Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$

Open Access

Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet $α − {RuCl}_{3}$

K. Imamura, Y. Mizukami, O. Tanaka, R. Grasset, M. Konczykowski, N. Kurita, H. Tanaka, Y. Matsuda, M. G. Yamada, K. Hashimoto, and T. Shibauchi

Phys. Rev. X 14, 011045 – Published 11 March 2024

Abstract

The excitations in the Kitaev spin liquid (KSL) can be described by Majorana fermions, which have characteristic field dependence of bulk gap and topological edge modes. In the high-field state of layered honeycomb magnet $α − {RuCl}_{3}$ , experimental results supporting these Majorana features have been reported recently. However, there are challenges due to sample dependence, and the impact of inevitable disorder on the KSL is poorly understood. Here, we study how low-energy excitations are modified by introducing point defects in $α − {RuCl}_{3}$ using electron irradiation, which induces site vacancies and exchange randomness. High-resolution measurements of the temperature dependence of specific heat $C (T)$ under in-plane fields $H$ reveal that, while the field-dependent Majorana gap is almost intact, additional low-energy states with $C / T = A (H) T$ are induced by introduced defects. At low temperatures, we obtain the data collapse of $C / T \sim H^{- γ} (T / H)$ expected for a disordered quantum spin system but with an anomalously large exponent $γ$ . This leads us to find a power-law relationship between the coefficient $A (H)$ and the field-sensitive Majorana gap. These results are consistent with the picture that the disorder induces low-energy linear Majorana excitations, which may be considered as a weak localization effect of Majorana fermions in the KSL.

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Received 28 June 2023
Revised 22 January 2024
Accepted 13 February 2024

DOI:https://doi.org/10.1103/PhysRevX.14.011045

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Anderson localization Majorana fermions Specific heat Spin liquid

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

K. Imamura ^1,*, Y. Mizukami ^1,†, O. Tanaka¹, R. Grasset ², M. Konczykowski², N. Kurita ³, H. Tanaka ⁴, Y. Matsuda⁵, M. G. Yamada^6,7, K. Hashimoto¹, and T. Shibauchi ^1,‡

¹Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
²Laboratoire des Solides Irradiés, CEA/DRF/IRAMIS, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, F-91128 Palaiseau, France
³Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
⁴Innovator and Inventor Development Platform, Tokyo Institute of Technology, Yokohama 226-8502, Japan
⁵Department of Physics, Kyoto University, Kyoto 606-8502, Japan
⁶Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171-8588, Japan
⁷Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan

^*imamura@qpm.k.u-tokyo.ac.jp
^†Present address: Department of Physics, Tohoku University, Sendai 980-8578, Japan.
^‡shibauchi@k.u-tokyo.ac.jp

Popular Summary

The Kitaev model, a theoretical description of the interactions among electrons arranged in a 2D honeycomblike lattice, looms large in condensed matter physics. In particular, it offers characteristic excitations of certain quasiparticles—specifically, Majorana fermions—that hold promise for fault-tolerant quantum computations. Among the candidates for Kitaev materials, the layered honeycomb magnet $α − {RuCl}_{3}$ has garnered attention due to distinct electronic signatures associated with Majorana fermions. However, the presence of varying observations across different samples has emphasized the need to understand the impact of disorder commonly encountered in real materials. In our study, we investigate the effects of introducing defects in $α − {RuCl}_{3}$ on its low-energy excitations.

Using advanced techniques, including high-energy electron irradiation and high-resolution heat capacity measurements under magnetic field rotation, we find a unique impurity effect related to Majorana fermions. The introduced defects induce additional low-energy excitations that exhibit a distinct scaling behavior intimately connected to the field-dependent energy gap in the Majorana excitation spectrum. This scaling behavior indicates that the defect-induced, low-energy excitations have Majorana-based properties, which is likely related to a type of weak localization of Majorana fermions in the Kitaev spin liquid.

Our findings represent a significant advancement in understanding the influence of disorder on Kitaev materials and provide valuable insights into the behavior of Majorana fermions in the presence of defects.

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