Shiba bands formed by overlapping Yu-Shiba-Rusinov subgap states in magnetic impurities on a superconductor play an important role in topological superconductors. Here, we theoretically demonstrate the existence of a new type of Shiba bands (dubbed topological Shiba metal) on a magnetically doped $s$-wave superconducting surface with Rashba spin-orbit coupling in the presence of a weak in-plane magnetic field. Such topological gapless Shiba bands develop from gapped Shiba bands through Lifshitz phase transitions accompanied by second-order quantum phase transitions for the intrinsic thermal Hall conductance. We also find a mechanism in Shiba lattices that protects the first-order quantum phase transitions for the intrinsic thermal Hall conductance. Due to the long-range hopping in Shiba lattices, the topological Shiba metal exhibits intrinsic thermal Hall conductance with large nonquantized values. As a consequence, there emerge a large number of second-order quantum phase transitions.

Ning Dai Kai Li Yan-Bin Yang Yong Xu

Our team, Hibikino-Musashi@Home (HMA), was founded in 2010. It is based in Japan in the Kitakyushu Science and Research Park. Since 2010, we have annually participated in the RoboCup@Home Japan Open competition in the open platform league (OPL).We participated as an open platform league team in the 2017 Nagoya RoboCup competition and as a domestic standard platform league (DSPL) team in the 2017 Nagoya, 2018 Montreal, 2019 Sydney, and 2021 Worldwide RoboCup competitions.We also participated in theWorld Robot Challenge (WRC) 2018 in the service-robotics category of the partner-robot challenge (real space) and won first place. Currently, we have 27 members from nine different laboratories within the Kyushu Institute of Technology and the university of Kitakyushu. In this paper, we introduce the activities that have been performed by our team and the technologies that we use.

Tomoya Shiba Tomohiro Ono Shoshi Tokuno Issei Uchino Masaya Okamoto Daiju Kanaoka Kazutaka Takahashi Kenta Tsukamoto Yoshiaki Tsutsumi Yugo Nakamura Yukiya Fukuda Yusuke Hoji Hayato Amano Yuma Kubota Mayu Koresawa Yoshifumi Sakai Ryogo Takemoto Katsunori Tamai Kazuo Nakahara Hiroyuki Hayashi Satsuki Fujimatsu Akinobu Mizutani Yusuke Mizoguchi Yuhei Yoshimitsu Mayo Suzuka Ikuya Matsumoto Yuga Yano Yuichiro Tanaka Takashi Morie Hakaru Tamukoh

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles' edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

Philip Beck Lucas Schneider Levente Rózsa Krisztián Palotás András Lászlóffy László Szunyogh Jens Wiebe Roland Wiesendanger

Using the numerical renormalization group (NRG), we analyze the temperature dependence of the spectral function of a magnetic impurity described by the single-impurity Anderson model coupled to superconducting contacts. With increasing temperature the spectral weight is gradually transferred from the $\delta$-peak (Shiba/Yu-Shiba-Rusinov/Andreev bound state) to the continuous sub-gap background, but both spectral features coexist at any finite temperature, i.e., the $\delta$-peak itself persists to temperatures of order $\Delta$. The continuous background is due to inelastic exchange scattering of Bogoliubov quasiparticles off the impurity and it is thermally activated since it requires a finite thermal population of quasiparticles above the gap. In the singlet regime for strong hybridization (charge-fluctuation regime) we detect the presence of an additional sub-gap structure just below the gap edges with thermally activated behavior, but with an activation energy equal to the Shiba state excitation energy. These peaks can be tentatively interpreted as Shiba bound states arising from the scattering of quasiparticles off the thermally excited sub-gap doublet Shiba states, i.e., as high-order Shiba states.

Rok Zitko

We study theoretically the dynamics of a Shiba state forming around precessing classical spin in an s-wave superconductor. Utilizing a rotating wave description for the precessing magnetic impurity, we find the resulting Shiba bound state quasi-energy and the spatial extension of the Shiba wavefunction. We show that such a precession pertains to dc charge and spin currents flowing through a normal STM tip tunnel coupled to the superconductor in the vicinity of the impurity. We calculate these currents and find that they strongly depend on the magnetic impurity precession frequency, precession angle, and on the position of the Shiba energy level in the superconducting gap. The resulting charge current is found to be proportional to the difference between the electron and hole wavefunctions of the Shiba state, being a direct measure for such an asymmetry. By dynamically driving the impurity one can infer the spin dependence of the Shiba states in the absence of a spin-polarized STM tip

V. Kaladzhyan S. Hoffman M. Trif

The invariant form of the hyperfine interaction between multipolar moments and the nuclear spin is derived, and applied to discuss possibilities to identify the antiferro-octupolar (AFO) moments by NMR experiments. The ordered phase of NpO$_{2}$ and the phase IV of Ce$_{1-x}$La$_{x}$B$_{6}$ are studied in detail. Recent $^{17}$O NMR for polycrystalline samples of NpO$_{2}$ are discussed theoretically from our formulation. The observed feature of the splitting of $^{17}$O NMR spectrum into a sharp line and a broad line, their intensity ratio, and the magnetic field dependence of the shift and of the width can be consistently explained on the basis of the triple $\bq$ AFO ordering model proposed by Paix\~{a}o {\it et. al.} Thus, the present theory shows that the $^{17}$O NMR spectrum gives a strong support to the model. The 4 O sites in the fcc NpO$_2$ become inequivalent due to the secondary triple $\bq$ ordering of AF-quadrupoles: one cubic and three non-cubic sites. It turns out that the hyperfine field due to the antiferro-dipole and AFO moments induced by the magnetic field, and the quadrupolar field at non-cubic sites are key ingredients to understand the observed spectrum. The controversial problem of the nature of phase IV in Ce$_{1-x}$La$_{x}$B$_{6}$ is also studied. It is pointed out that there is a unique feature in the NMR spectra, if the $\Gamma_{5}$($T^{\beta}_{x}=T^{\beta}_{y}=T^{\beta}_{z}$) AFO ordering is realized in Ce$_{1-x}$La$_{x}$B$_{6}$. Namely, the hyperfine splitting of a B atom pair on the $({1/2},{1/2},\pm u)$ sites crosses zero on the $(1\bar{1}0)$ plane when the magnetic field is rotated around the $[001]$ axis.

Osamu Sakai Ryousuke Shiina Hiroyuki Shiba

When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity1. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap2-4. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes5 suitable for topological quantum computing6. Here we report the first realization of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms. We induce superconductivity in graphene by proximity effect7-9 brought by adsorbing nanometer scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy we measure the superconducting proximity gap in graphene and we visualize Yu-Shiba-Rusinov states in graphene grain boundaries. Our results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long sought experimental confirmation that graphene grain boundaries host local magnetic moments10-14 and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system.

E. Cortés-del Río J. L. Lado V. Cherkez P. Mallet J-Y. Veuillen J. C. Cuevas J. M. Gómez-Rodríguez J. Fernández-Rossier I. Brihuega

Conventional in-gap Yu-Shiba-Rusinov states require two ingredients: magnetic atoms and a superconducting host that, in the normal phase, has a finite density of states at the Fermi energy. Here we show that hydrogenated graphene can host Yu-Shiba-Rusinov states without any of those two ingredients. Atomic hydrogen chemisorbed in graphene is known to act as paramagnetic center with a weakly localized magnetic moment. Our calculations for hydrogenated graphene in proximity to a superconductor show that individual adatoms induce in-gap Yu-Shiba-Rusinov states with an exotic spectrum whereas chains of adatoms result in a gapless Yu- Shiba-Rusinov band. Our predictions can be tested using state of the art techniques, combining recent progress of atomic manipulation of atomic hydrogen on graphene together with the well tested proximity effect in graphene.

J. L. Lado J. Fernandez-Rossier

Regular arrays of magnetic atoms on a superconductor provide a promising platform for topological superconductivity. In this work we study effects of disorder in these systems, focusing on vacancies realized by missing magnetic atoms. We develop approaches that allow treatment of ferromagnetic dense chains as well as long-range hopping ferromagnetic and helical Shiba chains at arbitrary subgap energies. Vacancies in magnetic chains play an analogous role to magnetic impurities in a clean $s$-wave superconductor. A single vacancy in a topological chain gives rise to a low-lying "anti-Shiba" state below the band edge of a regular magnetic chain. Proliferation of the anti-Shiba band formed by a finite density of hybridized vacancy states leads to deterioration of the topological phase, which exhibits unusual fragility in a particular parameter region in dilute chains. We also consider local fluctuation in the Shiba coupling and discuss how vacancy states could contribute to experimental verification of topological superconductivity.

Alex Westström Kim Pöyhönen Teemu Ojanen

In superconductors, magnetic impurities induce a pair-breaking potential for Cooper pairs, which locally affects the Bogoliubov quasiparticles and gives rise to Yu-Shiba-Rusinov (YSR or Shiba, in short) bound states in the density of states (DoS). These states carry information on the magnetic coupling strength of the impurity with the superconductor, which determines the many-body ground state properties of the system. Recently, the interest in Shiba physics was boosted by the prediction of topological superconductivity and Majorana modes in magnetically coupled chains and arrays of Shiba impurities. Here, we review the physical insights obtained by scanning tunneling microscopy into single magnetic adsorbates on the $s$-wave superconductor lead (Pb). We explore the tunneling processes into Shiba states, show how magnetic anisotropy affects many-body excitations, and determine the crossing of the many-body groundstate through a quantum phase transition. Finally, we discuss the coupling of impurities into dimers and chains and their relation to Majorana physics.

Benjamin W. Heinrich Jose I. Pascual Katharina J. Franke