Magnetotransport in the doped Mott insulator

We investigate the Hall effect and the magnetoresistance of strongly correlated electron systems using the dynamical mean-field theory. We treat the low- and high-temperature limits analytically, and explore some aspects of the intermediate-temperature regime numerically. We observe that a bipartite-lattice condition is responsible for the high-temperature result s xy;1/T 2 obtained by various authors, whereas the generic behavior is s xy;1/T, as for the longitudinal conductivity. We find that Kohler’s rule is obeyed neither at high nor at intermediate temperatures. @S0163-1829~99!06203-7# I. INTRODUCTION The Hubbard model 1‐3 of strongly correlated electron systems has been an enduring problem in condensed-matter theory. It is believed to capture some of the anomalous physics of heavy-fermion systems and high-Tc superconductors. 4 Its crucial feature is the interplay of itineracy and a local interaction U that is either comparable with or much greater than the bare bandwidth. In this paper, we investigate the impact of a magnetic field on the charge transport in strongly correlated electron systems within the Hubbard model. This issue involves different quantities that are closely related, and should therefore be considered within the same approximation scheme. We meet this condition by using the dynamical mean-field theory which becomes exact in the limit of infinite dimensions. A major though nontrivial simplification of this approach is that transport properties are described solely by the singleparticle spectrum. 5‐8 While the dynamical mean-field theory still captures many properties of real three-dimensional transition-metal oxides, it fails to describe cuprate superconductors equally well, mainly because it does not properly take into account magnetic correlations. Nevertheless, it is important to explore this approximation scheme fully in order to establish a sound starting point for future improvements. The Hall constant of the single-band Hubbard model has already been considered within the dynamical mean-field theory by Pruschke, Jarrell, and Freericks 8 and Majumdar and Krishnamurthy. 9 The former authors computed the Hall constant and Hall angle as functions of temperature for various doping levels at—in our units— U52A2D(D is the halfbandwidth! using the noncrossing approximation ~NCA! and a quantum Monte Carlo ~QMC! technique to solve the single-impurity problem. Majumdar and Krishnamurthy mainly focused on the relation between the infinitefrequency Hall constant investigated by Shastry, Shraiman and Singh, 10 and the dc Hall constant, using the iteratedperturbation theory ~IPT! of Ref. 11. In addition to the Hall effect and the ordinary resistivity, we investigate the magnetoresistance. We tie our numerical analysis at intermediate temperatures to analytical results valid in the low- and high-temperature limits. This allows to disentangle the coherent and incoherent contributions of the single-particle spectrum to the magnetotransport and to gain some understanding of either. We always mainly focus on the parameter regime close to the density-driven Mott transition. This paper is organized as follows: In Sec. II, we briefly summarize the dynamical mean-field theory within the single-band Hubbard model, and derive expressions for the quantities to be calculated. Then, by using a Fermi-liquid parametrization for the spectral function, we examine all quantities in the low-temperature regime ~Sec. III!, and study their dependences on temperature and on the doping level. Moreover, we discuss the impact of correlations close to half-filling. In Sec. IV, we employ a recently developed scheme to expand transport coefficients in powers of 1/T ~Ref. 12! within the U5‘ Hubbard model to study the opposite limit of high temperatures. We show that the hightemperature behaviors of the Hall constant and Hall angle can be affected by specific lattice symmetries, and that the Hall angle increases at most linearly with temperature. Then we explore the intermediate-temperature regime numerically ~Sec. V! by either using the NCA or the IPT, depending on whether our focus is more on higher or lower temperatures, respectively. Finally, in Sec. VI, we summarize and discuss our results.