Tunable Josephson Diode Effect on the Surface of Topological Insulators.

The Josephson rectification effect, where the resistance is finite in one direction while zero in the other, has been recently realized experimentally. The resulting Josephson diode has many potential applications on superconducting devices, including quantum computers. Here, we theoretically show that a superconductor-normal metal-superconductor Josephson junction diode on the two-dimensional surface of a topological insulator has large tunability. The magnitude and sign of the diode quality factor strongly depend on the external magnetic field, gate voltage, and the length of the junction. Such rich properties stem from the interplay between different current-phase relations for the multiple transverse transport channels, and can be used for designing realistic superconducting diode devices.

Optical Responses of Chiral Majorana Edge States in Two-Dimensional Topological Superconductors.

Majorana fermions exist on the boundaries of two-dimensional topological superconductors (TSCs) as charge-neutral quasiparticles. The neutrality makes the detection of such states challenging from both experimental and theoretical points of view. Current methods largely rely on transport measurements in which Majorana fermions manifest themselves by inducing electron-pair tunneling at the lead-contacting point. Here we show that chiral Majorana fermions in TSCs generate enhanced local optical response. The features of local optical conductivity distinguish them not only from trivial superconductors or insulators but also from normal fermion edge states such as those in quantum Hall systems. Our results provide a new applicable method to detect dispersive Majorana fermions and may lead to a novel direction of this research field.

Majorana Multipole Response of Topological Superconductors.

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry. The latter property provides a way to identify unconventional pairing symmetry via the magnetic response of helical MFs. We also find that most helical MFs exhibit a magnetic-dipole response, but those on superconductors with spin-3/2 electrons may display a magnetic-octupole response in leading order, which uniquely characterizes high-spin superconductors. Detection of such an octupole response provides direct evidence of high-spin superconductivity, such as in half-Heusler superconductors.

Study on Green's function on topological insulator surface.

In the theory of superconducting junctions, Green's function has an important role for obtaining Andreev bound states, local density of states and Josephson current in a systematic way. In this article, we show how to construct Green's function on the surface of a topological insulator following McMillan's formalism where the energy spectrum of electrons obeys a linear dispersion. For a model of a superconductor (S)/ferromagnet (F)/normal metal (N) junction, we show that the generation of a Majorana fermion gives rise to the enhanced local density of states and pair amplitude of odd-frequency pairing. We also derive an extended Furusaki-Tsukada's formula of DC Josephson current in S/F/S junctions. The obtained Josephson current depends on the direction and magnitude of the magnetization.This article is part of the theme issue 'Andreev bound states'.

Crossed surface flat bands of Weyl semimetal superconductors.

It has been noted that certain surfaces of Weyl semimetals have bound states forming open Fermi arcs, which are never seen in typical metallic states. We show that the Fermi arcs enable them to support an even more exotic surface state with crossed flat bands in the superconducting state. We clarify the topological origin of the crossed flat bands and the relevant symmetry that stabilizes the cross point. Our symmetry analysis is applicable to known candidate materials of time-reversal breaking Weyl semimetals. We also discuss their possible experimental verification by tunneling spectroscopy.

Symmetry-protected Majorana fermions in topological crystalline superconductors: theory and application to Sr2RuO4.

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.

Majorana bound states and nonlocal spin correlations in a quantum wire on an unconventional superconductor.

We study theoretically the proximity effect of a one-dimensional metallic quantum wire (in the absence of spin-orbit interaction) lying on top of an unconventional superconductor. Three different material classes are considered as a substrate: (i) a chiral superconductor in class D with broken time-reversal symmetry and a class DIII superconductor (ii) with and (iii) without a nontrivial Z(2) number. Interestingly, we find degenerate zero energy Majorana bound states at both ends of the wire for all three cases. They are unstable against spin-orbit interaction in case (i), while they are topologically protected by time-reversal symmetry in cases (ii) and (iii). Remarkably, we show that nonlocal spin correlations between the two ends of the wire can be simply controlled by a gate potential in our setup.

The supercurrent diode effect and nonreciprocal paraconductivity due to the chiral structure of nanotubes.

The phenomenon that critical supercurrents along opposite directions become unequal is called the supercurrent diode effect (SDE). It has been observed in various systems and can often be understood by combining spin-orbit coupling and Zeeman field, which break the spatial-inversion and time-reversal symmetries, respectively. Here, we theoretically investigate another mechanism of breaking these symmetries and predict the existence of the SDE in chiral nanotubes without spin-orbit coupling. The symmetries are broken by the chiral structure and a magnetic flux through the tube. With a generalized Ginzburg-Landau theory, we obtain the main features of the SDE in its dependence on system parameters. We further show that the same Ginzburg-Landau free energy leads to another important manifestation of the nonreciprocity in superconducting systems, i.e., the nonreciprocal paraconductivity (NPC) slightly above the transition temperature. Our study suggests a new class of realistic platforms to investigate nonreciprocal properties of superconducting materials. It also provides a theoretical link between the SDE and the NPC, which were often studied separately.

Phase-dependent Andreev molecules and superconducting gap closing in coherently-coupled Josephson junctions.

The Josephson junction (JJ) is an essential element of superconducting (SC) devices for both fundamental and applied physics. The short-range coherent coupling of two adjacent JJs forms Andreev molecule states (AMSs), which provide a new ingredient to engineer exotic SC phenomena such as topological SC states and Andreev qubits. Here we provide tunneling spectroscopy measurements on a device consisting of two electrically controllable planar JJs sharing a single SC electrode. We discover that Andreev spectra in the coupled JJ are highly modulated from those in the single JJs and possess phase-dependent AMS features reproduced in our numerical calculation. Notably, the SC gap closing due to the AMS formation is experimentally observed. Our results help in understanding SC transport derived from the AMS and promoting the use of AMS physics to engineer topological SC states and quantum information devices.

Topological superconductivity in bilayer Rashba system.

We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the heterostructures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity without breaking time-reversal symmetry is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the interlayer interaction is repulsive, both of which can be satisfied in realistic systems. Edge channels are studied in a tight-binding model numerically, and the several predictions on experiments are also given.

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.

Anomalous Meissner effect in a normal-metal-superconductor junction with a spin-active interface.

We investigate Meissner effect in normal-metal-superconductor junctions where the interface is spin active. We find that orbital magnetic susceptibility of the normal metal shows highly nontrivial behavior. In particular, the magnetic susceptibility depends on the temperature in an oscillatory fashion, accompanied by its sign change. Correspondingly, the magnetic field and current density can spatially oscillate in the normal metal. These results are attributed to the generation of odd-frequency pairing due to the spin-active interface.

Unconventional surface impedance of a normal-metal film covering a spin-triplet superconductor due to odd-frequency cooper pairs.

We discuss the dynamic response of odd-frequency Cooper pairs to an electromagnetic field. By using the quasiclassical Green function method, we calculate the impedance (Z=R-iX) of a normal-metal thin film which covers a superconductor. In contrast with the standard relation (i.e., R≪X), the impedance in spin-triplet proximity structures shows anomalous behavior (i.e., R>X) in the low frequency limit. This unusual relation is a result of the penetration of odd-frequency pairs into the normal metal and reflects the negative Cooper pair density.

Edge states of Sr2RuO4 detected by in-plane tunneling spectroscopy.

Tunneling spectroscopy has been performed on Sr(2)RuO(4) searching for the edge states peculiar to topological superconductivity. Conductance spectra exhibit broad humps with three types of peak shape: domelike peak, split peak, and two-step peak. By comparing the experiments with predictions for unconventional superconductivity, these varieties are shown to originate from multiband chiral p-wave symmetry with weak anisotropy of pair amplitude. The broad hump in the conductance spectrum is a direct manifestation of the edge state due to chiral p-wave superconductivity.

Topological Superconductivity in Cu(x)Bi(2)Se(3).

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ∼3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ∼20 K and coexists with the topological superconducting state.

Minimum ignition energies and laminar burning velocities of ammonia, HFO-1234yf, HFC-32 and their mixtures with carbon dioxide, HFC-125 and HFC-134a.

Given the safety issues associated with flammability characteristics of alternative environmentally-friendly refrigerants, it is vital to establish measurement systems to accurately analyse the flammability of these mildly flammable refrigerants. In this study, we used a customised Hartmann bomb analogue to measure the minimum ignition energy (MIE) and laminar burning velocity (BV) for refrigerant/air mixtures of pure ammonia (R717), R32, R1234yf and mixtures of R32 and R1234yf with non-flammable refrigerants of R134a, R125 and carbon dioxide (R744). The MIEs of R717, R32, and R1234yf were measured at an ambient temperature of 24 °C to be (18.0 ± 1.4), (8.0 ± 1.5) and (510 ± 130) mJ at equivalence ratios of 0.9, 1.27 and 1.33, respectively. Adding the non-flammable refrigerants R134a, R125 and R744 along with R32 at volumetric concentrations of 5% each to R1234yf reduced the latter compound's flammability and increased its MIE by one order of magnitude. The laminar burning velocities of pure R717 and R32 were measured at an equivalence ratio of 1.1 using the flat flame method and found to be 8.4 and 7.4 cm/s, respectively. Adding 5% R1234yf to R32 decreased the laminar burning velocity by 11%, while a further 5% addition of R1234yf resulted in a decrease of over 30% in the laminar burning velocity.

Observation of domain wall bimerons in chiral magnets.

Topological defects embedded in or combined with domain walls have been proposed in various systems, some of which are referred to as domain wall skyrmions or domain wall bimerons. However, the experimental observation of such topological defects remains an ongoing challenge. Here, using Lorentz transmission electron microscopy, we report the experimental discovery of domain wall bimerons in chiral magnet Co-Zn-Mn(110) thin films. By applying a magnetic field, multidomain structures develop, and simultaneously, chained or isolated bimerons arise as the localized state between the domains with the opposite in-plane components of net magnetization. The multidomain formation is attributed to magnetic anisotropy and dipolar interaction, and domain wall bimerons are stabilized by the Dzyaloshinskii-Moriya interaction. In addition, micromagnetic simulations show that domain wall bimerons appear for a wide range of conditions in chiral magnets with cubic magnetic anisotropy. Our results promote further study in various fields of physics.

Tunneling between two helical superconductors via Majorana edge channels.

We discuss electric transport through a point contact which bridges Majorana fermion modes appearing at edges of two helical superconductors. The contents focus on the effects of interference and interaction unique to the Majorana fermions and the role of spin-orbit interaction (SOI). Besides the Josephson current, the quasiparticle conductance depends sensitively on the phase difference and relative helicity between the two superconductors. The interaction among the Majorana fermions causes the power-law temperature dependences of conductance for various tunneling channels. Especially, in the presence of SOI, the conductance always increases as the temperature is lowered.

Anomalous Andreev bound state in noncentrosymmetric superconductors.

We study edge states of noncentrosymmetric superconductors where spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by spin-orbit coupling. For d(xy)-wave pairing, the obtained Andreev bound state has an anomalous dispersion as compared to conventional helical edge modes. A unique topologically protected time-reversal invariant Majorana bound state appears at the edge. The charge conductance in the noncentrosymmetric superconductor junctions reflects the anomalous structures of the dispersions, particularly the time-reversal invariant Majorana bound state is manifested as a zero bias conductance peak.

Unconventional superconductivity on a topological insulator.

We study proximity-induced superconductivity on the surface of a topological insulator (TI), focusing on unconventional pairing. We find that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed. For spin-singlet pairing, the zero-energy surface state in the d(xy)-wave case becomes a Majorana fermion, in contrast with the situation realized in the topologically trivial high-T(c) cuprates. We also study the influence of a Zeeman field on the surface states. Both the magnitude and direction of this field are shown to strongly influence the transport properties, in contrast with the case without TI. We predict an experimental signature of the Majorana states via conductance spectroscopy.