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.

[1] A. Pustogow et al, arXiv 1904.090047 (2019)
[2] K. Ishida, M. Manago, and Y. Maeno, arXiv 1907.12236 (2019)
[3] A. Steppke et al, Science 355, 148 (2017)
[4] V. Grinenko et al, arXiv 2001.08152 (2020)
[5] Y.-S. Li et al, arXiv 1906.07597 (2019)
[6] C. A. Watson, A. S. Gibbs, A. P. Mackenzie, C. W. Hicks, and K. A. Moler, Phys. Rev. B 98, 094521 (2018)

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].

[1] For a recent review, see S. Yonezawa, Condens. Matter 4, 2 (2019)
[2] K. Matano et al., Nature Phys. 12, 852 (2016)
[3] S. Yonezawa et al., Nature Phys. 13, 123 (2017)
[4] Y. Pan et al., Sci. Rep. 6, 28632 (2016)
[5] I. Kostylev, S. Yonezawa et al., Nature Commun. 11, 4152 (2020)
[6] I. Kostylev, S. Yonezawa, Y. Maeno, J. Appl. Phys. 125, 082535 (2019)

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.

[1] A. Sasaki, S. Ikegaya, T. Habe, A. A. Golubov, and YA, Phys Rev. B 101, 184501 (2020)
[2] T. Sato and YA, Phys Rev. B 102, 024516 (2020)

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].

[1] R. Naaman, Y. Paltiel, D,H, Waldeck, J. Phys. Chem. Lett., 11 (2020) 3660
[2] K. Michaeli, V. Varade, R. Naaman, D. A Waldeck, J. of Physics: Condensed Matter. 29 (2017) 103002
[3] E. Z. B. Smolinsky et al. J. Phys. Chem. Lett. 10 (2019) 1139
[4] K. Banerjee-Ghosh, et. al., Science 360 (2018) 1331

Takasada Shibauchi

The FeSe1-xSx superconductors involving non-magnetic nematic phase and its quantum criticality provide a unique platform to investigate the relationship between nematicity and superconductivity [1]. It has been shown that across the nematic quantum critical point, the superconducting properties change drastically [2,3], and the non-nematic tetragonal FeSe1-xSx (x>0.17) exhibits substantial low-energy states despite the high-quality of crystals. Here we have perform the muon spin rotation (μSR) measurements on FeSe1-xSx (x=0, 0.20, 0.22) and observed the spontaneous internal field below the superconducting transition temperature Tc, providing strong evidence for time-reversal breaking (TRSB) state in bulk FeSe1-xSx [4]. We also find that the superfluid density in the tetragonal crystals is suppressed from the expected value, indicating the presence of non-superconducting carriers. These results in FeSe1-xSx are consistent with the recently proposed topological phase transition to a novel ultranodal pair state with Bogoliubov Fermi surface [5].

[1] See, for a review, T. Shibauchi, T. Hanaguri, and Y. Matsuda, J. Phys. Soc. Jpn. (in press); arXiv:2005.07315 (2020).
[2] Y. Sato et al., Proc. Natl. Acad. Sci. USA 115, 1227-1231 (2018).
[3] T. Hanaguri et al., Sci. Adv. 4, eaar6419 (2018).
[4] K. Matsuura et al., (unpublished).
[5] C. Setty, S. Bhattacharyya, Y. Cao, A. Kreisel, and P. J. Hirschfeld, Nat. Commun.11, 523 (2020).

Ramón Aguado

Recent experimental efforts have focused on replacing the weak link in the Josephson Junction (JJ) of a superconducting qubit by electrostatically-gateable technologies compatible with high magnetic fields [1]. Such alternatives are crucial in order to reach a regime relevant for readout of topological qubits based on Majorana zero modes (MZMs) [2]. In my talk, I will focus on JJs based on semiconducting nanowires that can be driven to a topological superconductor phase with MZMs. A fully microscopic theoretical description of such hybrid semiconductor-superconducting qubit allows to unveil new physics originated from the coherent interaction between the MZMs and the superconducting qubit degrees of freedom [3]. The corresponding microwave spectroscopy presents nontrivial features, including a full mapping of zero energy crossings and fermionic parity switches in the nanowire owing to Majorana oscillations [4].

[1]Superconducting gatemon qubit based on a proximitized two-dimensional electron gas, Casparis et al, Nature Nanotechnology, 13, 915, (2018); Semiconductor-Nanowire-Based Superconducting Qubit, T. W. Larsen et al. Phys. Rev. Lett. 115, 127001 (2015); Realization of Microwave Quantum Circuits Using Hybrid Superconducting-Semiconducting Nanowire Josephson Elements, G. de Lange et al. Phys. Rev. Lett. 115, 127002 (2015)
[2] Majorana qubits for topological quantum computing, R. Aguado and Leo Kouwenhoven, Physics Today 73, 6, 44 (2020)
[3]Superconducting islands with semiconductor-nanowire-based topological Josephson junctions, J. Avila, E. Prada, P. San-Jose and R. Aguado, arXiv:2003.02852 (Physical Review B, in press)
[4] Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits, J. Avila, E. Prada, P. San-Jose and R. Aguado, arXiv:2003.02858 (Physical Review Research, in press)