Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.Introduction-Weyl semimetals (WSM), which are characterized by the gapless bulk states whose Fermi surfaces are either nodal points or lines, have been an intense area of research 1-9 . The bulk nodal points of a WSM possess non-degenerate band crossings that are robust under a small perturbations to the Hamiltonian. The low energy excitations of these materials are Weyl fermions that are described by two component spinors. The topological nature of the WSM are revealed through examination of the monopoles of Berry curvature present in the Brillouin zone(BZ) referred to as Weyl nodes. In the WSM, the net monopole charge integrated over the entire BZ is zero as the WSM possesses an equal number of the nodes with the positive and the negative charges 10;11 . In the noninteracting theory, these nodal points can only be eliminated by coming into contact with an oppositely charged Weyl node in momentum space, thereby annihilating one another. WSM have been predicted in a number of different materials and structures each of which is characterized by the symmetries broken. The most studied WSM are type-I WSM (WSM1), characterized by the presence of broken inversion or time-reversal symmetry, and type-II WSM (WSM2) 5;6 , which possess broken Lorentz invariance. Inversion broken WSM1, such as T aAs 4;12 , are characterized by the presence of disconnected Fermi arcs at the surface 1 that give rise to unconventional transport signatures such as quantum anomalous Hall (QAH) effect 13 and the chiral anomaly 14 . More recently, promising materials that may harbor experimental signatures of WSM2, such as M oT e 2 and W T e 2 , have been proposed thereby bringing WSM2 closer to realization 15-18 . WSM2 are characterized by an exotic hyperboloid Fermi surface, where the nodes are tilted in the BZ. Due to the tilted nodes, WSM2 exhibit transport properties that are distinct from the WSM1 including the absence of the chiral anomaly at certain magnetic field angles 19 , magnetic break down re...

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As experimental probes have matured to observe ultrafast transient and high frequency responses of materials and devices, so to have the theoretical methods to numerically and analytically simulate time-and frequency-resolved transport. In this review article, we discuss recent progress in the development of the time-dependent and frequency-dependent nonequilibrium Green function (NEGF) technique. We begin with an overview of the theoretical underpinnings of the underlying Kadanoff-Baym equations and derive the fundamental NEGF equations in the time and frequency domains. We discuss how these methods have been applied to a variety of condensed matter systems such as molecular electronics, nanoscale transistors, and superconductors. In addition, we survey the application of NEGF in fields beyond condensed matter, where it has been used to study thermalization in ultra-cold atoms and to understand leptogenesis in the early universe. Throughout, we pay special attention to the challenges of incorporating contacts and interactions, as the NEGF method is uniquely capable of accounting for such features.

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