P-wave Pairing Research Articles

Self-localization of magnons and a magnetoroton in a binary Bose-Einstein condensate

We consider a two-component Bose-condensed mixture characterized by positive s-wave scattering lengths. We assume equal densities and intra-species interactions. By doing the Bogoliubov transformation of an effective Hamiltonian we obtain the lower energy magnon dispersion incorporating the superfluid entrainment between the components. We argue that p-wave pairing of distinct bosons should be accompanied by self-localization of magnons and formation of a magnetoroton. We demonstrate the effect on a model system of particles interacting via step potentials.

Topological Features in a Chiral p-wave Superconductor under Uniaxial Strain

Uniaxial strain effects in the superconducting phase are investigated assuming chiral p-wave pairing for the unconventional superconductor Sr2RuO4. The Fermi surface structure of the γ-band is espe...

Conversion of a conventional superconductor into a topological superconductor by topological proximity effect

Realization of topological superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topological insulator contacted with a superconductor hosts an effective p-wave pairing by the penetration of Cooper pairs across the interface. However, this approach suffers a difficulty in accessing the topological interface buried deep beneath the surface. Here, we propose an alternative approach to realize topological superconductivity without SPE. In a Pb(111) thin film grown on TlBiSe2, we discover that the Dirac-cone state of substrate TlBiSe2 migrates to the top surface of Pb film and obtains an energy gap below the superconducting transition temperature of Pb. This suggests that a Bardeen-Cooper-Schrieffer superconductor is converted into a TSC by the topological proximity effect. Our discovery opens a route to manipulate topological superconducting properties of materials.

Superconducting behavior of BaTi2Bi2O and its pressure dependence.

A new superconducting sample, BaTi2Bi2O, was synthesized and characterized over a wide pressure range. The superconducting transition temperature, Tc, of BaTi2Bi2O was 4.33 K at ambient pressure. The crystal structure was tetragonal (space group of P4/mmm (No. 123)), according to the X-ray diffraction (XRD) pattern at ambient pressure. The XRD pattern was analyzed using the Le Bail method. The magnetic-field dependence of the magnetization at different temperatures was precisely investigated to elucidate the characteristics of the superconductivity. The pressure-dependent XRD patterns showed absence of structural phase transitions up to 19.8 GPa. The superconducting properties of BaTi2Bi2O were investigated under pressure. Tc monotonously increased with the pressure (p) up to 4.0 GPa and saturated above 4.0 GPa. The variations in the Tc-p plot were thoroughly analyzed. The Cooper pair symmetry (or superconducting pairing mechanism) was analyzed based on the magnetic field dependence of the superconductivity at ambient and high pressures, which indicated a sign of p-wave pairing for the superconductivity of BaTi2Bi2O, i.e., topologically nontrivial sign was suggested for BaTi2Bi2O.

Surface superconductivity in the type II Weyl semimetal TaIrTe4.

The search for unconventional superconductivity in Weyl semimetal materials is currently an exciting pursuit, since such superconducting phases could potentially be topologically non-trivial and host exotic Majorana modes. The layered material TaIrTe4 is a newly predicted time-reversal invariant type II Weyl semimetal with the minimum number of Weyl points. Here, we report the discovery of surface superconductivity in Weyl semimetal TaIrTe4. Our scanning tunneling microscopy/spectroscopy (STM/STS) visualizes Fermi arc surface states of TaIrTe4 that are consistent with the previous angle-resolved photoemission spectroscopy results. By a systematic study based on STS at ultralow temperature, we observe uniform superconducting gaps on the sample surface. The superconductivity is further confirmed by electrical transport measurements at ultralow temperature, with an onset transition temperature (Tc) up to 1.54 K being observed. The normalized upper critical field h*(T/Tc) behavior and the stability of the superconductivity against the ferromagnet indicate that the discovered superconductivity is unconventional with the p-wave pairing. The systematic STS, and thickness- and angular-dependent transport measurements reveal that the detected superconductivity is quasi-1D and occurs in the surface states. The discovery of the surface superconductivity in TaIrTe4 provides a new novel platform to explore topological superconductivity and Majorana modes.

A magnetic field boost for superconductors

High-magnetic-field experiments on the recently discovered unconventional superconductor UTe2 are consistent with p-wave pairing arising while time-reversal symmetry is broken. In turn, this suggests that this material is a candidate for a chiral superconductor that may be exploited for topological quantum computing.

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.

Fractional excitations in one-dimensional fermionic systems

We study the soliton modes carrying fractional quantum numbers in one-dimensional fermionic systems. In particular, we consider the solitons in the one-dimensional fermionic superfluids. For the s-wave order parameter with phase twisted by an angle φ, the complex Z2 soliton may occur carrying a localized fractional quantum number φ/(2π). If the system is finite with length L, we show the existence of a uniform background −φ/(2πL) which, though vanishing in the thermodynamic limit, is essential to maintain the conservation of the total integer quantum number. This analysis is also applicable to other systems with fractional quantum numbers, thus providing a mechanism to understand the compatibility of the emergence of fractional quantum number in the thermodynamic limit of a finite system with only integer quantum numbers. For the p-wave pairing case, the Majorana zero mode may occur associated with a real Z2 soliton, and the fractionalized quantum number is the dimension of the single particle Hilbert space, which turns out to be 1/2. Again for a finite system with length L, there is an accompanying uniform dimension density −1/(2L) to maintain the dimension of the Hilbert space invariant. We conjecture a connection of the dimension density of one-dimensional solitons with the quantum dimension of topological excitations.

Experimental evidence of anomalously large superconducting gap on topological surface state of β-Bi2Pd film

Connate topological superconductor (TSC) combines topological surface states with nodeless superconductivity in a single material, achieving effective p-wave pairing without interface complication. By combining angle-resolved photoemission spectroscopy and in-situ molecular beam epitaxy, we studied the momentum-resolved superconductivity in β-Bi2Pd film. We found that the superconducting gap of topological surface state (ΔTSS ∼ 3.8 meV) is anomalously enhanced from its bulk value (Δb ∼ 0.8 meV). The ratio of 2ΔTSS/kBTc ∼ 16.3, is substantially larger than the BCS value. By measuring β-Bi2Pd bulk single crystal as a comparison, we clearly observed the upward-shift of chemical potential in the film. In addition, a concomitant increasing of surface weight on the topological surface state was revealed by our first principle calculation, suggesting that the Dirac-fermion-mediated parity mixing may cause this anomalous superconducting enhancement. Our results establish β-Bi2Pd film as a unique case of connate TSCs with a highly enhanced topological superconducting gap, which may stabilize Majorana zero modes at a higher temperature.

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.

Analytical derivation of expressions for the specific heat of superfluid Fermi liquids with anisotropic spin-triplet p-wave pairing at finite temperatures

Analytical expressions for the specific heat of superfluid Fermi liquids (SFLs) with anisotropic spin-triplet p-wave pairing of the 3He-A type have been obtained based on a generalised Fermi-liquid approach both at the low temperatures of 0 < T ≪Tc0 (n) and near the temperature of the phase transition [Tc0 (n)] from a normal to a superfluid phase in the absence of a magnetic field. Apart from liquid 3He-A, we also study dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing (similar to 3He-A) at subnuclear (n < n0, where n0 = 0.17 fm–3 is the nuclear density) and supernuclear densities (n > n0) in view of generalised Skyrme forces (with additional terms depending on the density n). At 0 < T ≪Tc0 (n), we have obtained an asymptotic expansion for the specific heat CSNM(SFL)(T,n), in which, apart from the main term ∼ T 3 (known for 3He-A in the limit of T → 0) there is an additional correction term (∼ T5), which may reach several percent of the contribution from the main term to the decomposition of the specific heat of SNM (or SFLs). An analytical formula has also been derived for calculating the specific heat CSNM(SFL)(T,n) at temperatures near Tc0(n). The expressions obtained for the CSNM(T,n) functions (valid for an arbitrary parametrisation of the effective Skyrme interaction in neutron matter) have been defined for SNM with the generalised BSk21 parametrisation of Skyrme forces. In addition, dependency graphs were plotted for the specific heat CBSk21(t, y) in the reduced temperature range of 0 < t ≡ T/Tc0(n) ≪ 1 and at t ≲ 1 for dense SNM (at 0.1 ≤ y ≡ n/n0 ≤ 1.7). These results may be of interest for neutron star physics in connection with neutron star cooling (in the presence of neutron superfluidity with anisotropic spin-triplet p-wave Cooper pairing in the outer part of dense liquid neutron star cores).

BCS – BEC crossover, collective excitations, and hydrodynamics of superfluid quantum liquids and gases

A Fermi gas described within the Bardeen–Cooper–Schrieffer (BCS) theory can be converted into a Bose–Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning the interaction. The sequence of states that emerge in the process of such a conversion is referred to as the BCS–BEC crossover. We here review the theoretical and experimental results obtained for the BCS–BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of superfluid quantum gases and fluids, including the collective excitation spectrum in the BCS–BEC crossover, the hydrodynamics of rotating Bose condensates containing a large number of quantized vortices, and the intriguing problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the potential to realize the triplet p-wave pairing via the Kohn–Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and the observation of fluctuation phenomena related to the Berezinskii–Kosterlitz–Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS–BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.

Tunable superconducting effective gap in graphene-TMDC heterostructures

Growth of graphene on monolayer transition-metal dichalcogenides presents opening on band gap and giant spin-orbit coupling which paves the way to achieve a useful hybrid structure for electronics and spintronics applications. Increase of the atomic number of transition-metal results in a large SOC, where eventually a band inversion appears in graphene-WSe2. We consider superconductor induction by proximity effect to the graphene-TMDC hybrid structure. As a necessity of formalism, we introduce a proper time-reversal and particle-hole symmetry operators, under which the 8 × 8 Dirac-Bogoliubov-de Gennes low-energy effective Hamiltonian is invariant. Resulting superconducting electron-hole excitations shows that, the essential dynamical parameters λIA,B and λR have significant effect on superconducting excitations and, specifically, subgap energy. Dependence of the superconducting energy excitation on chemical potential is explored. The signature of spin triplet p-wave pairing symmetry in the system is found to increase the subgap superconducting energy, in comparing to s-wave symmetry.

Proximity Effects of Superconductivity and Antiferromagnetism in a Nanowire

In this paper, we theoretically study the proximity effects of s-wave superconductivity(SC) and antiferromagnetism(AFM) in a nanowire. For the half-filling case, it was found that the Andreev bound states form near the boundary between the AFM and the SC which are accompanied by the strongly localized p-wave pairing. These in-gap states remain when the system is slightly doped. For the electron or hole doped system, they merge into the upper or the lower antiferromagnetic bands gradually with the increase of doping, respectively.

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.

P -wave superfluidity in mixtures of ultracold Fermi and spinor Bose gases

We reveal that the p-wave superfluid can be realized in a mixture of fermionic and F=1 bosonic gases. We derive a general set of the gap equations for gaps in the s- and p-channels. It is found that the spin-spin bose-fermi interactions favor the p-wave pairing and naturally suppress the pairing in the s-channel. The gap equations for the polar phase of p-wave superfluid fermions are numerically solved. It is shown that a pure p-wave superfluid can be observed in a well-controlled environment of atomic physics.

Topological phase transition of the anisotropic XY model with Dzyaloshinskii-Moriya interaction

Within the real space renormalization group we obtain the phase portrait of the anisotropic quantum XY model on square lattice in presence of Dzyaloshinskii-Moriya (DM) interaction. The model is characterized by two parameters, $\lambda$ corresponding to XY anisotropy, and $D$ corresponding to the strength of DM interaction. The flow portrait of the model is governed by two global Ising-Kitaev attractors at $(\lambda=\pm1,D=0)$ and a repeller line, $\lambda=0$. Renormalization flow of concurrence suggests that the $\lambda=0$ line corresponds to a topological phase transition. The gap starts at zero on this repeller line corresponding to super-fluid phase of underlying bosons; and flows towards a finite value at the Ising-Kitaev points. At these two fixed points the spin fields become purely classical, and hence the resulting Ising degeneracy can be interpreted as topological degeneracy of dual degrees of freedom. The state of affairs at the Ising-Kitaev fixed point is consistent with the picture of a p-wave pairing of strength $\lambda$ of Jordan-Wigner fermions coupled with Chern-Simons gauge fields.

Phase diagram of the incommensurate off-diagonal Aubry–André model with p-wave pairing

Using exact numerical methods, we study the interplay between p-wave superconductivity and off-diagonal modulation in the incommensurate off-diagonal Aubry–André model with p-wave pairing. When chemical potential is zero, the modulation not only leads to an Anderson-like localization with all bulk states changing into critical ones, but also induces a topological phase transition accompanying the disappearing of exponentially localized zero-energy edge Majorana fermions. These two transitions happen at different places and true Anderson localization is absent. With a finite chemical potential, the quasi-periodicity of the modulation causes band splitting and drives the system into a band insulator phase. It has a fixed incommensurate particle density which is determined by the modulation frequency. Phase diagrams are identified, and can be tested with existing proposals for experimental realizations of the effective off-diagonal disorder and the p-wave pairing.

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.

Direct Observation of Composite Fermions and Their Fully-Spin-Polarized Fermi Sea near ν=5/2.

The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor ν=5/2 is arguably the most promising candidate for harboring Majorana quasiparticles with non-Abelian statistics and, thus, of potential use for topological quantum computing. The theoretical description of the ν=5/2 state is generally believed to involve a topological p-wave pairing of fully-spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near ν=5/2 or for an underlying fully-spin-polarized Fermi sea. Here, we report the observation of composite fermions very near ν=5/2 through geometric resonance measurements and find that the measured Fermi wave vector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of 5/2 fractional quantum Hall effect as a topological p-wave paired state of composite fermions.