P-wave Pairing Research Articles

P-wave Pairing Near a Spin-Split Josephson Junction

Superconductivity and magnetism are competing effects that can coexist in certain regimes. Their co-existence leads to unexpected new behaviors that include the onset of exotic electron pair mechanisms and topological phases. In this work, we study the properties of a Josephson junction between two spin-split superconductors. The spin-splitting in the superconductors can arise from either the coupling to a ferromagnetic material or an external magnetic field. The properties of the junction are dominated by the Andreev bound states that are also split. One of these states can cross the superconductor’s Fermi level, leading to a ground-state transition characterized by a suppressed supercurrent. We interpret the supercurrent blockade as coming from a dominance of p-wave pairing close to the junction, where the electrons are at both sides. To support this interpretation, we analyze the different pairing channels and show that p-wave pairing is favored in the case where the magnetization of the two superconductors is parallel and suppressed in the anti-parallel case. We also analyze the noise spectrum that shows signatures of the ground-state transition in the form of an elevated zero-frequency noise.

Effect of the mixing of s-wave and chiral p-wave pairings on electrical shot noise properties of normal metal/superconductor tunnel junctions

Abstract We study theoretically the electrical shot noise properties of tunnel junctions between a normal metal and a superconductor with the mixture of singlet $s$-wave and chiral triplet $p$-wave pairing due to broken inversion symmetry. We investigate how the shot noise properties vary as the relative amplitude between the two parity components in the pairing potential is changed. It is demonstrated that some characteristics of the electrical shot noise properties of such tunnel junctions may depend sensitively on the relative amplitude between the two parity components in the pairing potential, and some significant changes may occur in the electrical shot noise properties when the relative amplitude between the two parity components is varied from the singlet $s$-wave pairing dominated regime to the chiral triplet $p$-wave pairing dominated regime. In the chiral triplet $p$-wave pairing dominated regime, the ratio of noise power to electric current is close to $2e$ both in the in-gap and in the out-gap region. In the singlet $s$-wave pairing dominated regime, the value of this ratio is close to $4e$ in the inner gap region but may reduce to about $2e$ in the outer gap region as the relative amplitude of the chiral triplet pairing component is increased. The variations of the differential shot noise with the bias voltage also exhibit some significantly different features in different regimes. Such different features can serve as useful diagnostic tools for the determination of the relative magnitude of the two parity components in the pairing potential.

Optomechanical realization of thebosonic Kitaev chain.

The fermionic Kitaev chain is a canonical model featuring topological Majorana zero modes1. We report the experimental realization of its bosonic analogue2 in a nano-optomechanical network, in which the parametric interactions induce beam-splitter coupling and two-mode squeezing among the nanomechanical modes, analogous to hopping and p-wave pairing in the fermionic case, respectively. This specific structure gives rise to a set of extraordinary phenomena in the bosonic dynamics and transport. We observe quadrature-dependent chiral amplification, exponential scaling of the gain with system size and strong sensitivity to boundary conditions. All these are linked to the unique non-Hermitian topological nature of the bosonic Kitaev chain. We probe the topological phase transition and uncover a rich dynamical phase diagram by controlling interaction phases and amplitudes. Finally, we present an experimental demonstration of an exponentially enhanced response to a small perturbation3,4. These results represent the demonstration of a new synthetic phase of matter whose bosonic dynamics do not have fermionic parallels, and we have established a powerful system for studying non-Hermitian topology and its applications for signal manipulation and sensing.

Unconventional superconductivity in Cr-based compound Pr3Cr10−xN11

We report results of specific heat and muon spin relaxation (μSR) measurements on a polycrystalline sample of Pr3Cr10−xN11, which shows superconducting state below Tc = 5.25 K, a large upper critical field Hc2 ~ 20 T and a residual Sommerfeld coefficient γ0. The field dependence of γ0(H) resembles γ of the U-based superconductors UTe2 and URhGe at low temperatures. The temperature-dependent superfluid density measured by transverse-field μSR experiments is consistent with a p-wave pairing symmetry. ZF-μSR experiment suggests a time-reversal symmetry broken superconducting transition, and temperature-independent spin fluctuations at low temperatures are revealed by LF-μSR experiments. These results indicate that Pr3Cr10−xN11 is a candidate of p-wave superconductor which breaks time-reversal symmetry.

About magnetic properties of superfluid neutron matter with spin-triplet anisotropic p-wave pairing in superstrong magnetic fields and at supranuclear densities

Magnetic properties of a dense superfluid neutron matter (relevant to the physics in cores of magnetars, namely the strongly magnetized neutron stars) at supranuclear densities n > n0 (where n0 = 0.17 fm–3 is the saturation nuclear density) with generalized Skyrme effective forces (with three density-dependent terms) and with spin-triplet anisotropic p-wave pairing (similar to 3He-A in magnetic fields, i.e. with spin S = 1 and orbital moment L = 1 of anisotropic Cooper pairs of neutrons) in the presence of a superstrong magnetic field (exceeding the 1017 G) are studied within the framework of the non-relativistic generalized Fermi-liquid theory at zero temperature. The upper limit for the density range of a neutron matter is restricted by the magnitude 3n0 in order to avoid the account of relativistic corrections growing with density. The approximate general formula (valid for any parameterization of the Skyrme forces) is derived here analytically for the magnetic susceptibility (which contains additional correction depending nonlinearly on superstrong magnetic field H and on the density n) of a superfluid neutron matter in the limit of zero temperature. The obtained general formula for magnetic susceptibility is specified for the generalized BSk21 parameterization of the Skyrme forces and figures for corresponding values are plotted on the interval 1.5n0 ≤ n ≤ 3n0 and for superstrong magnetic fields 2⋅1017 G ≤ H ≤ 2⋅1018 G. It is established that the high-density ferromagnetic instability is removed in neutron matter with the generalized Skyrme forces (in particular, with the generalized BSk21 parameterization) not only in normal, but also in superfluid neutron matter with spin-triplet anisotropic p-wave pairing at supranuclear densities and in superstrong magnetic fields.

Spontaneous rotational symmetry breaking in KTaO3 heterointerface superconductors

Broken symmetries play a fundamental role in superconductivity and influence many of its properties in a profound way. Understanding these symmetry breaking states is essential to elucidate the various exotic quantum behaviors in non-trivial superconductors. Here, we report an experimental observation of spontaneous rotational symmetry breaking of superconductivity at the heterointerface of amorphous (a)-YAlO3/KTaO3(111) with a superconducting transition temperature of 1.86 K. Both the magnetoresistance and superconducting critical field in an in-plane field manifest striking twofold symmetric oscillations deep inside the superconducting state, whereas the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute this behavior to the mixed-parity superconducting state, which is an admixture of s-wave and p-wave pairing components induced by strong spin-orbit coupling inherent to inversion symmetry breaking at the heterointerface of a-YAlO3/KTaO3. Our work suggests an unconventional nature of the underlying pairing interaction in the KTaO3 heterointerface superconductors, and brings a new broad of perspective on understanding non-trivial superconducting properties at the artificial heterointerfaces.

Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene.

Motivated by the observation of even denominator fractional quantum Hall effect in the n=3 Landau level of monolayer graphene [Kim etal., Nat. Phys. 15, 154 (2019)NPAHAX1745-247310.1038/s41567-018-0355-x], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n=2 graphene Landau level, whereas no pairing instability is found at half filling in the n=0 and n=1 graphene Landau levels. The relevance of these results to experiments is discussed.

Anisotropic differential conductance of a mixed-parity superconductor/ferromagnet structure

We study the electronic transport properties of a superconductor (S) with a mixed s+p-wave pairing attached to a ferromagnetic metal (F) and a normal electrode (N) in an SFN configuration. Using the quasiclassical Green's function method, we compute the differential conductance $\sigma$ of the junction and demonstrate its dependence on the direction of the exchange field relative to the direction of the d-vector of the pair potential. If the p-wave triplet dominates the pairing, the zero bias conductance depends on the relative direction between the triplet d-vector and the exchange field. In contrast, if the s-wave singlet dominates the pairing, the zero bias conductance is isotropic with respect to the field direction. Furthermore, at zero temperature, the zero bias conductance height can only take two values as a function of $r$, the parameter quantifying the relative amount of s- and p-wave pairing, with an abrupt change at $r=1$ when the superconductor goes from a singlet to triplet dominated ground state. Moreover, we show that the relative amount of s- and p-wave pairing, can be estimated from the dependence of the finite bias conductance on the exchange field direction. Our results provide a way to characterize parity-mixed superconductors performing electrical measurements.

Competition between pairing and tripling in one-dimensional fermions with coexistent s - and p -wave interactions

We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity s-wave and odd-parity p-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as Cooper triple by solving the corresponding in-medium variational equations. We further feature the phase diagram consisting of the s- and p-wave Cooper pairing phase, and Cooper tripling phase, in the plane of s- and p-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both s- and p-wave interactions are moderately strong.

Two-dimensional superconductors with intrinsic p-wave pairing or nontrivial band topology

Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC), enabled by real-space superconducting proximity effect, reciprocal-space superconducting proximity effect, and intrinsic TSC. Whereas the first scheme has so far been most extensively explored, the subtle difference between the other two remains to be fully substantiated. We then move on to candidate intrinsic or p-wave superconductors, including Sr2RuO4,UTe2,Pb3Bi, and graphene-based systems. For TSC systems that rely on proximity effects, the emphases are mainly on the coexistence of superconductivity and nontrivial band topology, as exemplified by transition metal dichalcogenides, cobalt pnictides, and stanene, all in monolayer or few-layer regime. The review completes with discussions on the three dominant tuning schemes of strain, gating, and ferroelectricity in acquiring one or both essential ingredients of the TSC, and optimizations of such tuning capabilities may prove to be decisive in our drive towards braiding of Majorana zero modes and demonstration of topological qubits.

Topological Superconductivity Based on Antisymmetric Spin-Orbit Coupling.

Topological superconductivity (TSC) has drawn much attention for its fundamental interest and application in quantum computation. An outstanding challenge is the lack of intrinsic TSC materials with a p-wave pairing gap, which has led to the development of an effective p-wave theory of coupling s-wave gap with Rashba spin-orbit coupling (RSOC). However, the RSOC-strict mechanism and materials pose still both fundamental and practical limitations. Here, we generalize this theory to antisymmetric SOC (ASOC). Using k·p perturbation theory, we demonstrate that 2D crystals, with point groups of C2, C4, C6, C2v, C4v, C6v, D2, D4, D6, S4, or D2d, can all facilitate the desired ASOC. Remarkably, this enables us to discover 314 TSC candidates by screening 2D material databases, which are further confirmed by first-principles calculations of Majorana boundary modes and the topological invariant of the superconducting gap. Our work fundamentally enriches TSC theory and greatly expands the classes of TSC materials for experimental exploration.

Exploring unconventional quantum criticality in the p -wave-paired Aubry-André-Harper model

We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-Andr\'{e}-Harper model with p-wave pairing, which have rarely been exploited as most investigations focus on the localization transition from the critical phase to the localized phase. We find that the spectrum averaged entanglement entropy and the generalized fidelity susceptibility act as eminent universal order parameters of the corresponding critical point without gap closing. We introduce a Widom scaling ansatz for these criticality probes to develop a unified theory of critical exponents and scaling functions. We thus extract the correlation-length critical exponent $\nu$ and the dynamical exponent $z$ through the finite-size scaling given the system sizes increase in the Fibonacci sequence. The retrieved values of $\nu \simeq 1.000$ and $z \simeq 3.610$ indicate that the transition from the extended phase to the critical phase belongs to a different universality class from the localization transition. Our approach sets the stage for exploring the unconventional quantum criticality and the associated universal information of quasiperiodic systems in state-of-the-art quantum simulation experiments.

Functional renormalization of spinless triangular-lattice fermions: N-patch vs. truncated-unity scheme

We study competing orders of spinless fermions in the triangular-lattice Hubbard model with nearest-neighbor interaction. We calculate the effective, momentum-resolved two-particle vertex in an unbiased way in terms of the functional renormalization group method and compare two different schemes for the momentum discretization, one based on dividing the Fermi surface into patches and one based on a channel decomposition. We study attractive and repulsive nearest-neighbor interaction and find a competition of pairing and charge instabilities. In the attractive case, a Pomeranchuk instability occurs at Van Hove filling and f-wave and p-wave pairing emerge when the filling is reduced. In the repulsive case, we obtain a charge density wave at Van Hove filling and extended p-wave pairing with reduced filling. The p-wave pairing solution is doubly degenerate and can realize chiral p+ip superconductivity with different Chern numbers in the ground state. We discuss implications for strongly correlated spin-orbit coupled hexagonal electron systems such as moiré heterostructures.Graphic

Supercurrent-Induced Weyl Superconductivity

We show that Weyl superconductivity can be induced by finite supercurrent in noncentrosymmetric spin–orbit-coupled superconductors with line nodes. We introduce a three-dimensional tight-binding model of a tetragonal superconductor in a D+p-wave pairing state with a finite center-of-mass momentum, and elucidate that a line-nodal to point-nodal spectral transition occurs by applying an infinitesimal supercurrent. We also clarify that the higher-order effect in spin–orbit coupling is particularly important for this phenomenon. The point nodes are protected by topologically nontrivial Weyl charges, and therefore gapless arc states appear on the surface of the superconductor. Furthermore, both the positions and the Weyl charges of the point nodes depend on the direction of the current. In addition, a quantized Berry phase defined on high-symmetry planes characterizes the Weyl nodes when the in-plane supercurrent is considered. Our proposition paves a new way for controlling the superconducting gap structures by using an external field.

Diagnosis of pairing symmetry by vortex and edge spectra in kagome superconductors

Layered kagome metals AV3Sb5 (A=K, Rb, Cs) exhibit diverse correlated electron phenomena. It includes charge density wave formation and superconductivity the pairing symmetry of which, however, is controversial due to contradictory experimental evidence. Through calculations based on real-space lattice models at the mean-field level, we investigate the vortex and surface spectra of all competitive pairing propensities suggested for AV3Sb5 from a weak coupling analysis of unconventional superconductivity. Chiral p-wave pairing emerges as the only option to host Majorana bound states in the vortex core. We find chiral edge states for both p-wave and d-wave pairing, along with flat Andreev surface bound states for f -wave pairing. Our results expand the fingerprint of superconducting pairing, and thus will contribute to resolving the nature of superconductivity in AV3Sb5.

Kondo screening cloud in a superconductor with mixed s-wave and p-wave pairing states

We study the Kondo screening of a spin-1/2 magnetic impurity coupled to a superconductor, which is fabricated by combination of an s-wave superconductor, a ferromagnet and a semiconductor with Rashba spin–orbit coupling (RSOC). The proximity induced superconducting states include the s-wave and p-wave pairing components with the aids of RSOC, and the ferromagnet induces a Zeeman field which removes the spin degeneracy of the quasiparticles in the triplet states. Thus, the Kondo screening of magnetic impurity involves the orbital degrees of freedom, and is also affected by the Zeeman field. Using the variational method, we calculate the binding energy and the spin–spin correlation between the magnetic impurity and the electrons in the coexisting s-wave and p-wave pairing states. We find that Kondo singlet forms more easily with stronger RSOC, but Zeeman field in general decreases the binding energy. The spin–spin correlation decays fast in the vicinity of the magnetic impurity. Due to the RSOC, the spatial spin–spin correlation becomes highly anisotropic, and the Zeeman field can induce extra asymmetry to the off-diagonal components of the spin–spin correlation. Our study can offer some insights into the studies of extrinsic topological superconductors fabricated from the hybrid structures containing chains of magnetic impurities.

Emergent force and work fluctuations in a bilayer superfluid Bose–Fermi mixture in mixed dimensions

We investigate a system of two-atomic species in mixed dimensions, in which one species is spread in a three-dimensional space and the other species is confined in two parallel layers. The presence of atoms in three-dimensions creates an induced potential for the ones confined in layers. Depending on the scattering (coherence) length and the layer separation, the formation of p-wave pairing within the same layer or s-wave pairing between different layers has been suggested. It was shown that these pairs cannot coexist when time-reversal symmetry is on, and there appears a transition from p-wave to s-wave as the ratio of the layer separation and the effective scattering length decreases. Here, we study the thermodynamical signatures of such transition and find that with the formation of the inter-layer pairing, an emergent force to be present at the critical point and show that it can be derived from the ground state energy. This result offers a tool for experimentally realizing such transitions, and can find notable potential in the field of quantum-thermodynamics.

Instability of Majorana states in Shiba chains due to leakage into a topological substrate

We revisit the problem of Majorana states in chains of scalar impurities deposited on a superconductor with a mixed s-wave and p-wave pairing. We also study the formation of Majorana states for magnetic impurity chains. We find that the magnetic impurity chains exhibit well-localized Majorana states when the substrate is trivial, but these states hybridize and get dissolved in the bulk when the substrate is topological. Most surprisingly, and contrary to previous predictions, the scalar impurity chain does not support fully localized Majorana states except for very small and finely tuned parameter regimes, mostly for a non-topological substrate close to the topological transition. Our results indicate that a purely p-wave or a dominant p-wave substrate are not good candidates to support either magnetic or scalar impurity topological Shiba chains.

Calculations of in-gap states of ferromagnetic spin chains on s -wave wide-band superconductors

Magnetic impurities create in-gap states on superconductors. Recent experiments explore the topological properties of one-dimensional arrays of magnetic impurities on superconductors, because in certain regimes p-wave pairing can be locally induced leading to new topological phases. A by-product of the new accessible phases is the appearance of zero-energy edge states that have non-Abelian exchange properties and can be used for topological quantum computation. Despite the large amount of theory devoted to these systems, most treatments use approximations that render their applicability limited when comparing with usual experiments of 1-D impurity arrays on wide-band superconductors. These approximations either involve tight-binding-like approximations where the impurity energy scales match the minute energy scale of the superconducting gap and are many times unrealistic, or they assume strongly-bound in-gap states. Here, we present a theory for s-wave superconductors based on a wide-band normal metal, with any possible energy scale for the magnetic impurities. The theory is based on free-electron Green's functions. We include Rashba coupling and compare with recent experimental results, permitting us to analyze the topological phases and the experimental edge states. The infinite-chain properties can be analytically obtained, giving us a way to compare with finite-chain calculations. We show that it is possible to converge to the infinite limit by doing finite numerical calculation, paving the way for numerical calculations not based on analytical Green's functions.

Local spin-triplet superconductivity in half-metallic manganites: A perspective platform for high-temperature topological superconductivity

Topological materials and their unusual properties are nowadays a focus of experimental and theoretical research. Promising systems where topological superconducting phases can be realized are materials with a spin-triplet superconducting state. Yet, in the nature superconductors with a spin-triplet p-wave pairing are exceptions. The experimentally accessible way to overcome this bottleneck is spin-triplet pairing induced in proximitized structures of spin-singlet superconductors with time-reversal symmetry breaking counterparts. We discuss the possibility of creating such materials using superconductor–half-metallic manganite nano-structures. A unique promising feature of the proximity-coupled hybrid structures is high-temperature local triplet superconductivity in half-metallic manganites. The experimental evidence of a latent spin-triplet pairing in half-metallic manganites is presented and conditions favoring the topological superconducting state in nanostructures based on them are discussed.