Disorder-mediated linear and nonlinear magnetotransport in the charge-density-wave material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> <mml:msub> <mml:mi mathvariant="normal">a</mml:mi

We report disorder-mediated first-order linear and higher-order nonlinear (magneto-)transport of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="normal">T</a:mi> <a:msub> <a:mi mathvariant="normal">a</a:mi> <a:mn>2</a:mn> </a:msub> <a:mi>NiS</a:mi> <a:msub> <a:mi mathvariant="normal">e</a:mi> <a:mn>7</a:mn> </a:msub> </a:mrow> </a:math> (TNS) in the charge-density-wave (CDW) regime. CDW transition temperature ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>T</e:mi> <e:mi>CDW</e:mi> </e:msub> </e:math> ) and carrier density are proportional and inversely proportional to residual resistance ratio of samples, respectively. Such relation helps to understand the unique CDW order therein. High- <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>T</f:mi> <f:mi>CDW</f:mi> </f:msub> </f:math> TNS exhibits negative first-harmonic magnetoresistance ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi mathvariant="normal">M</g:mi> <g:msup> <g:mrow> <g:mi mathvariant="normal">R</g:mi> </g:mrow> <g:mrow> <g:mn>1</g:mn> <g:mi>ω</g:mi> </g:mrow> </g:msup> </g:mrow> </g:math> ) under a magnetic field ( <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mi>B</j:mi> </j:math> ) parallel to the direction of alternating current ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:msup> <k:mrow> <k:mi>I</k:mi> </k:mrow> <k:mi>ω</k:mi> </k:msup> </k:math> ), which may arise from the anomalous velocity induced by the Berry curvature of three-dimensional topological bands near the Fermi level. As <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:msub> <l:mi>T</l:mi> <l:mi>CDW</l:mi> </l:msub> </l:math> drops, a positive-to-negative <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="normal">M</m:mi> <m:msup> <m:mrow> <m:mi mathvariant="normal">R</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> <m:mi>ω</m:mi> </m:mrow> </m:msup> </m:mrow> </m:math> transition is observed with decreasing perpendicular <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mi>B</p:mi> </p:math> , which is likely due to the contribution of Zeeman effect on current pathways in the disordered system. Moreover, interestingly, the second-harmonic nonlinear signals are suppressed, while the third-harmonic signals are significant and sensitive to both <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mi>B</q:mi> </q:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:msub> <r:mi>T</r:mi> <r:mi>CDW</r:mi> </r:msub> </r:math> . Such observations, together with scaling analysis, suggest the quantum geometry quadrupole at play and the modulation of disorder on third-order nonlinearity. Our results pave an avenue for tailoring distinct-order magnetoresistive phases in disordered topological materials.