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

Abstract

We calculate the longitudinal (${\sigma }_{xx}$) and Hall (${\sigma }_{xy}$) optical conductivities for two-dimensional metals with thermally disordered antiferromagnetism using a generalization of an approximation introduced by Lee, Rice and Anderson for the 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, with relaxation time $\tau$. ${\sigma }_{xx}(\Omega )$ satisfies the $f$-sum rule. For the infinitely peaked spin correlation function, $\chi (\mathbf{q})\propto \delta (\mathbf{q}-\mathbf{Q})$, we recover the expressions for the conductivities in the mean-field theory of the ordered state. When the spin correlation length $\xi$ is large but finite, both ${\sigma }_{xx}$ and ${\sigma }_{xy}$ show behaviors characteristic of the state with long-range order. The calculation runs into difficulty for $\Omega \lesssim 1/\tau$. The difficulties are traced to an inaccurate treatment of the very low energy density of states within the Lee-Rice-Anderson approximation. The results for ${\sigma }_{xx}(\Omega )$ and ${\sigma }_{xy}(\Omega )$ are qualitatively consistent with data on electron-doped cuprates when $\Omega >1/\tau$.

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Cited by in corpus (7)

• Quantum critical response at the onset of spin density wave order in two-dimensional metals
• Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections
• Intermediate Coupling Model of the Cuprates
• Spin and charge dynamics of a quasi-one-dimensional antiferromagnetic metal
• Disorder effects on hot spots in electron-doped cuprates
• A critical nematic phase with pseudogap-like behavior in twisted bilayers
• Ward identities for charge and heat currents of particle-particle and particle-hole pairs