Language：English   Publishing type：Research paper (scientific journal)  

DOI： https://doi.org/10.1103/PhysRevB.101.024509

Language：Japanese   Publisher：Physical Review B  

The spin-orbital polarization of superconducting excitations in momentum space is shown to provide distinctive marks of unconventional pairing in the presence of inversion symmetry breaking. Taking the prototypical example of an electronic system with atomic spin-orbit and orbital-Rashba couplings, we provide a general description of the spin-orbital textures and their most striking changeover moving from the normal to the superconducting state. We find that the variation of the spin texture is strongly imprinted by the combination of the misalignment of spin-triplet d vector with the inversion asymmetry g-vector coupling and the occurrence of superconducting nodal excitations. Remarkably, the multiorbital character of the superconducting state allows us to unveil a unique type of topological transition for the spin winding around the nodal points. This finding indicates the fundamental topological relation between chiral and spin winding in nodal superconductors. By analogy between spin- and orbital-triplet pairing we point out how orbital polarization patterns can also be employed to assess the character of the superconducting state.

DOI： 10.1103/PhysRevB.100.104524

Web of Science

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Language：Japanese   Publisher：Physical Review B  

Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of topological superconductors are a useful physical quantity for characterizing the topological properties of these materials. In this work, we show that the odd-frequency Cooper pair amplitudes can be expressed by a winding number extended to a nonzero frequency, which is called a "spectral bulk-boundary correspondence," and can be evaluated from the spectral features of the bulk. The odd-frequency Cooper pair amplitudes are classified into two categories: the amplitudes in the first category have the singular functional form ∼1/z (where z is a complex frequency) that reflects the presence of a topological surface Andreev bound state, whereas the amplitudes in the second category have the regular form ∼z and are regarded as nontopological. We discuss the topological phase transition by using the coefficient in the latter category, which undergoes a power-law divergence at the topological phase transition point and is used to indicate the distance to the critical point. These concepts are established based on several concrete models, including a Rashba nanowire system that is promising for realizing Majorana fermions.

DOI： 10.1103/PhysRevB.99.184512

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Language：Japanese   Publisher：Physical Review B  

We study the anomalous proximity effect in diffusive normal metal (DN)/unconventional superconductor junctions, where the local density of states (LDOS) in the DN has a zero-energy peak due to the penetration of the odd-frequency spin-triplet s-wave pairing. In this study, we consider a two-dimensional unconventional superconductor on the substrate in the presence of a Rashba spin-orbit coupling (RSOC) λ, where the Rashba vector is parallel to the z direction. The anomalous proximity effect, originally predicted in spin-triplet p-wave superconductor junctions, is sensitive to the RSOC. It disappears with the increase of λ. On the other hand, the anomalous proximity effect can be switched on by the large λ values in the spin-singlet dxy-wave superconductor junctions. The resulting zero-energy LDOS and the magnitude of the odd-frequency spin-triplet s-wave pair amplitude increase with the increase of λ.

DOI： 10.1103/PhysRevB.99.184501

Web of Science

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Language：Japanese   Publisher：Physical Review B  

We study the superconducting state of multiorbital spin-orbit coupled systems in the presence of an orbitally driven inversion asymmetry assuming that the interorbital attraction is the dominant pairing channel. Although the inversion symmetry is absent, we show that superconducting states that avoid mixing of spin-triplet and spin-singlet configurations are allowed, and remarkably, spin-triplet states that are topologically nontrivial can be stabilized in a large portion of the phase diagram. The orbital-dependent spin-triplet pairing generally leads to topological superconductivity with point nodes that are protected by a nonvanishing winding number. We demonstrate that the disclosed topological phase can exhibit Lifshitz-type transitions upon different driving mechanisms and interactions, e.g., by tuning the strength of the atomic spin-orbit and inversion asymmetry couplings or by varying the doping and the amplitude of order parameter. Such distinctive signatures of the nodal phase manifest through an extraordinary reconstruction of the low-energy excitation spectra both in the bulk and at the edge of the superconductor.

DOI： 10.1103/PhysRevB.97.174522

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Language：Japanese   Publisher：Journal of Low Temperature Physics  

In this review, we summarize the achievement of the physics of surface Andreev bound states (SABS) up to now. The route of this activity has started from the physics of SABS of unconventional superconductors where the pair potential has a sign change on the Fermi surface. It has been established that SABS can be regarded as a topological edge state with topological invariant defined in the bulk Hamiltonian. On the other hand, SABS accompanies odd-frequency pairing like spin-triplet s-wave or spin-singlet p-wave. In a spin-triplet superconductor junction, induced odd-frequency pairing can penetrate into a diffusive normal metal (DN) attached to the superconductor. It causes so called anomalous proximity effect where the local density of states of quasiparticle in DN has a zero energy peak. When bulk pairing symmetry is spin-triplet px-wave, the anomalous proximity effect becomes prominent and the zero bias voltage conductance is always quantized independent of the resistance in DN and interface. Finally, we show that the present anomalous proximity effect is realized in an artificial topological superconducting system, where a nanowire with spin-orbit coupling and Zeeman field is put on the conventional spin-singlet s-wave superconductor.

DOI： 10.1007/s10909-018-1849-8

Web of Science

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Language：Japanese   Publisher：Physical Review B  

The order parameter of bulk two-dimensional superconductors is classified as nodal if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Nonmagnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between normal-metal and unconventional superconductors by solving the quasiclassical Eilenberger equation self-consistently, including the presence of nonmagnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge e, and (ii) for finite bias, the current-voltage characteristics follows that of a normal-state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only px-wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency s-wave Cooper pairs near the interface. Due to their anisotropic dependence on the wave vector, impurity scattering is an effective pair-breaking mechanism for the remaining nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.

DOI： 10.1103/PhysRevB.95.224502

Web of Science

Scopus

Language：Japanese   Publisher：Physical Review B  

We study the surface Andreev bound states (SABSs) and quasiparticle tunneling spectroscopy of three-dimensional (3D) chiral superconductors by changing their surface (interface) misorientation angles. We obtain an analytical formula for the SABS energy dispersion of a general pair potential, for which an original 4×4 BdG Hamiltonian can be reduced to two 2×2 blocks. The resulting SABS for 3D chiral superconductors with a pair potential given by kz(kx+iky)ν (ν=1,2) has a complicated energy dispersion owing to the coexistence of both point and line nodes. We focus on the tunneling spectroscopy of this pairing in the presence of an applied magnetic field, which induces a Doppler shift in the quasiparticle spectra. In contrast to the previously known Doppler effect in unconventional superconductors, a zero-bias conductance dip can change into a zero-bias conductance peak owing to an external magnetic field. We also study SABSs and tunneling spectroscopy for possible pairing symmetries of UPt3. For this purpose, we extend a standard formula for the tunneling conductance of unconventional superconductor junctions to treat spin-triplet nonunitary pairings. Magnetotunneling spectroscopy, i.e., tunneling spectroscopy in the presence of a magnetic field, can serve as a guide to determine the pairing symmetry of this material.

DOI： 10.1103/PhysRevB.95.104511

Web of Science

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