Disorder-mediated linear and nonlinear magnetotransport in the charge-density-wave material ${\rm Ta_2NiSe_7 }$

We report disorder-mediated first-order linear and higher-order nonlinear (magneto-)transport of Ta$_2$NiSe$_7$ (TNS) in the charge-density-wave (CDW) regime. CDW transition temperature ($T_{CDW}$) 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-$T_{CDW}$ TNS exhibits negative first-harmonic magnetoresistance (MR$^{1\omega}$) under a magnetic field ($B$) parallel to the direction of alternating current ($I^{\omega}$), which may arise from the anomalous velocity induced by the Berry curvature of three-dimensional topological bands near the Fermi level. As $T_{CDW}$ drops, a positive-to-negative MR$^{1\omega}$ transition is observed with decreasing perpendicular $B$, 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 $B$ and $T_{CDW}$. 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.