Manfred Sigrist

Chiral superconductors are two-fold degenerate and domains of opposite chirality can form, separated by domain walls. While there are experimental indications for domain formation in some unconventional superconductors assumed to realize chiral Cooper pairing, there has not been any unambiguous proof for their existence. In this talk we consider the impact domain walls in chiral superconductors can have on the critical currents. For this purpose we consider various domain wall orientations for both chiral p-wave and chiral d-wave superconductors. We demonstrate that selection rules and crystalline anisotropy play an essential role in connecting the two chiral domains coherently through the domain wall. In particular, we illustrate the case of a domain wall parallel to the basal plane for a chiral p-wave superconductor. The possibility to realize half-flux vortices in these domain walls will be analyzed and used as a tool to estimate the critical currents. The possibility of experimental verication will be discussed.

Eli Zeldov

The emergence of flat bands and of strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels and derive nanoscale high precision maps of the twist-angle disorder in high quality hBN encapsulated devices, which reveal substantial twist-angle gradients and a network of jumps [1]. We show that the twist-angle gradients generate large gate tunable in-plane electric fields, unscreened even in the metallic regions, which drastically alter the quantum Hall state by forming edge channels in the bulk of the samples. The correlated states are found to be particularly fragile with respect to twist-angle disorder. We establish the twist-angle disorder as a fundamentally new kind of disorder, which alters the local band structure and may significantly affect the correlated and superconducting states.

Clifford Hicks

Several previous experimental results give evidence that the superconductivity of Sr2RuO4 is chiral. These include measurements of the Kerr effect, critical currents across junctions between Sr2RuO4 and conventional superconductors, sound velocities, and muon spin relaxation. Through recent NMR Knight shift measurements it is now understood that the pairing is most likely spin-singlet [1,2], and on the tetragonal lattice of Sr2RuO4 the combination of singlet pairing and chirality compels consideration of an unlikely order parameter: dxz ± idyz. It is unlikely because it has a horizontal line noad at kz=0, and Sr2RuO4 has a very low c-axis conductivity. Therefore, a firm determination of whether or not the superconductivity of Sr2RuO4 is chiral is highly important, as it may imply a new form of pairing. Here, I present evidence from experiments under uniaxial stress applied along the [100] direction. Tc rises rapidly [3]. By lifting the tetragonal symmetry of the lattice, uniaxial stress is expected to induce a splitting between Tc and the onset temperature of chirality, TTRSB. In muon spin rotation experiments under uniaxial stress, a large splitting is observed: TTRSB is found to remain low while Tc i ncreases [4]. However, in heat capacity measurements, no second heat capacity anomaly is observed; the upper limit on any heat capacity anomaly at TTRSB is ~5% of that at Tc [5]. In scanning SQUID magnetometry studies [6], a cusp in the strain dependence of Tc, implied by transition splitting, is not observed. In this talk I will discuss possibilities to reconcile these results.

Christian Schönenberger

WTe2 is a layered material with rich topological properties. As a bulk crystal it is a type-II Weyl semimetal and as a monolayer a two-dimensional topological insulator. Recently, it has been predicted that higher order topological insulator states can appear in WTe2. An observation of 1D, highly conductive channels, known in this case as hinge states, is hindered by the bulk conductivity of WTe2. Here, we employ the Josephson effect to disentangle the contribution of the hinge states from the bulk in electronic transport. We observe 1D current carrying states on edges and steps in few-layer WTe2. The width of the states is deduced to be below 100 nm. A supercurrent in them can be measured over distances up to 3 µm and in perpendicular magnetic field up to 2 T. Moreover, the dependence of the supercurrent with field is compatible with the asymmetric Josephson effect predicted to occur in topological systems with broken inversion symmetry. We note, that superconductivity is induced into WTe2 at the interface to the contacts made from Pd, which is a normal metal. The induced superconductivity has a critical temperature of about 1.2 K. By studying the superconductivity in perpendicular magnetic field, we obtain the coherence length and the London penetration depth. These parameters hint to a possible origin of superconductivity due to the formation of flat bands. Furthermore, the critical in-plane magnetic field exceeds the Pauli limit, suggesting a non-trivial nature of the superconducting state.
A.K. was supported by the Georg H. Endress foundation. This project has received funding from the European Research Council (ERC) under the Horizon 2020 research and innovation programme: grant No 787414 TopSupra, by the NCCR on Quantum Science and Technology (QSIT), and by the Swiss Nanoscience Institute (SNI). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan and the CREST (JPMJCR15F3), JST. D.G.M. and J.Y. acknowledge support from the U.S. Department of Energy (U.S.-DOE), Office of Science - Basic Energy Sciences (BES), Materials Sciences and Engineering Division. D.G.M. acknowledges support from the Gordon and Betty Moore Foundations EPiQS Initiative, Grant GBMF9069.

Shingo Yonezawa

Topological superconductivity, accompanying non-trivial topology in its superconducting wave function, has been one of the central topics in condensed-matter physics. During the recent extensive efforts to search for topological superconducting phenomena, nematic superconductivity, exhibiting spontaneous rotational symmetry breaking in bulk superconducting quantities, has been discovered in the topological-superconductor candidates AxBi2Se3 (A = Cu, Sr, Nb) [1]. In the in-plane field-angle dependence of various superconducting properties, such as the spin susceptibility [2], the specific heat [3], and the upper critical field [4], exhibit pronounced two-fold symmetric behavior although the underlying lattice has three-fold rotational symmetry.
More recently, we succeeded in controlling nematic superconductivity in SrxBi2Se3 via external uniaxial strain [5]. In the trigonal AxBi2Se3 material, six kinds of nematic domains can be realized. By applying uniaxial strain in situ using a piezo-based uniaxial-strain device [6], we reversibly controlled the superconducting nematic domain structure. Namely, the multi-domain state under zero strain can be changed into a nearly single-domain state under 1% uniaxial compression along the a axis. This result indicates strong coupling between nematic superconductivity and lattice distortion. Moreover, this is the first achievement of domain engineering using nematic superconductors.
In this talk, I overview experiments on nematic superconductivity, with a focus on our specific-heat study of CuxBi2Se3 [3]. I then explain our recent demonstration of uniaxial-strain control of nematic superconductivity in SrxBi2Se3 [5,6].

Yasuhiro Asano

We have been interested in physics of an odd-frequency Cooper pair. At this conference, we will discuss two phenomena of two-band (two-orbital) superconductors. At first, we discuss the Josephson effect between two two-band superconductors respecting time-reversal symmetry, where we assume a spin-singlet s-wave pair potential in each conduction band. The superconducting phase at the first band ! and that at the second band " characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green’s function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band !, the phase difference at the second band ", and the difference at the center-of-mass phase (! +")/2. A Cooper pair generated by the band hybridization carries the last current component.[1] Secondly, we also discuss the effects of random nonmagnetic impurities on superconducting transition temperature in a Cu doped Bi2Se3, for which four types of pair potentials have been proposed. Although all the candidates belong to s-wave symmetry, two orbital degrees of freedom in electronic structures enrich the symmetry variety of a Cooper pair such as even-orbital-parity and odd-orbital-parity. We consider realistic electronic structures of Cu-doped Bi2Se3 by using a tight-binding Hamiltonian on a hexagonal lattice and consider effects of impurity scatterings through the self-energy of the Green’s function within the Born approximation. We find that even-orbital-parity spin-singlet superconductivity is basically robust even in the presence of impurities. The degree of the robustness depends on the electronic structures in the normal state and on the pairing symmetry in orbital space. On the other hand, two odd-orbital-parity spin- triplet order parameters are always fragile in the presence of potential disorder. We also discuss relations between our conclusions and the results of another theoretical studies on the same issue.

Ady Stern

In this talk I will describe how the Josephson effect may be employed to realize one dimensional topological superconductivity. I will describe the basic idea, the experimental observations, the relation to topological superconductivity based on quantum wires, a surprising effect of disorder, and a scheme for braiding Majorana zero modes in Josephson junctions.

Ron Naaman

Spin based properties, applications, and devices are commonly related to magnetic effects and to magnetic materials or materials with large spin orbit coupling. However, we found that chiral molecules act as spin filters for photoelectrons transmission, in electron transfer, and in electron transport.
The new effect, termed Chiral Induced Spin Selectivity(CISS) [1], was found, among others, in bio-molecules and in bio-systems as well as in inorganic chiral crystals. It has interesting implications for the production of new types of spintronics devices [2], in controlling magnetization [3], and on electron transfer and conduction. Recently we also found that charge polarization in chiral molecules is accompanied by spin polarization. This finding shed new light on spin dependent interaction between chiral molecules and between them and magnetic surfaces [4].