Weyl semimetals (WSMs) host charged Weyl fermions as emergent quasiparticles. We develop a unified analytical theory for the anomalous positive longitudinal magnetoconductance (LMC) in a WSM, which bridges the gap between the classical and ultra-quantum approaches. More interestingly, the LMC is found to exhibit periodic-in-1/B quantum oscillations, originating from the oscillations of the nonequilibrium chiral chemical potential. The quantum oscillations, superposed on the positive LMC, are a remarkable fingerprint of a WSM phase with chiral anomaly, whose observation is a valid criteria for identifying a WSM material. In fact, such quantum oscillations were already observed by several experiments.Weyl semimetals (WSMs), whose low-energy excitations are Weyl fermions [1] carrying charges, have recently spurred intensive and innovative research in the field of condensed matter physics [2][3][4][5][6][7][8]. The ultrahigh mobility and spectacular transport properties of the charged Weyl fermions can find applications in highspeed electronic circuits and computors [9][10][11]. The lowenergy spectrum of a WSM forms non-degenerate threedimensional (3D) Dirac cones around isolated degenerate band touching points, referred to as Weyl points [2]. Weyl points with opposite chiralities, playing the parts of the source and sink of Berry curvature in momentum space, always come in pairs [12,13]. The appearance of the Weyl points requires breaking either the spatial inversion or time-reversal symmetry. Weyl points with opposite chiralities in momentum space are connected by the nonclosed Fermi arc surface states [2].The WSM state was first realized experimentally in TaAs [14-16], following the theoretical predictions [17,18], and later in several different compounds [10,[19][20][21][22][23][24][25][26][27][28][29]. WSMs display many anomalous transport properties, such as positive longitudinal magnetoconductance (LMC), optical gyrotropy [30], planar Hall effect [31], all of which are induced by the chiral anomaly [13], and nonlocal quantum oscillations of the Fermi arc surface states [32]. The chiral anomaly, also termed as the Adler-Bell-Jackiw anomaly, means the violation of the separate number conservation laws of Weyl fermions of different chiralities. Parallel electric and magnetic fields can pump Weyl fermions between Weyl valleys of opposite chiralities, and create a population imbalance between them, therefore resulting in a positive LMC (or negative magne- * shengli@nju.edu.cn † dyx@nju.edu.cn toresistance). The anomalous LMC, as an exotic macroscopic quantum phenomenon, has been attracting intense experimental [10,[20][21][22][23][24][25][26][27][28][29] and theoretical [7,[33][34][35][36] interest.In order to identify a WSM material, the ARPES experiments were used to directly observe the Weyl nodes and Fermi arcs [14][15][16]19]. However, the ARPES identification is sometime limited by spectroscopic resolutions. Another widely-employed method is to measure the positive LMC induced by the chiral anomaly [10,[20][2...