Particle-hole symmetry and transport properties of the flux state in underdoped cuprates

Abstract

Transport properties, i.e., conductivities σµν, Hall constant RH , and thermopower S are studied for the flux state with the gauge flux φ per plaquett, which may model the underdoped cuprates, with the emphasis on the particle-hole and parity/chiral symmetries. This model is reduced to the Dirac fermions in (2+1)D with a mass gap introduced by the antiferromagnetic (AF) long range order and/or the stripe formation. Without the mass gap, the Hall constant RH and the thermopower S obey the two-parameter scaling laws,, with a being the lattice constant, x the hole concentration, τ the transport lifetime. The RH and S show the strong temperature dependence due to the recovery of the particle-hole symmetry at high temperature. The x-dependences of σxx(∝ √ x) and σxy (independent of x) are in a sharp contradiction with the experiments. Therefore there is no signature of the particle-hole symmetry or the massless Dirac fermions in the underdoped cuprates even above the Neel temperature TN . With the mass gap introduced by the AF order, there occurs the parity anomaly for each of the Dirac fermions. However the contributions from different valleys and spins cancel with each other to result in no spontaneous Hall effect even if the time-reversal symmetry is broken with φ = π. The effects of the stripes are also studied. The diagonal and vertical (horizontal) stripes have quite different influence on the transport properties. The suppression of RH occurs at low temperature only when (i) both the AF order and the vertical (horizontal) stripe coexist, and (ii) the average over the in-plane direction is taken. Discussions on the recent experiments are given from the viewpoint of these theoretical results.

The spin chirality induced anomalous Hall effect in pyrochlore ferromagnets

“…Such a gauge flux acts as a fictitious magnetic field and affects the charge dynamics in the same way as a real magnetic field does. Recently, the anomalous Hall effect or transverse conductivity has been discussed in terms of this phase (termed the Berry phase) in several ferromagnetic transition-metal oxides, for example perovskite-type manganites [14][15][16], molybdates with pyrochlore structure [18][19][20][21][22], and rutile-type CrO 2 [23]. The weak coupling regime has also been examined very recently in connection with the canonical spin glass system [24].…”