Fig. 2: Phase transition with enhanced NLHE in few-layer TaIrTe4.

a The 2D map of the NLH voltage \({V}_{{{{\rm{ab}}}}}^{2\omega }\) as a function of temperature and input current. b Corresponding map of the NLH phase \({\theta }_{{{{\rm{ab}}}}}^{2\omega }\). Both maps indicate the onset of state II below 60 K and low driving current below 20 \({{{\rm{\mu }}}}{{{\rm{A}}}}\). Crosscuts of \({V}_{{{{\rm{ab}}}}}^{2\omega }\) and \({\theta }_{{{{\rm{ab}}}}}^{2\omega }\) for state I and state II are shown in c and d respectively. In both panel, dashed lines represent linear fits to the \({V}_{{{{\rm{ab}}}}}^{2\omega }\) data and the solid lines are guides to the \({\theta }_{{{{\rm{ab}}}}}^{2\omega }\) data. Phase transition between state I and state II with hysteresis window, driven by current and temperature independently, are shown in e, f, respectively. In e the dashed curves represent quadratic fits to the V–I characteristics. In f error bars represent the standard error of \({\eta }_{{{{\rm{ab}}}}}\) from quadratic fitting and the dashed line marks \({\eta }_{{{{\rm{ab}}}}}=0\) as a reference for the direction of the NLHE.