Chiral anomaly and classical negative magnetoresistance of Weyl metals

Abstract

We consider the classical magnetoresistance of a Weyl metal in which the electron Fermi surface possess nonzero fluxes of the Berry curvature. Such a system may exhibit large negative magnetoresistance with unusual anisotropy as a function of the angle between the electric and magnetic fields. In this case the system can support a new type of plasma waves. These phenomena are consequences of chiral anomaly in electron transport theory.PACS numbers: 72.10.Bg Materials with nontrivial topological properties have attracted considerable interest after the discovery of topological insulators [1]. One type of such materials is the so-called Weyl semimetals, characterized by the the presence of points of band touching (Dirac points) [2][3][4][5][6][7][8][9][10]. In this paper, we study the metallic counterparts of these materials-the Weyl metals, where Dirac points are hidden inside a Fermi surface. We show that these materials may exhibit large negative magnetoresistance with unusual anisotropy. We also find a new type of plasma waves in these systems.At low magnetic field B and at relatively high temperature Landau quantization can be neglected, and electron transport in metals can be described using the semiclassical Boltzmann kinetic equationHere n p (r, t) is the electron distribution function, p is the quasimomentum, I coll {n p } is the collision integral, andṙThe last, "anomalous," term in Eq. (2a), proportional to the Berry curvaturewas introduced in Ref. [11]. (See also reviews on the subject in Refs. [12,13].) In systems with time-reversal symmetry Ω p = Ω −p , while in centro-symmetric systems Ω p = −Ω −p . Thus, in systems which are both time-and centro-symmetric Ω p = 0. In this case the magneto-resistance described by Eq. (1) is positive and is governed by the parameter (ω c τ tr ) 2 [14]. Here ω c is the cyclotron frequency and τ tr is the electron transport mean free path. The Berry curvature is divergence-free except at isolated points in p space, which are associated with band degeneracies. As a result, in the case where the electronic spectrum has several valleys, they can be characterized by integers (see, for example, Ref.[15])Here the index "i" labels the valleys, dS is the elementary area vector. Nonzero values of k (i) are realized if near the degeneracy points, electrons can be described by the massless Dirac Hamiltonian [27] H = ±vσ ·P.(5)A is the momentum operator, A is the vector potential, σ is the operator of pseudospin, v is the quasiparticle velocity, and the signs ± correspond to the different chiralities of the Weyl fermions.It is well known that massless Dirac fermions exhibit chiral anomaly which can be understood in the language of level crossing in the presence of a magnetic field [16]. According to the Nielsen-Ninomiya theorem [17], the number of valleys with opposite chiralities (positive and negative values of k (i) ) should be equal, and so i k (i) = 0. Recently, gapless semiconductors with topologically protected Dirac points (Weyl semimetals) have attracted significant atten...

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“…Note that, as 2B > t[1−cos(k 0 a)] is assumed in Eq. (15), the condition of 4B > −∆(k z ) > 0 is simply equivalent to…”

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

“…5 (proportional to E · B) is the source of chiral anomaly, triggering negative magnetoresistance. It has been shown recently that negative magnetoresistance can be derived using the semi-classical equations of motion employing Boltzmann transport 60 . Other recent works have also developed a modified Boltzmann equation, taking into account Berry curvature and chiral anomaly effects 45,46,[78][79][80] .…”

“…an imbalance of charge between two distinct species of chiral fermions in the presence of non-orthogonal applied electric and magnetic fields. Several transport signatures have been proposed to test chiral anomaly such as negative longitudinal magenoresistance 16,21,60,61 and chiral magnetic effect 16,62,63 of which the former has been recently claimed to be observed in experiments 24,37,41,42 .…”

Topological semimetals with helicoid surface states

“…Bloch states in the vicinity of the band crossing possess a nonzero topological index, e.g., the Chern number in case of Weyl semimetals. The nontrivial topology gives rise to anomalous bulk properties of topological semimetals such as the chiral anomaly [3][4][5]. Several classes of topological semimetals have been theoretically proposed so far, including Weyl, [2,[6][7][8][9][10][11][12][13], Dirac [14][15][16][17] and nodal line semimetals [7,[17][18][19][20][21][22][23][24][25][26][27][28][29][30], some among which have been experimentally observed [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”