P-wave Pairing Research Articles

Competing orders in a dipolar Bose-Fermi mixture on a square optical lattice: mean-field perspective

We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar Bose-Einstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of $D_4$, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of $D_4$. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the d_{x^{2}-y^{2}}-wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with $d_{xy}$- and g-wave symmetries but not enough for them to dominate other competing phases.

21pAG-11 ディラック電子系におけるバレー内ペアリングによるp波超伝導状態

21pAG-11 ディラック電子系におけるバレー内ペアリングによるp波超伝導状態

Analytical solutions of equation for the order parameter of dense superfluid neutron matter with anisotropic spin-triplet p-wave pairing at finite temperatures

The previously derived equations for the components of the order parameter (OP) of dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing and with taking into account the effects of magnetic field and finite temperatures are reduced to the single equation for the one-component OP in the limit of zero magnetic field. Here this equation is solved analytically for arbitrary parametrization of the effective Skyrme interaction in neutron matter and as the main results the energy gap (in the energy spectrum of neutrons in SNM) is obtained as nonlinear function of temperature T and density n in two limiting cases: for low temperatures near T = 0 and in the vicinity of phase transition temperature Tc0(n) for dense neutron matter from normal to superfluid state. These solutions for the energy gap are specified for generalized BSk21 and BSk24 parametrizations of the Skyrme forces (with additional terms dependent on density n) and figures are plotted on the interval 0.1n0 < n < 2.0n0, where n0 = 0.17 fm−3 is nuclear density.

Identifying the mobility edges in a one-dimensional incommensurate model with p-wave superfluid

The mobility edges which separate the localized energy eigenstates from the extended ones exist normally only in three dimensional systems. For one-dimensional systems with random on-site potentials, one never encounters mobility edges, where all the eigenstates are localized. However, there are two kinds of 1D systems such as correlated disordered models, and the systems of exponentially decaying hopping kinetics, features of mobility edges at some specific values become possible. We study in this paper the properties of the mobility edges in a one-dimensional p-wave superfluid on an incommensurate lattice with exponentially decaying hopping kinetics. Without the p-wave superluid, the system displays a single mobility edge, which separates the extended regime from the localized one at a certain energy. Without the exponentially decaying hopping term, the system displays a phase transition from a topological superconductor to an Anderson localization at a certain disorder strength, where no mobility edge exists. We are interested in the influence of the p-wave superfluid on the mobility edge. By solving the Bogoliubov-de Gennes equation, the eigenvalues and the eigenfunctions are obtained. In order to identify the extending or the localized properties of the eigenvectors, we define an inverse participation ratio IPR. For an extended state, IPRn～1/L which goes to zero at a large L, and for a localized one, IPRn being constant. Therefore, the IPR can be taken as a criterion to distinguish the extended state from the localized one, while the mobility edge is defined as the boundary between two different states. We find that, with a p-wave superfluid, the system changes from a single mobility edge to a multiple one, and the number of mobility edges increases with the increased superfluid pairing order parameter. To further obtain the energy or the location of the mobility edge, we investigate the scaling behavior of wave functions by using a multifractal analysis, which is calculated through the scaling index . The minimum value of the index, with the values min= 1, 0min1, and min= 0, mean the extended, critical, and localized states, respectively. For the two consecutive states, the minima of the scaling index min when extrapolating to the large size limit between 0 and 1 signal the mobility edge. By exploring the corresponding Bogoliubov quasi-particle wave functions for the system under open boundary conditions together with the multifractal analysis for the system under periodic boundary conditions, we identify two mobility edges for the system of the p-wave superfluid pairing. Furthermore, we will investigate how the existence of the mobility edges influences the p-wave superfluid, and identify the phase diagram at the given parameters. We will in the future try to understand the relationship between the topological superfluid and the mobility edges.

Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions

We study the effects of Majorana modes and interactions between electrons on transport in a one-dimensional system with a junction of three p-wave superconductors (SCs) which are connected to normal metal leads. For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads,and, depending on the signs of the p-wave pairings in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various sub-gap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next, we use a renormalization group approach to study the scattering matrix of the system at energies far from the SC gap. The fixed points of the renormalization group flows and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. We discuss the implications of this for the conductances. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs.

Zeeman Field-Induced Nodal Structures in Rashba-Type Noncentrosymmetric Superconductors

We study theoretically the effect of Zeeman field on the Bogoliubov–de Gennes quasiparticle excitation spectrum of a three-dimensional noncentrosymmetric \((s+p)\)-wave model. The quasiparticle excitation spectrum may possess line nodes due to the mixing of s-wave and p-wave pairing in the absence of Zeeman field. Our calculations show that, depending on the magnitude and the orientation of an applied Zeeman field, a variety of nodal structures including nodal points, nodal lines, and nodal surfaces may be generated in the excitation spectrum. These results are corroborated by numerical computations of the low-temperature electronic specific heat. Specifically, we demonstrate rigorously that the zero-field nodal lines will be robust against a weak z-axis oriented Zeeman field. It is also found that the electronic specific heat calculated for a Zeeman field in the x–y plane may qualitatively account for the novel feature of specific heat observed experimentally in CePt\(_3\)Si.

Route to Topological Superconductivity via Magnetic Field Rotation.

The verification of topological superconductivity has become a major experimental challenge. Apart from the very few spin-triplet superconductors with p-wave pairing symmetry, another candidate system is a conventional, two-dimensional (2D) s-wave superconductor in a magnetic field with a sufficiently strong Rashba spin-orbit coupling. Typically, the required magnetic field to convert the superconductor into a topologically non-trivial state is however by far larger than the upper critical field Hc2, which excludes its realization. In this article, we argue that this problem can be overcome by rotating the magnetic field into the superconducting plane. We explore the character of the superconducting state upon changing the strength and the orientation of the magnetic field and show that a topological state, established for a sufficiently strong out-of-plane magnetic field, indeed extends to an in-plane field orientation. We present a three-band model applicable to the superconducting interface between LaAlO3 and SrTiO3, which should fulfil the necessary conditions to realize a topological superconductor.

Induced p-wave superfluidity in imbalanced Fermi gases in a synthetic gauge field

We study the pairing formation and the appearance of induced spin-triplet p-wave superfluidity in dilute three-dimensional imbalanced Fermi gases in the presence of a uniform non-Abelian gauge field. This gauge field generates a synthetic Rashba-type spin–orbit interaction which has remarkable consequences in the induced p-wave pairing gaps. Without the synthetic gauge field, the p-wave pairing occurs in one of the components due to the induced (second-order) interaction via an exchange of density fluctuations in the other component. We show that this p-wave superfluid gap induced by density fluctuations is greatly enhanced due to the Rashba-type spin–orbit coupling.

Observability of surface Andreev bound states in a topological insulator in proximity to an s-wave superconductor

To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. We show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realise a Majorana zero-energy mode useful for quantum computation. Our main result is the relation between odd-frequency pairing and Majorana zero energy modes by using Green functions techniques in three-dimensional topological insulators in the so-called Majorana regime. We discuss thereafter how the pairing relations in the different regimes can be observed in the tunneling conductance of an s-wave proximised three-dimensional topological insulator. We discuss the necessity to incorporate a ferromagnetic insulator to localise the zero-energy bound state to the interface as a Majorana mode.

Competing d-Wave and p-Wave Spin-Singlet Superconductivities in the Two-Dimensional Kondo Lattice.

The Kondo lattice model describes a quantum phase transition between the antiferromagnetic state and heavy-fermion states. Applying the dual-fermion approach, we explore possible superconductivities emerging due to the critical antiferromagnetic fluctuations. The d-wave pairing is found to be the leading instability only in the weak-coupling regime. As the coupling is increased, we observe a change of the pairing symmetry into a p-wave spin-singlet pairing. The competing superconductivities are ascribed to crossover between small and large Fermi surfaces, which occurs with the formation of heavy quasiparticles.

Majorana modes and transport across junctions of superconductors and normal metals

We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) and normal metal leads. For a system with an SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the p-wave pairing changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as L is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally, we propose a novel experimental realization of these systems, in particular of a system where changes sign at one point inside the SC.

Possible p-Wave Superconductivity in Epitaxial Bi/Ni Bilayers**Supported by the National Basic Research Program of China under Grant Nos 2015CB921400 and 2011CB921802, the National Natural Science Foundation of China under Grant Nos 11374057, 11434003 and 11421404, the research of Andreev reflection wassupported as part of the SHINES, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of

Superconductivity (SC) is one of the most intriguing physical phenomena in nature. Nucleation of SC has long been considered highly unfavorable if not impossible near ferromagnetism, in low dimensionality and, above all, out of non-superconductor. Here we report observation of SC with TC near 4K in Ni/Bi bilayers that defies all known paradigms of superconductivity, where neither ferromagnetic Ni film nor rhombohedra Bi film is superconducting in isolation. This highly unusual SC is independent of the growth order (Ni/Bi or Bi/Ni), but highly sensitive to the constituent layer thicknesses. Most importantly, the SC, distinctively non-?? pairing, is triggered from, but does not occur at, the Bi/Ni interface. Using point contact Andreev reflection, we show evidences that the unique SC, naturally compatible with magnetism, is triplet p-wave pairing.

Heavy-Fermion Superconductivity and Localized-Itinerant Crossover in the Kondo Lattice

Superconductivity in the two-dimensional Kondo lattice model is derived by means of the dual-fermion approach. This framework takes full account of local correlations based on the dynamical mean-field theory and further includes influence of critical antiferromagnetic fluctuations. It is found that pairing with dx2 −y2 symmetry similar to the Hubbard model appears only in the weak-coupling regime. As the coupling is increased, we observe transition to p-wave spin-singlet superconductivity. The emergence of the unconventional p-wave pairing is ascribed to formation of large Fermi surface, which embodies itinerancy of f electrons.

Doping and Raman scattering of strong spin-orbit-coupling compound Sr2-xLaxIrO4

Novel unconventional physical phenomena, such as metal-insulator transition, high temperature superconductivity, colossal magneto-resistance and quantum criticality, are usually found in transition metal oxides (TMOs) with layered perovskite structures. Great success has been achieved in 3d TMOs, in which the localized 3d states yield strongly correlated narrow bands with a large on-site Coulomb repulsion U and a small band width W. Anomalous insulating behaviors are reported in the 5d TMOs, such as Sr2IrO4 system, which is surprising since the 5d TMOs are usually considered as weakly correlated wide band systems with largely reduced on-site Coulomb repulsion U due to delocalized 5d states. The crystal structure of Sr2IrO4 consists of two-dimensional (2D) IrO2 layers, similar to the parent compound La2CuO4 of the cuprates. Theoretically, a variational Monte Carlo study of Sr2IrO4 suggests that d-wave like superconductivity may appear but only within a narrow region of electron doping. In contrast, an s±*-wave phase is established for hole doping deduced from functional renormalization group, and triggered by spin fluctuations within and across the two conduction bands. Moreover, triplet p-wave pairing state with relatively high transition temperature emerges on the hole-doped side when the Hund's coupling is comparable to spin-orbit coupling. Several experiments are tried to search for the predicted unconventional superconductivity due to both electron-and hole-doping. However, to the best of our knowledge, it has not been found yet in the carrier-doped Sr2IrO4 system. Hence, more detailed studies are needed to explore the potential superconductivity.#br#A series of La doped Sr2-xLaxIrO4 samples is synthesized based on solid state reaction method. The evolution of the crystal structure is studied by the X-ray diffraction, scanning electron microscopy, together with the Raman spectrum. It is found that the crystal constant of the c-axis decreases with increasing doping level as well as the apical Ir—O1 bond length, indicating the lattice construction. Moreover, the distortion of the IrO6 octahedron reduces with increasing doping level. Therefore, blue shift occurs of the Raman scattering peaks. The temperature dependence of the Raman spectrum is also studied. It is found that the frequencies of the A1g and B1g vibration modes increase with temperature decreasing and an abnormal jump occurs around 110 K, which is believed to be correlated with the structural change and the magnetic transition around this temperature.

Phase Coherence and Andreev Reflection in Topological Insulator Devices

Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to non-magnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate p-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics which can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Perot oscillations in a TI sandwiched between a superconducting and normal lead. For energies below the superconducting gap, we observe a doubling in the frequency of the oscillations, arising from the additional phase accumulated from Andreev reflection. When a magnetic field is applied perpendicular to the TI surface, a number of very sharp and gate-tunable conductance peaks appear at or near zero energy, which has consequences for interpreting spectroscopic probes of Majorana fermions. Our results demonstrate that TIs are a promising platform for exploring phase-coherent transport in a solid-state system.

Possible realization of a chiralp-wave paired state in a two-component system

There is much interest in the realization of systems with p-wave pairing in one dimension or chiral p-wave pairing in two dimensions, because these are believed to support Majorana modes at the ends or inside vortices. We consider a two component system of composite fermions and provide theoretical evidence that, under appropriate conditions, the screened interaction between the minority composite fermions is such as to produce an almost exact realization of p-wave paired state described by the so-called anti-Pfaffian wave function. This state is predicted to occur at filling $\nu=3/8$ or 13/8 in GaAs when the Zeeman energy is sufficiently small, and at $\nu=\pm 3/8$ or $\pm 13/8$ in single layer graphene when either the Zeeman or the valley splitting is sufficiently small.

Interplay of p-wave pairing potential and spin–orbit coupling in two-dimensional noncentrosymmetric superconductors

Both pairing potential and spin–orbit coupling (SOC) play important roles in two-dimensional noncentrosymmetric superconductivity. Supposing that p-wave pairing potential is present between quasiparticles, spin–singlet pairs arise and mix with spin–triplet pairs in the electron space. Our results show that the effect of SOC on the electron superconducting order parameters is different below and above a critical pairing potential V¯C. If the pairing potential V¯<V¯C, both the spin–singlet and triplet pairings are enhanced by the SOC. On the other hand, when V¯>V¯C, increasing SOC leads to increment of the spin–singlet pairing, but reduction of the triplet one. Moreover, V¯C increases with SOC.

Vortex Lattice Studies in Type-II Superconductors by SANS

When a type-II superconductor is placed in a magnetic field, it is threaded by swirling whirlpools of electric current known as vortices. The vortices behave like massive entities and provide a unique probe into the nature of the superconducting state in the host material. Furthermore, the collective vortex behavior is of crucial importance for practical applications since vortex motion will lead to dissipation. I will discuss two recent vortex lattice (VL) studies using small-angle neutron scattering (SANS) that exemplify the continuous evolution of this technique. In the first example we used SANS to determine the superconducting anisotropy of Sr2RuO4 (SRO) that is among the few superconductors believed to exhibit p-wave pairing [1]. While there is significant experimental support for unconventional pairing, there is a discrepancy between the anisotropies of the upper critical field and the Fermi surface. Taking advantage of the significant transverse VL field component that arises due to the large anisotropy of SRO we measured the superconducting anisotropy ≍ 60, roughly three times greater than the upper critical field anisotropy. This result imposes significant constraints on possible models of triplet pairing in SRO. In the second example we used a stop-motion technique to study VL transition dynamics in MgB2 [2,3]. Here the VL exhibit extensive metastability in connection with a second order rotational phase transition that cannot be understood based on the single VL domain free energy or vortex pinning. Instead, we have proposed that a jamming of VL domains acting as granular entities is responsible for the metastability. We have performed extensive SANS experiments, as the VL is driven from the metastable to the ground state by small-amplitude AC magnetic field oscillations. This shows a dual power-law behavior indicating a two-step process for the transition to the ground state. Supported by the US Department of Energy (Grant No. DE-FG02-10ER46783).

Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model

We study the quantum many-body instabilities of the t−JK−JH Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-1/2 model is believed to describe the magnetic properties of the layered transition-metal oxide Na2IrO3. We determine the ground state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow equations adapted to the lack of full spin-rotational invariance in the fermionic interactions, here represented by the highly frustrated and anisotropic Kitaev exchange term. Additionally employing a set of the Ward identities for the Kitaev-Heisenberg model, the numerical solution of the flow equations suggests a rich phase diagram emerging upon doping charge carriers into the ground-state manifold (Z2 quantum spin liquids and magnetically ordered phases). We corroborate superconducting triplet p-wave instabilities driven by ferromagnetic exchange and various singlet pairing phases. For filling δ>1/4, the p-wave pairing gives rise to a topological state with protected Majorana edge modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg exchanges, we obtain bond-order instabilities at van Hove filling supported by nesting and density-of-states enhancement, yielding dimerization patterns of the electronic degrees of freedom on the honeycomb lattice. Further, our flow equations are applicable to a wider class of model Hamiltonians.11 MoreReceived 1 May 2014Revised 30 June 2014DOI:https://doi.org/10.1103/PhysRevB.90.045135©2014 American Physical Society

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e 2 / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g s + 2Δ with Δ the p-wave pairing amplitude and g s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.