手征电荷序的极性克尔效应
Polar Kerr effect from chiral-nematic charge order
摘要：
我们分析了在一个巡游电子系统中的极性克尔效应在一个正方形晶格中的复合电荷的存在下提出的赝隙态在欠掺杂铜氧化物。这种复合电荷序保持了离散的平移对称性，并且在它打破时间反演对称性、$x$和$y$方向上的镜像对称性以及$C_4$晶格旋转对称性的意义上是“手征的”。在$C_4$对称体系中，克尔角$θ_K$与反常霍尔电导率$σ_{xy}-σ_{yx}$的反对称分量成正比.我们证明了当$C_4$对称性被破缺时，这个结果成立。我们表明，为了使$σ_{xy}$和$σ_{yx}$是非零的$x$和$y$方向的镜像对称性必须被打破，和$σ_{xy}-σ_{yx}$是非零的时间反演对称性必须被打破。手征电荷阶满足所有这些条件，使得在极性克尔效应实验中的非零信号是对称允许的。我们进一步表明，得到一个非零的$θ_K$在一个带的自旋波动的情况下，在没有障碍，一个必须扩展的自旋介导的相互作用动量远离$(π,π)$，并包括粒子空穴不对称性。或者，在存在无序的情况下，可以从杂质散射得到非零的$θ_K$：由于偏斜散射（具有非高斯无序）或由于高斯无序情况下的粒子-空穴不对称。在我们的例子中的杂质分析是类似的，在早期的工作中的克尔效应在$p_x+ip_y$超导体，但在我们的例子中，$θ_K$的幅度是增强的“热”区的费米面的平坦化，主要有助于电荷秩序。
英文摘要：
We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves discrete translational symmetries, and is "chiral-nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in $x$ and $y$ directions, and $C_4$ lattice rotation symmetry. The Kerr angle $θ_K$ in $C_4$-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity $σ_{xy}-σ_{yx}$. We show that this result holds when $C_4$ symmetry is broken. We show that in order for $σ_{xy}$ and $σ_{yx}$ to be non-zero the mirror symmetries in $x$ and $y$ directions have to be broken, and that for $σ_{xy}-σ_{yx}$ to be non-zero time-reversal symmetry has to be broken. The chiral-nematic charge order satisfies all these conditions, such that a non-zero signal in a polar Kerr effect experiment is symmetry allowed. We further show that to get a non-zero $θ_K$ in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from $(π,π)$ and has to include particle-hole asymmetry. Alternatively, in the presence of disorder one can get a non-zero $θ_K$ from impurity scattering: either due to skew scattering (with non-Gaussian disorder) or due to particle-hole asymmetry in case of Gaussian disorder. The impurity analysis in our case is similar to that in earlier works on Kerr effect in $p_x+ip_y$ superconductor, however in our case the magnitude of $θ_K$ is enhanced by the flattening of the Fermi surface in the "hot" regions which mostly contribute to charge order.
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