PC-10-INV Superconducting States in Doped Topological Materials

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1 PC-10-INV Superconducting States in Doped Topological Materials Masatoshi Sato (Department of Applied Physics, Nagoya University) There are considerable interests in topological superconductivity in condensed matter physics. In this talk, I will present our recent works on topological superconductors and the related phenomena. In particular, I will discuss how topological non-trivial structures in normal states may arise non-trivial quantum phenomena in the superconducting states. As examples, I will discuss odd parity superconductors [1], superconducting states in Cu-doped Bi2Se3[2, 3], and doped Weyl semi-metal[4]. In the latter two cases, I will show that topological surface states in the normal states give rise to novel topological quantum phenomena in superconducting states. [1] M. Sato, Phys. Rev. B81, (R) (2010) [2] A. Yamakage, K. Yada, M. Sato, Y. Tanaka, Phys. Rev. B85, (R) [2] T. Mizushima, A. Yamakage, M. Sato, Y. Tanaka, arxiv: [3] L. Bo, K. Yada, M. Sato, Y. Tanaka, arxiv:

2 PC-11-INV Spin-polarized Majorana Quasiparticle Bound States in Topological Superconductors Yuki Nagai *, Hiroki Nakamura, Masahiko Machida (CCSE, Japan Atomic Energy Agency) The discovery of topological superconductors opened a new research avenue on superconducting states. The topologically-protected nature results in gapless zero-energy quasi-particles identified as the Majorana fermions at surface edges, while the superconducting gap opens in the bulk. The experimental works on topological insulators have recently revealed that Bi 2 Se 3 and SnTe turn into superconductors with carrier doping. Their superconducting gap functions are not conventional, since zero-bias conductance peaks (ZBCP s) have been detected by the point contact spectroscopy [1]. ZBCP s can be regarded to originate from their non-trivial topology. The Majorana fermion appears at not only surface edges but also vortex cores in topological superconductors. We reveal that Majorana quasiparticle bound states inside the vortex core are spin-polarized by solving the massive Dirac Bogoliubov-de Gennes equations considering the spin-orbit coupling [2]. This results is universal for Dirac superconductivity whose rotational degree of freedom is characterized by the total angular momentum J = S + L. Spin-sensitive probes such as the neutron scattering and other measurements above the first critical magnetic field can easily detect the spin-polarized vortex core. [1] S. Sasaki, et a.l, Phys. Rev. Lett. 107, [2] Y. Nagai et al., J. Phys. Soc. Jpn. 83,

3 PC-12 Theory of low-energy behaviors in topological s-wave pairing superconductors Yukihiro Ota*, Yuki Nagai, Masahiko Machida (CCSE, Japan Atomic Energy Agency, Japan) Topological superconductors (TSC) attract a great deal of attention in condensed-matter physics, owing to the mathematical curiosity and the application potential. Studying such notable materials is actively done now, from both theoretical and experimental viewpoints. The bulk TSC emerges, by copper-intercalation into topological insulator Bi 2 Se 3 [1]. A ultra-cold atomic gas with spin-orbital couplings can lead to the intriguing realization of a 2D TSC [2]. A proximity-induced superconductor in a semiconductor nanowire is another interesting realization of a TSC in an artificial system [3]. The characterization of a TSC is done by a topological invariant. Apart from this mathematical characterization, the thermodynamical properties relies on a type of the gap function. The TSCs typically show unconventional behaviors, including T c -reduction via non-magnetic impurities [4]. They suggest that the TSCs be effectively described by an unconventional superconducting model. Indeed, a low-energy theory of the TSCs is equivalent to the chiral p-wave theory [3, 4-6]. However, in the typical model of TSCs, the pairing potential in the mean-field Hamiltonian is s-wave. Therefore, it is worth asking why the unconventional behaviors occur in the presence of s-wave paring. In this paper, we derive the low-energy effective theory of typical TSC models, a 3D model [1] and a 2D model [2]. The technique is similar to deriving the relativistic corrections in the Schrödinger equation from the Dirac equation. We find that the effective gap functions have both p-wave and s-wave characters, and, at a leading order, the theory reduces into the p-wave description. Comparing the resultant theory with numerical calculations of impurity effects [4-6], we argue how our approach is insightful. [1] S. Sasaki, M. Kriever, K. Segawa, K. Yada, Y. Tanaka, M. Sato, and Y. Ando, Phys. Rev. Lett. 107, (2011). [2] M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. B 82, (2010). [3] J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Nat. Phys. 7, 412 (2011) [4] Y. Nagai, Y. Ota, and M. Machida, arxiv: (Accepted for publication in J. Phys. Soc. Jpn.). [5] Y. Nagai, Y.Ota, and M. Machida, Phys. Rev. B 89, (2014). [6] Y. Nagai, Y.Ota, and M. Machida, arxiv:

4 PC-13 Excitation Spectra and Wave Functions of Quasiparticle Bound States in Bilayer Rashba Superconductors Yoichi Higashi *,1, Yuki Nagai 2, Tomohiro Yoshida 3, Masaru Kato 1, Youichi Yanase 3 ( 1 Osaka Prefecture University, 2 Japan Atomic Energy Agency, 3 Niigata University) We focus on the multilayered system, in which locally noncentrosymmetric systems (LNCS) are realized. The LNCS are characterized by the spatially inhomogeneous antisymmetric spin-orbit coupling. Especially for the LNCS where the paramagnetic pair breaking effect is dominant, the exotic superconducting phase called the pair-density wave (PDW) phase stabilizes in a high magnetic field perpendicular to the layer [1]. Exotic superconducting phase stabilizes in a magnetic field and the observation of the quasiparticle states around a vortex is effective to identify the exotic superconducting phase. Thus, we theoretically studied the vortex core structure in the PDW phase on the basis of the quasiclassical theory and obtained some features of the PDW phase [2]. In this study, we investigate the excitation spectra and the wave functions of bound quasiparticles by means of the Bogoliubov-de Gennes equation to obtain more microscopic informations on the core structure. We already confirmed that the excitation spectra of vortex bound states are consistent to the structure of the local density of states (LDOS) calculated by the quasiclassical theory. We try to understand the profiles of the pair potential and the zero energy LDOS from the excitation spectra and the wave functions. [1] T. Yoshida, M. Sigrist, and Y. Yanase, Phys. Rev. B 86, (2012). [2] Y. Higashi, Y. Nagai, T. Yoshida, and Y. Yanase, submitted to J. Phys.: Conf. Ser..

5 PC-14-INV NanoSQUID-on-tip: Towards scanning magnetic microscopy with single spin sensitivity L. Embon 1, Y. Anahory 1, J. Cuppens 1, D. Vasyukov 1, E. Lachman 1, D. Halbertal 1, N. Hoovinakatte 1, Y. Myasoedov 1, M. L. Rappaport 1, M. E. Huber 2 and E. Zeldov 1* 1 Weizmann Institute of Science, Rehovot 76100, Israel 2 Department of Physics, University of Colorado Denver, Denver, CO A scanning magnetic probe microscope based on a nanosquid which is fabricated on the apex of a quartz tip has been developed. The SQUID-on-tip (SOT) device is fabricated by pulling a quartz tube into a sharp pipette with diameters down to 50 nm followed by deposition of a thin superconducting Pb film onto the sides and the apex of the pipette. The devices operate at 4 K in applied magnetic fields of up to 1 T and display an extremely low flux noise of 50 nφ 0 /Hz 1/2. As a result, a record spin sensitivity of 0.4 μ B /Hz 1/2 is achieved that is sufficient for detecting the magnetic moment of a single electron [1]. Using a quartz tuningfork based AFM technique the nanosquid can be scanned tens of nm above the surface of the sample. The combination of high sensitivity, high spatial resolution, wide bandwidth, and close proximity to the sample opens the pathway to direct imaging and investigation of a wide range of static and dynamic magnetic phenomena on the nanoscale. Using the scanning SOT microscope we have carried out an investigation of controlled dynamics of vortices in superconducting films with sub-angstrom spatial resolution. We measured the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors. 1. D. Vasyukov, Y. Anahory, L. Embon, D. Halbertal, J. Cuppens, L. Neeman, A. Finkler, Y. Segev, Y. Myasoedov, M. L. Rappaport, M. E. Huber, and E. Zeldov, Nature Nanotech. 8, 639 (2013).

6 PC-15-INV Flux flow of Fe-based superconductors -Novel gap spectroscopy and universal large dissipation- A. Maeda *, T. Okada, H. Takahashi, F. Nabeshima, Y. Imai (Department of Basic Science, University of Tokyo) We investigated superfluid density (magnetic penetration depth) as a function of temperature and flux flow resistivity as a function of magnetic field of various kinds of Fe based superconductor systematically by microwave conductivity measurement techniques[1-7]. Reflecting the multiply gapped nature of these materials, large variety of the phenomena was observed both in the temperature dependence of the penetration depth and in the magnetic field dependence of flux flow resistivity. Qualitatively, these behaviors can be understood by considering the multiple gap nature and the anisotropy of each gap, which depends on each material. We developed a model that describes the superfluid density and the flux flow resistivity for a two gap superconductor, which take the Fermi surface structure explicitly into account. With available data of the Fermi surface measured by ARPES experiments, we succeeded in explaining the observed behaviors of these two independent quantities QUANTITATIVELY very well in terms of the two band model. Depending on the magnitude of the obtained anisotropy parameters, we confirmed the presence/the absence of the nodes on each Fermi surface. Thus, we can determine the superconducting gap structure investigating these two quantities in detail. Therefore, our method can be called as a novel method to discuss the structure of the superconducting order parameter. In Fe(Se,Te), the dissipation by the flux flow was found to be exceptionally small, which turn out to be the result of the backflow of supercurrent by the disorder, which is mostly believed to be magnetic, specific to this system. Another interesting aspect is, in all materials investigated, the quasiparticle scattering time in the vortex core is rather short so that the mean free path of the quasiparticle mean free path in the vortex core is limited by the core radius (GL coherence length). We have the same result even in very clean FeSe single crystals, which became available quite recently by the vapor transport method. Furthermore, these results are in line with what we already obtained in many other superconductors, such as copper oxide high T c superconductors, Y 2 C 3, and boron-carbide superconductors etc. This universal feature of large dissipation by the quasiparticle inside the vortex core cannot be explained exactly by any existing theories, and may suggest the presence of a novel mechanism of dissipation by quasiparticles in the vortex core. We deeply acknowledge many other collaborators as hig-quality sample suppliers; K. Kitagawa (Kochi University), K. Matsubayashi, Y. Uwatoko, M. Takigawa (ISSP, University of Tokyo) for LiFe(As,P),Na(Fe, Co)As and SrFe 2 (As,P) 2, and M. Nakajima (Osaka University), A. Iyo, H. Eisaki (AIST) for BaFe 2 (As, P) 2, and T. Urata, Y. Tanabe, K. Tanigaki (Tohoku University) for very high-quality FeSe. [1] T. Okada et al., Phys. Rev. B86 (2012) [2] H. Takahashi et al., Phys. Rev. B86 (2012) [3] T. Okada et al., Physica C484 (2013) 27. [4] T. Okada et al., Physica C494 (2013) 109. [5] T. Okada et al., Physica C, in press. [6] T. Okada et al., arxiv [7] A. Maeda et al., Quantum Matt., in press.