Unveiling defect-related Raman modes of topological phononic β−MoB2 single crystal via angle-resolved polarized Raman spectra

As a rare topological phonon material, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>β</a:mi><a:mtext>−</a:mtext><a:msub><a:mi>MoB</a:mi><a:mn>2</a:mn></a:msub></a:mrow></a:math> exhibits superconductivity (SC) and undergoes structural transitions when subjected to pressure or doping. This unique property makes it an intriguing platform for investigating the interplay of diverse quantum order. However, the current understanding of phonons in this material remains limited. Therefore, in this study, we employ a combination of Raman scattering and first-principle calculations to investigate the phonon properties of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>β</b:mi><b:mtext>−</b:mtext><b:msub><b:mi>MoB</b:mi><b:mn>2</b:mn></b:msub></b:mrow></b:math>. Several noteworthy observations were made during the study. (1) We identified five Raman-active modes (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>3</c:mn><c:msub><c:mi>A</c:mi><c:mrow><c:mn>1</c:mn><c:mi>g</c:mi></c:mrow></c:msub><c:mo>+</c:mo><c:mn>2</c:mn><c:msub><c:mi>E</c:mi><c:mi>g</c:mi></c:msub></c:mrow></c:math>) and two abnormal modes in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>β</d:mi><d:mtext>−</d:mtext><d:msub><d:mi>MoB</d:mi><d:mn>2</d:mn></d:msub></d:mrow></d:math>. The authenticity of the five Raman-active modes was further confirmed through angle-resolved polarized Raman spectra (ARPRS) measurements and theoretical calculations. (2) We found that all Raman spectra obtained at various temperatures exhibited symmetric Lorentzian profiles. This finding implies a weak electron-phonon coupling (EPC) strength in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>β</e:mi><e:mtext>−</e:mtext><e:msub><e:mi>MoB</e:mi><e:mn>2</e:mn></e:msub></e:mrow></e:math>. We calculated the EPC strength <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>λ</f:mi></f:math> of bulk <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>β</g:mi><g:mtext>−</g:mtext><g:msub><g:mi>MoB</g:mi><g:mn>2</g:mn></g:msub></g:mrow></g:math> to be 0.37, which is significantly lower than 1.71 of superconducting <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>α</h:mi><h:mtext>−</h:mtext><h:msub><h:mi>MoB</h:mi><h:mn>2</h:mn></h:msub></h:mrow></h:math>. (3) Based on ARPRS measurements and the phonon dispersion, we attributed the origin of the two abnormal modes to structural distortions with regard to B atom layers of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>β</i:mi><i:mtext>−</i:mtext><i:msub><i:mi>MoB</i:mi><i:mn>2</i:mn></i:msub></i:mrow></i:math>. This research provides a foundation for exploring the relationship between defect structures and various intriguing physical phenomena observed in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>β</j:mi><j:mtext>−</j:mtext><j:msub><j:mi>MoB</j:mi><j:mn>2</j:mn></j:msub></j:mrow></j:math>.