Chiral P-wave Research Articles

Anomalous switching in Nb/Ru/Sr2RuO4 topological junctions by chiral domain wall motion

A spontaneous symmetry breaking in a system often results in domain wall formation. The motion of such domain walls is utilized to realize novel devices like racetrack-memories, in which moving ferromagnetic domain walls store and carry information. Superconductors breaking time reversal symmetry can also form domains with degenerate chirality of their superconducting order parameter. Sr2RuO4 is the leading candidate of a chiral p-wave superconductor, expected to be accompanied by chiral domain structure. Here, we present that Nb/Ru/Sr2RuO4 topological superconducting-junctions, with which the phase winding of order parameter can be effectively probed by making use of real-space topology, exhibit unusual switching between higher and lower critical current states. This switching is well explained by chiral-domain-wall dynamics. The switching can be partly controlled by external parameters such as temperature, magnetic field and current. These results open up a possibility to utilize the superconducting chiral domain wall motion for future novel superconducting devices.

Half-Fluxon on Long Josephson Junction with Chiral Superconductors

A half-fluxon on a long Josephson junction with a chiral p-wave superconductor is studied. The half-fluxon is similar to the half quantum vortex (half-fluxoid) proposed by Volovik and Mineev in that the half quantum vortex results from the cooperation between two kinds of phases provided by a superconducting order parameter: one is a global phase related to the symmetry \(U(1)\) and the other is the rotation phase of a \(\hat{\mathbf{d}}\) vector related to the symmetry \(\hat{D}^{(+)}_{(1)}\) in spin space. Each phase for the half-fluxon varies with \(\pi\) along a long Josephson junction. In contrast, each phase varies with \(2\pi(n+1/2)\) along a half-fluxoid. A half-fluxon and a half-fluxoid are accompanied by a spin current, which is induced by the spatial modulation of a \(\hat{\mathbf{d}}\) vector. This half-fluxon is different from a half-fluxon on a Josephson 0–\(\pi\)-junction in terms of the spin current. A spin current is parallel or antiparallel to a supercurrent. Therefore, the spin current ...

Dynamical mass generation of composite Dirac fermions and fractional quantum Hall effects near charge neutrality in graphene

We develop a composite Dirac fermion theory for the fractional quantum Hall effects (QHE) near charge neutrality in graphene. We show that the interactions between the composite Dirac fermions lead to a dynamical mass generation through exciton condensation. The four-fold spin–valley degeneracy is fully lifted due to the mass generation and exchange effects such that the odd-denominator fractional QHE observed in the vicinity of charge neutrality can be understood in terms of the integer QHE of composite Dirac fermions. At a filling factor ν = 1/2, we show that the massive composite Dirac fermion liquid is unstable against chiral p-wave pairing for weak Coulomb interactions and the ground state is a paired non-Abelian quantum Hall state described by the Moore–Read Pfaffian in the long wavelength limit.

Interaction Between Domain Walls in Chiral p-Wave Superfluids

We calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix.

Effect of Born and unitary impurity scattering on the Kramer–Pesch shrinkage of a vortex core in a chiral p-wave superconductor

We theoretically investigate a non-magnetic impurity effect on the temperature dependence of the vortex core shrinkage (Kramer–Pesch effect) in a chiral p-wave superconductor. The Born limit and the unitary limit scattering are compared within the framework of the quasiclassical theory of superconductivity. We find that the robustness of the Kramer–Pesch effect against the impurity scattering in the Born limit is lost in the unitary limit.

Spin Density Wave Fluctuations andp-Wave Pairing inSr2RuO4

Recently, a debate has arisen over which of the two distinct parts of the Fermi surface of Sr(2)RuO(4) is the active part for the chiral p-wave superconductivity exhibited. Early theories proposed p-wave pairing on the two-dimensional γ band, whereas a recent proposal focuses on the one-dimensional (α, β) bands whose nesting pockets are the source of the strong incommensurate spin density wave (SDW) fluctuations. We apply a renormalization group theory to study quasi-one-dimensional repulsive Hubbard chains and explain the form of SDW fluctuations, reconciling the absence of long-range order with their nesting Fermi surface. The mutual exclusion of p-wave pairing and SDW fluctuations in repulsive Hubbard chains favors the assignment of the two-dimensional γ band as the source of p-wave pairing.

Vortex structures in modelp-wave superconducting Sr2RuO4: Single two-dimensional band vs quasi-one-dimensional bands

There have been an interesting debate on the primary source of chiral p-wave superconductivity in Sr2RuO4. We present a comparative study on the vortex structure between a single 2-dimensional (2D) band and quasi-1D band model by using Bogoliubov-de Gennes theory. The pattern of the iso-values of the local density of state around a vortex has a diamond shape in the quasi-1D model and is much more isotropic in the 2D model. The spin lattice relaxation rate well below the superconducting transition temperature is greatly enhanced in the vortex state in the 2D model but not in the quasi-1D model. These features can be tested by using scanning tunneling microscope and NMR to distinguish the models for the superconductivity in Sr2RuO4.

Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions: Approach from Bulk Calculations

We discuss thermal transport of two-dimensional topological superconductors (TSCs) with broken time reversal symmetry, which are described by Bogoliubov-de Gennes (BdG) Hamiltonians. From the calculations of bulk quantities only, without refereeing to Majorana edge states, we show that the thermal Hall conductivity of two-dimensional TSCs in the low-temperature limit is quantized in multiples of $1/2\frac{\pi T}{6}$, which is exactly one half of the value of quantization in the case of the integer quantum Hall effect, and that this exact half-quantization is caused by the structure of the Nambu spinor and the particle-hole symmetry, which BdG Hamiltonians generally have. In the case of spinless chiral p-wave superconductors, this result is in perfect agreement with the argument based on the Ising conformal field theory with the central charge $c=1/2$, which is an effective low-energy theory of the Majorana edge states.

Effect of thermal fluctuations in topologicalp-wave superconductors

We study the effect of thermal fluctuations on the topological stability of chiral p-wave superconductors. We consider two models of superconductors: spinless and spinful with a focus on topological properties and Majorana zero-energy modes. We show that proliferation of vortex-antivortex pairs above the Kosterlitz-Thouless temperature T_KT drives the transition from a thermal Quantum Hall insulator to a thermal metal/insulator, and dramatically modifies the ground-state degeneracy splitting. Therefore, in order to utilize 2D chiral p-wave superconductors for topological quantum computing, the temperature should be much smaller than T_KT. Within the spinful chiral p-wave model, we also investigate the interplay between half-quantum vortices carrying Majorana zero-energy modes and full-quantum vortices having trivial topological charge, and discuss topological properties of half-quantum vortices in the background of proliferating full-quantum vortices.

Quasi-particle structures around a pair of half-quantum vortices in chiral p-wave super conductors

Quasi-particle structures around a pair of half-quantum vortices (HQVs) and two singly quantized vortices are investigated, using the Bogoliubov-de Gennes equation. For this purpose, a new numerical method, which incorporates the two phase singularity points, is developed, using elliptic coordinates and the (modified) Mathieu functions. We investigate the local density of states around two singly quantized vortices and a pair of HQVs in chiral p-wave superconductors. As a result, we found that there is a difference between them: Quasiparticle bound states interfere with each other for two singly quantized vortices case and do not for a pair of HQVs case.

Vortex States of Chiral p-wave Superconductors

In chiral p-wave superconductors a flux lattice of doubly quantized vortices is shown to be energetically stable for fields Hc1 < HFL < H < Hc2, while at low fields a lattice of singly quantized vortices is stable. Here we report self-consistent calculations by Eilenberger theory for spatial structures of the pair potential and current density for vortex states of single- and double-winding vortices in chiral p-wave superconductors with a cylindrical Fermi surface.

Magnetism of Multi-Orbital Edge States in Sr2RuO4

Magnetic properties of edge states in the chiral p-wave superconductor Sr2RuO4 are investigated based on a multi-band model restricting to the two bands derived from the 4d-t2g dyz/dzx-orbitals. While generally low-energy gapless Andreev bound states appear at the edges which carry spontaneous charge current, they are not topologically protected. Including spin-orbit coupling of the two orbitals we find additionally edge spin currents which are present in the normal as well as the superconducting phase. They contribute to the anomalous and the spin Hall effect and generate in the superconducting phase a finite spin polarization at the surface. Repulsive onsite interaction strengthens the spin polarization through the coupling to a nesting driven incipient magnetic phase of the system. We speculate that the magnetizations of the spin polarization and the chiral edge currents could partially compensate each other, in view of recent experimental results.

Possible pairing symmetries in SrPtAs with a local lack of inversion center

We discuss possible pairing symmetries in the hexagonal pnictide superconductor SrPtAs. The local lack of inversion symmetry of the two distinct conducting layers in the unit cell results in a special spin-orbit coupling with a staggered structure. We classify the pairing symmetry by the global crystal point group D_3d, and suggest some candidates for the stable state using a tight-binding model with an in-plane, density-density type pairing interaction. We may have some unconventional states like s+f-wave and a mixture of chiral d-wave and chiral p-wave. The spin orbit coupling is larger than the interlayer hopping, and the mixing between spin-singlet and triplet states can be seen in spite of the fact that the system has a global inversion center.

Odd-frequency Cooper-pair amplitude around a vortex core in a chiralp-wave superconductor in the quantum limit

Solving the Bogoliubov-de Gennes equation, we study the spatial structure of odd-frequency s-wave Cooper pair amplitudes at each quantized energy level of vortex bound states in chiral p-wave superconductors. For zero energy Majorana states, the odd-frequency s-wave pair amplitude has the same spatial structure as that of the local density of states even in atomic length scale. This relation also holds in finite energy bound states for single vortex winding anti-parallel to the chirality, but not for parallel vortex winding. The double winding vortex case is also studied.

Properties of edge states in a spin-triplet two-band superconductor

Motivated by Sr2RuO4 the magnetic properties of edge states in a two-band spin-triplet superconductor with electron- and hole-like Fermi surfaces are investigated assuming chiral p-wave pairing symmetry. The two bands correspond to the alpha-beta-bands of Sr2RuO4 and are modeled within a tight-binding model including inter-orbital hybridization and spin-orbit coupling effects. Including superconductivity the quasiparticle spectrum is determined by means of a self-consistent Bogolyubov-de Gennes calculation. While a full quasiparticle excitation gap appears in the bulk, gapless states form at the edges which produce spontaneous spin and/or charge currents. The spin current is the result of the specific band structure while the charge current originates from the superconducting condensate. Together they induce a small spin polarization at the edge. Furthermore onsite Coulomb repulsion is included to show that the edge states are unstable against the formation of a Stoner-like spin polarization of the edge states. Through spin-orbit coupling the current- and the correlation-induced magnetism are coupled to the orientation of the chirality of the superconducting condensate. We speculate that this type of phenomenon could yield a compensation of the magnetic fields induced by currents and also explain the negative result in the recent experimental search for chiral edge currents.

Counterflow of spontaneous mass currents in trapped spin-orbit-coupled Fermi gases

We use the Bogoliubov-de Gennes formalism and study the ground-state phases of trapped spin-orbit coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e. $\uparrow$ and $\downarrow$ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular BEC limit, which can be achieved either by increasing the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in $x$ and $y$ directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral p-wave superfluids/superconductors.

Superconductivity in a Correlated E⊗e Jahn–Teller System

By numerically solving the Eliashberg equation in the RPA as well as employing the Landau’s theory for phase transitions, we have investigated superconductivity, especially its pairing character, in a two-orbital Hubbard model coupled with E⊗e Jahn–Teller phonons on a two-dimensional square lattice at half filling. If the electron hopping between neighboring sites keeps the orbital character invariant in this E⊗e Jahn–Teller crystal, we find that a new superconducting phase characterized by the pairing of spin singlet, orbital singlet, and odd in momentum space, named a chiral p-wave pairing, is brought about by the collaboration of orbital fluctuations enhanced mainly by the electron–phonon interaction with spin fluctuations induced by the electron–electron one.

Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization

We study Andreev bound states (ABS) and the resulting charge transport of a Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures are sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode in the topological phase (TP). We clarify two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether or not ABS exists at QCP. In the former type, ABS has an energy gap and does not cross at zero energy in the nontopological phase. These complex properties can be detected by tunneling conductance between normal metal-RSC junctions.

Vortex configuration and vortex–vortex interaction in nano-structured superconductors

We study the vortex structures and quasi-particle structures in nano-structured superconductors. We used the Bogoliubov–de Gennes equation and the finite element method and obtained stable magnetic flux structures and the quasi-particle states. We found the vortex configurations are affected by the interference of the quasi-particle bound states around the vortices. In order to clarify the interference between the quasi-particle wave-functions around two vortices we have developed a numerical method using the elliptic coordinates and the Mathieu functions. We apply this method to two singly quantized vortex state in a conventional s-wave superconductor and a pair of half-quantum vortices in a chiral p-wave superconductor.

Surface states, edge currents, and the angular momentum of chiralp-wave superfluids

The spectra of fermionic excitations, pairing correlations and edge currents confined near the boundary of a chiral p-wave superfluid are calculated to leading order in $\hbar/p_f\xi$. Results for the energy- and momentum-resolved spectral functions, including the spectral current density, of a chiral p-wave superfluid near a confining boundary are reported. The spectral functions reveal the subtle role of the chiral edge states in relation to the edge current and the angular momentum of a chiral p-wave superfluid, including the rapid suppression of $L_z(T)$ for $0 \lesssim T\ll T_c$ in the fully gapped 2D chiral superfluid. The edge current and ground-state angular momentum are shown to be sensitive to boundary conditions, and as a consequence the topology and geometry of the confining boundaries. For perfect specular boundaries the edge current accounts for the ground-state angular momentum, $L_z=(N/2)\hbar$, of a cylindrical disk of chiral superfluid with $N/2$ fermion pairs. Non-specular scattering can dramatically suppress the edge current. In the limit of perfect retro-reflection the edge states form a flat band of zero modes that are non-chiral and generate no edge current. For a chiral superfluid film confined in a cylindrical toroidal geometry the ground-state angular momentum is, in general, non-extensive, and can have a value ranging from $L_z > (N/2)\hbar$ to $L_z < -(N/2)\hbar$ depending on the ratio of the inner and outer radii and the degree of back scattering on the inner and outer surfaces. Non-extensive scaling of $L_z$, and the reversal of the ground-state angular momentum for a toroidal geometry, would provide a signature of broken time-reversal symmetry of the ground state of superfluid \Hea, as well as direct observation of chiral edge currents.