Nodeless kagome superconductivity in ${\mathrm{LaRu}}_{3}{\mathrm{Si}}_{2}$

Nodeless kagome superconductivity in ${LaRu}_{3} {Si}_{2}$

C. Mielke, III, Y. Qin, J.-X. Yin, H. Nakamura, D. Das, K. Guo, R. Khasanov, J. Chang, Z. Q. Wang, S. Jia, S. Nakatsuji, A. Amato, H. Luetkens, G. Xu, M. Z. Hasan, and Z. Guguchia

Phys. Rev. Materials 5, 034803 – Published 29 March 2021

Abstract

We report muon spin rotation ( $μ SR$ ) experiments together with first-principles calculations on microscopic properties of superconductivity in the kagome superconductor ${LaRu}_{3} {Si}_{2}$ with $T_{c} ≃$ 7K. Below $T_{c}$ , $μ SR$ reveals type-II superconductivity with a single s-wave gap, which is robust against hydrostatic pressure up to 2 GPa. We find that the calculated normal state band structure features a kagome flat band, and Dirac as well as van Hove points formed by the Ru- $d z^{2}$ orbitals near the Fermi level. We also find that electron-phonon coupling alone can only reproduce a small fraction of $T_{c}$ from calculations, which suggests other factors in enhancing $T_{c}$ such as the correlation effect from the kagome flat band, the van Hove point on the kagome lattice, and the high density of states from narrow kagome bands. Our experiments and calculations taken together point to nodeless moderate coupling kagome superconductivity in ${LaRu}_{3} {Si}_{2}$ .

Received 1 January 2021
Revised 15 February 2021
Accepted 8 March 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.034803

Physics Subject Headings (PhySH)

Electronic structure

Kagome lattice Unconventional superconductors

Muon spin relaxation & rotation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Mielke, III ^1,2,*, Y. Qin^3,*, J.-X. Yin^4,*, H. Nakamura^5,*, D. Das ¹, K. Guo ^6,7, R. Khasanov ¹, J. Chang ², Z. Q. Wang⁸, S. Jia^6,7, S. Nakatsuji⁵, A. Amato ¹, H. Luetkens ¹, G. Xu^3,†, M. Z. Hasan^{4,9,10,11,‡}, and Z. Guguchia ^1,§

¹Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
²Physik-Institut, Universitat Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
³Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
⁴Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
⁵Institute for Solid State Physics, University of Tokyo, Kashiwa, 277-8581, Japan
⁶International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China
⁷CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Science, Beijing 100864, China
⁸Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
⁹Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA
¹⁰Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
¹¹Quantum Science Center, Oak Ridge, Tennessee 37831, USA

^*These authors contributed equally to the paper.
^†gangxu@hust.edu.cn
^‡mzhasan@princeton.edu
^§zurab.guguchia@psi.ch

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Vol. 5, Iss. 3 — March 2021

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Figure 1
Top view (a) and side view (b) of the atomic structure of ${LaRu}_{3} {Si}_{2}$ . The Ru atoms construct a kagome lattice (red middle-size circles), while the Si (green small-size circles) and La atoms (blue large-size circles) form a honeycomb and triangular structure, respectively. (c) Tight-binding band structure of kagome lattice exhibiting two Dirac bands at the $K$ point and a flat band across the whole Brillouin zone (BZ). (d) The band structures (black) and orbital-projected band structure (red) for the Ru- $d z^{2}$ orbital without SOC along the high symmetry $k$ path, presented in conformal kagome BZ. The width of the line indicates the weight of each component. The blue-colored region highlights the manifestation of the kagome flat band.
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Figure 2
(a) The calculated total DOS and projected DOS for the Ru, Si, and La atoms in the bulk ${LaRu}_{3} {Si}_{2}$ . (b) Three-dimensional Fermi surface of ${LaRu}_{3} {Si}_{2}$ in the first Brillouin zone.
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Figure 3
(a) The temperature dependence of the electrical resistivity for ${LaRu}_{3} {Si}_{2}$ , recorded for various applied magnetic fields. (b–d) Transverse-field (TF) and zero-field (ZF) $μ SR$ time spectra for ${LaRu}_{3} {Si}_{2}$ to probe the SC vortex state and magnetic responses, respectively. The TF spectra are obtained above and below $T_{c}$ (after field cooling the sample from above $T_{c}$ ): (b) $p = 0$ GPa and (c) $p = 1.85$ GPa. The solid lines in (b) and (c) represent fits to the data by means of Eq. (1) of the supplementary information. Inset illustrates how muons, as local probes, sense the inhomogeneous field distribution in the vortex state of the type-II superconductor. (d) ZF $μ SR$ time spectra for ${LaRu}_{3} {Si}_{2}$ recorded above and below $T_{c}$ . The line represents the fit to the data using a standard Kubo-Toyabe depolarization function [36], reflecting the field distribution at the muon site created by the nuclear moments. Temperature dependence of the diamagnetic shift $Δ μ_{0} H_{int}$ (e) and the muon spin depolarization rate $σ_{sc} (T$ ) (f), measured at various hydrostatic pressures in an applied magnetic field of $μ_{0} H = 70$ mT. The arrows mark the $T_{c}$ values.
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Figure 4
The temperature dependence of $λ_{eff}^{- 2}$ measured at various applied hydrostatic pressures for ${LaRu}_{3} {Si}_{2}$ : (a) $p = 0$ GPa, (b) 1.3 GPa, and (c) 1.85 GPa. The solid line corresponds to an $s$ -wave model and the dashed line represents fitting with a $d$ -wave model. (d) A plot of $T_{c}$ versus the $λ_{eff}^{- 2} (0)$ obtained from our $μ SR$ experiments in ${LaRu}_{3} {Si}_{2}$ . The dashed red line represents the relation obtained for layered transition metal dichalcogenide superconductors $T_{d} − {MoTe}_{2}$ [45] and 2H- ${NbSe}_{2}$ [46]. The data are taken at ambient conditions as well as under pressure. The relation observed for underdoped cuprates is also shown (solid line for hole doping [47, 48, 49, 50] and the dashed black line for electron doping [51, 52]). The points for various conventional BCS superconductors are also shown.
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Physical Review Materials

Nodeless kagome superconductivity in LaRu3Si2

C. Mielke, III, Y. Qin, J.-X. Yin, H. Nakamura, D. Das, K. Guo, R. Khasanov, J. Chang, Z. Q. Wang, S. Jia, S. Nakatsuji, A. Amato, H. Luetkens, G. Xu, M. Z. Hasan, and Z. Guguchia

Phys. Rev. Materials 5, 034803 – Published 29 March 2021

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Nodeless kagome superconductivity in ${LaRu}_{3} {Si}_{2}$