Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: Two-particle response in the pseudogap regime of electron-doped high-Tc superconductors

Jie Lin; A. J. Millis

doi:10.1103/PhysRevB.83.125108

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Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: Two-particle response in the pseudogap regime of electron-doped high-Tc superconductors

Jie Lin, A. J. Millis

DOI 10.1103/PhysRevB.83.125108 · Physical Review B

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Abstract

We calculate the frequency-dependent longitudinal (σxx) and Hall (σxy) conductivities for two-dimensional metals with thermally disordered antiferromagnetism using a generalization of a theoretical model, involving a one-loop quasistatic fluctuation approximation, which was previously used to calculate the electron self-energy. The conductivities are calculated from the Kubo formula, with current vertex function treated in a conserving approximation satisfying the Ward identity. In order to obtain a finite dc limit, we introduce phenomenologically impurity scattering, characterized by a relaxation time τ. σxx(Ω) satisfies the f-sum rule. For the infinitely peaked spin-correlation function, χ(q)∝δ(q−Q), we recover the expressions for the conductivities in the mean-field theory of the ordered state. When the spin-correlation length ξ is large but finite, both σxx and σxy show behaviors characteristic of the state with long-range order. The calculation runs into difficulty for Ω≲1/τ. The difficulties are traced to an inaccurate treatment of the very-low-energy density of states within the one-loop quasistatic approximation for the self-energy. The results for σxx(Ω) and σxy(Ω) are qualitatively consistent with data on electron-doped cuprates when Ω>1/τ.