, and the relative jump in specific heat at the superconducting transition temperature, and find that all the deduced physical parameters strongly indicate that NdFeAs(O,F) is a bulk p-wave superconductor. Further investigation revealed that single atomic layer FeSe also shows p-wave pairing. In an attempt to generalize these findings, we re-examined the whole inventory of superfluid density measurements in iron-based superconductors and show quite generally that single-band weak-coupling p-wave superconductivity is exhibited in iron-based superconductors.

Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance.

Phases of matter are usually identified through spontaneous symmetry breaking, especially regarding unconventional superconductivity and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analogue to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected 'split' transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temperature were observed3,4. Here we use nuclear magnetic resonance (NMR) spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of superconductivity in Sr2RuO4 and its evolution under strain. A reduction of the Knight shift is observed for all strain values and at temperatures below the critical temperature, consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theoretical interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its superconductivity emerges from a strongly correlated Fermi liquid, and our work imposes tight constraints on the order parameter symmetry of this archetypal system.

Alternative paths to realize Majorana Fermions in Superconductor-Ferromagnet Heterostructures

A fundamental obstacle for achieving quantum computation is local decoherence. One way to circumvent this problem rests on the concepts of topological quantum computation using non-local information storage, for example on pairs of Majorana fermions (MFs). The arguably most promising way to generate MFs relies at present on spin-triplet p-wave states of superconductors (SC), which are not abundant in nature, unfortunately. Thus, proposals for their engineering in devices, usually via proximity effect from a conventional SC into materials with strong spin-orbit coupling (SOC), are intensively investigated nowadays. Here we take an alternative path, exploiting the different connections between fields based on a quartet coupling rule for fields introduced by one of us, we demonstrate that, for instance, coexisting Zeeman field with a charge current would provide the conditions to induce p-wave pairing in the presence of singlet superconductivity. This opens new avenues for the engineering of robust MFs in various, not necessarily (quasi-)one-dimensional, superconductor-ferromagnet heterostructures, including such motivated by recent pioneering experiments that report MFs, in particular, without the need of any exotic materials or special structures of intrinsic SOC.

Production of doubly charmed baryons with the excited heavy diquark at LHC

The yield of doubly charmed baryons with excited heavy diquark in S-wave and P-wave states has been estimated at LHC energies. The observation possibility of such baryons is discussed.

Superfluid3He in Aerogel

Superfluid3He is an unconventional neutral superfluid in a p-wave state with three different superfluid phases, each identified by a unique set of characteristic broken symmetries and nontrivial topology. Despite natural immunity of3He from defects and impurity of any kind, it has been found that they can be artificially introduced with high-porosity silica aerogel. Furthermore, it has been shown that this modified quantum liquid becomes a superfluid with remarkably sharp thermodynamic transitions from the normal state and between its various phases. These phases include new superfluid phases that are stabilized by anisotropy from uniform strain imposed on the silica aerogel framework, and they include new phenomena in a new class of anisotropic aerogels consisting of nematically ordered alumina strands. The study of superfluid3He in the presence of correlated, quenched disorder from aerogel serves as a model for understanding the effect of impurities on the symmetry and topology of unconventional superconductors.

Influence of diffuse surface scattering on the stability of superconducting phases with spontaneous surface current generated by Andreev bound states

We report a theoretical study on the phase transition between superconducting states with and without spontaneous surface current. The phase transition takes place due to the formation of surface Andreev bound states in unconventional superconductors. Based on the quasiclassical theory of superconductivity, we examine the influence of atomic-scale surface roughness on the surface phase transition temperature $T_s$. To describe the surface effect, the boundary condition for the quasiclassical Green's function is parameterized in terms of specularity (the specular reflection probability in the normal state at the Fermi level). This boundary condition allows systematic study of the surface effect ranging from the specular limit to the diffuse limit. We show that diffuse quasiparticle scattering at a rough surface causes substantial reduction of $T_s$ in the d-wave pairing state of high-$T_c$ cuprate superconductors. We also consider a p-wave pairing state in which Andreev bound states similar to those in the d-wave state are generated. In contrast to the d-wave case, $T_s$ in the p-wave state is insensitive to the specularity. This is because the Andreev bound states in the p-wave superconductor are robust against diffuse scattering, as implied from symmetry consideration for odd-frequency Cooper pairs induced at the surface; the p-wave state has odd-frequency pairs with s-wave symmetry, while the d-wave state does not.

Breakdown of Nonrelativistic QCD Factorization in Processes Involving Two Quarkonia and its Cure.

We study inclusive processes involving two heavy quarkonia in nonrelativistic QCD (NRQCD) and demonstrate that, in the presence of two P-wave Fock states, NRQCD factorization breaks down, leaving uncanceled infrared singularities. As phenomenologically important examples, we consider the decay ϒ→χ_{cJ}+X via bb[over ¯](^{3}P_{J_{b}}^{[8]})→cc[over ¯](^{3}P_{J}^{[1]})+gg and the production process e^{+}e^{-}→J/ψ+χ_{cJ}+X via e^{+}e^{-}→cc[over ¯](^{3}P_{J_{1}}^{[8]})+cc[over ¯](^{3}P_{J}^{[1]})+g. We infer that such singularities will appear for double quarkonium hadroproduction at next-to-leading order. As a solution to this problem, we introduce to NRQCD effective field theory new types of operators whose quantum corrections absorb these singularities.

Exotic doubly charmed Ds0*(2317)D and Ds1*(2460)D* molecules

The $D_{s0}^*(2317) D$ and $D_{s1}^*(2460) D^*$ heavy meson systems can exchange a kaon that is emitted in S-wave owing to the opposite intrinsic parity of the $D_{s0}^*$($D_{s1}^*$) and $D$($D^*$) mesons. As a consequence of the mass difference of the $D_{s0}^*$($D_{s1}^*$) and $D$($D^*$) mesons, the range of the kaon exchange potential will be significantly longer than expected, corresponding to an effective mass of about $200\,{\rm MeV}$. The potential will be very strong: the strength of the interaction is proportional to $(m_{D_{s0}} - m_D)^2 / f_{\pi}^2$ and $(m_{D_{s1}} - m_{D^*})^2 / f_{\pi}^2$. This combination of range and strength almost guarantees the existence of $D_{s0}^*(2317) D$ and $D_{s1}^*(2460) D^*$ bound states with $J^P = 0^{-}$ and $J^P = 0^{-}, 2^{-}$ respectively. Concrete calculations indicate a binding energy of $5-15\,{\rm MeV}$ independently of $J^P$. The $D_{s0}^*(2317) D$ and $D_{s1}^*(2460) D^*$ molecules have manifestly exotic flavour quantum numbers: $C=2$, $S=1$ and $I=1/2$. We expect the existence of bottom counterparts composed of the $B B_{s0}$ and $B^* B_{s1}^*$ mesons, which will be more bound and have a richer spectrum that might include a shallow P-wave state and an excited S-wave state.