Absence of metallicity and bias-dependent resistivity in low-carrier-density EuCd₂As₂

EuCd₂As₂ was theoretically predicted to be a minimal model of Weyl semimetals with a single pair of Weyl points in the ferromagnet state. However, the heavily p-doped EuCd₂As₂ crystals in previous experiments prevent direct identification of the semimetal hypothesis. Here, we present a comprehensive magneto-transport study of high-quality EuCd₂As₂ crystals with ultralow bulk carrier density (10¹³ cm⁻³). In contrast to the general expectation of a Weyl semimetal phase, EuCd₂As₂ shows insulating behavior in both antiferromagnetic and ferromagnetic states as well as surface-dominated conduction from band bending. Moreover, the application of a dc bias current can dramatically modulate the resistance by over one order of magnitude, and induce a periodic resistance oscillation due to the geometric resonance. Such nonlinear transport results from the high nonequilibrium state induced by an electrical field near the band edge. Our results suggest an insulating phase in EuCd₂As₂ and put a strong constraint on the underlying mechanism of anomalous transport properties in this system.