Topological phase transitions, influenced by magnetic fields, dopants, pressure, and temperature, create Berry curvature in band structures, challenging to detect due to resolution and scattering issues in spectroscopy and transport. Here, we propose nonlinear electrical transport phenomena as fingerprints of a topological phase transition in ZrTe₅ under magnetic fields. Both a nonlinear longitudinal conductivity Δσ_L in a magnetic-field-aligned electric field and a third-order nonlinear Hall (transverse) conductivity Δσ_xy in a magnetic-field-perpendicular electric field arise below a characteristic temperature T^*. The sensitivity of nonlinear transport to the band topology allows the detection of a subtle change in the band topology hidden in linear transport coefficients. Extending the previous scaling theory between linear transport coefficients (σ_xx and σ_xy), we also propose scaling relations for both linear (σ_xx and σ_xy) and nonlinear (Δσ_L and Δσ_xy) transport coefficients. These scaling relations will help understand the interplay between the mechanisms of nonlinear transport coefficients and the influence of Berry curvature.

受磁场、掺杂剂、压力和温度影响的拓扑相变会在能带结构中产生贝里曲率，由于光谱和传输中的分辨率和散射问题，检测起来很困难。在这里，我们提出非线性电输运现象作为磁场下ZrTe ₅拓扑相变的指纹。磁场对准电场中的非线性纵向电导率Δσ _L和磁场垂直电场中的三阶非线性霍尔（横向）电导率Δσ _xy都出现在特征温度T ^*以下。非线性传输对能带拓扑的敏感性允许检测隐藏在线性传输系数中的能带拓扑的细微变化。扩展线性传输系数（ σ _xx和σ _xy ）之间的先前标度理论，我们还提出了线性（σ _xx和σ _xy）和非线性（Δσ _L和Δσ _xy）传输系数的标度关系。这些标度关系将有助于理解非线性传输系数机制与贝里曲率影响之间的相互作用。