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We have investigated the magnetoresistive behavior of Dirac semi-metal Cd3As2 down to low temperatures and in high magnetic fields. A positive and linear magnetoresistance (LMR) as large as 3100% is observed in a magnetic field of 14 T, on high-quality single crystals of Cd3As2 with ultralow electron density and large Lande g factor. Such a large LMR occurs when the magnetic field is applied perpendicular to both the current and the (100) surface, and when the temperature is low such that the thermal energy is smaller than the Zeeman splitting energy. Tilting the magnetic field or raising the temperature all degrade the LMR, leading to a less pronounced quadratic behavior. We propose that the phenomenon of LMR is related to the peculiar field-induced shifting/distortion of the helical electrons' Fermi surfaces in momentum space.Compared with those negative magnetoresistive behaviors such as giant magnetoresistance [1] and colossal magnetoresistance [2] whose mechanisms have been well understood, positive large LMR was also reported in past decades but its mechanism is not fully clarified. Such behavior was found in highly disordered nonmagnetic narrow-band semiconductors such as Ag 2±δ Te and Ag 2±δ Se [3], in bismuth thin films [4], and in Dirac electron systems such as epitaxial graphene [5] and topological insulators-related materials [6][7][8][9][10]. Large LMR was also observed in InSb [11], a material with very small electron effective mass and very large electron Lande g factor. Several theories have been proposed to explain the phenomenon. Abrikosov proposed that the LMR is a quantum magnetoresistance of linearly dispersed electron systems, arising when all the electrons are filled in the first Landau level (LL), i.e., in the extreme quantum limit [12,13]. Wang and Lei proposed that the LMR can still arise when the LLs are smeared, if with a positive g factor [14]. There are also pictures involving no LLs. Parish and Littlewood explained the LMR in Ag 2±δ Te and Ag 2±δ Se by modeling the materials as a network due to disorder-induced mobility fluctuation [15]. So far the mechanism of LMR is still waiting to be clarified.In this work, we revisit the LMR issue by investigating the magnetoresistive behavior of Cd 3 As 2 single crystals. Cd 3 As 2 is predicted to be a three-dimensional (3D) Dirac semimetal [16], with linearly dispersed electron states in the bulk, and Fermi arcs at the surface which connect the bulk Dirac cones. The existence of 3D Dirac cones has been confirmed by angular resolved photoemission spectroscopy study [17]. And a LMR behavior has recently been observed on samples with Fermi level well above the Dirac point [9, 10], i.e., with carrier density of the order 10 18 cm −3 . Here, we report our investigations on single crystals of Cd 3 As 2 with a much lower carrier density, such that the Fermi surfaces are small spheres very close to the Dirac points in the momentum space, rather than near the Lifshitz transition (i.e., touching with each other). We observed a positive, very large an...

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