Defect-Induced Low-Energy Majorana Excitations in the Kitaev Magnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mrow><mml:mi>RuCl</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
K. Imamura, Yuta Mizukami, O. Tanaka, Romain Grasset, M. Kończykowski, Nobuyuki Kurita, Hidekazu Tanaka, Yuji Matsuda, Masahiko Yamada, K. Hashimoto, T. Shibauchi
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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>α</a:mi><a:mtext>−</a:mtext><a:msub><a:mrow><a:mi>RuCl</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub></a:mrow></a:math>, 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>α</c:mi><c:mtext>−</c:mtext><c:msub><c:mrow><c:mi>RuCl</c:mi></c:mrow><c:mrow><c:mn>3</c:mn></c:mrow></c:msub></c:mrow></c:math> using electron irradiation, which induces site vacancies and exchange randomness. High-resolution measurements of the temperature dependence of specific heat <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>C</e:mi><e:mo stretchy="false">(</e:mo><e:mi>T</e:mi><e:mo stretchy="false">)</e:mo></e:math> under in-plane fields <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>H</i:mi></i:math> reveal that, while the field-dependent Majorana gap is almost intact, additional low-energy states with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>C</k:mi><k:mo>/</k:mo><k:mi>T</k:mi><k:mo>=</k:mo><k:mi>A</k:mi><k:mo stretchy="false">(</k:mo><k:mi>H</k:mi><k:mo stretchy="false">)</k:mo><k:mi>T</k:mi></k:math> are induced by introduced defects. At low temperatures, we obtain the data collapse of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>C</o:mi><o:mo>/</o:mo><o:mi>T</o:mi><o:mo>∼</o:mo><o:msup><o:mi>H</o:mi><o:mrow><o:mo>−</o:mo><o:mi>γ</o:mi></o:mrow></o:msup><o:mo stretchy="false">(</o:mo><o:mi>T</o:mi><o:mo>/</o:mo><o:mi>H</o:mi><o:mo stretchy="false">)</o:mo></o:math> expected for a disordered quantum spin system but with an anomalously large exponent <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>γ</s:mi></s:math>. This leads us to find a power-law relationship between the coefficient <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>A</u:mi><u:mo stretchy="false">(</u:mo><u:mi>H</u:mi><u:mo stretchy="false">)</u:mo></u:math> 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. Published by the American Physical Society 2024