Optical Birefringence and Dichroism of Cuprate Superconductors in the THz Regime

The presence of optical polarization anisotropies, such as Faraday or Kerr effects, linear birefringence, and magnetoelectric birefringence are evidence for broken symmetry states of matter. The recent discovery of a Kerr effect using near-IR light in the pseudogap phase of the cuprates can be regarded as a strong evidence for a spontaneous symmetry breaking and the existence of an anomalous long-range ordered state. In this work we present a high precision study of the polarimetry properties of the cuprates in the THz regime. While no Faraday effect was found in this frequency range to the limits of our experimental uncertainty (1.3 milli-radian or 0.07°), a small but significant polarization rotation was detected that derives from an anomalous linear dichroism. In ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ the effect has a temperature onset that mirrors the pseudogap temperature $T^{*}$ and is enhanced in magnitude in underdoped samples. In $x=1/8$ ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$, the effect onsets above room temperature, but shows a dramatic enhancement near a temperature scale known to be associated with spin- and charge-ordered states. These features are consistent with a loss of both $C_4$ rotation and mirror symmetry in the electronic structure of the ${\mathrm{CuO}}_2$ planes in the pseudogap state.

Figure 1

The polarization rotating angle in transmitted THz beam through underdoped YBCO thin film ($T_c=52\mathrm{K}$) as a function of temperature and frequency. (a) The real part which represents the polar rotating angle. (b) The imaginary part which represents the ellipticity. The inset diagram demonstrates each quantity in a tilted oval propagating wave.

Figure 2

The rotation angle as a function of the film’s orientation $\varphi$. The panel in the top left demonstrate the definition of $\varphi$ as the angle between the incident polarization and the film’s lattice constants. (a) Polar presentation of rotating angle (radial axis) vs $\varphi$ (angular axis) in underdoped YBCO ($T_c=52\mathrm{K}$) at $T=10\mathrm{K}$. The direction of the rotation changes periodically from positive (blue background) to negative (red background). (b) Temperature dependence of the effect in two orthogonal directions from the same film. (c) Real part of the rotating angle vs temperature of three different doping.

Figure 3

Real and imaginary parts of the rotation angle vs temperature of the LBCO film. Inset: Temperature dependence of the effect in two orthogonal directions from the same LBCO film.

Figure 4

The quantities plotted are as explained in Fig. 2. (a) and (b) The dichroism pattern upon flipping the LBCO film at $T=300\mathrm{K}$. The upper cartoon demonstrates forward and reverse propagation through the film and the substrate. The lower diagram represents a schematic of flipping the sample. The black arrows represent the optical axes. The dotted gray arrow shows the flipping axis. The red ones indicate the direction of the polarization rotation.