O ne of the mysteries of modern con- densed-matter physics is the nature of the pseudogap state of the super- conducting cuprates. Kaminski et al. 1 claim to have observed signatures of time-rever- sal symmetry breaking in the pseudogap regime in underdoped Bi 2 Sr 2 CaCu 2 O 8+Ȏ (Bi2212). Here we argue that the observed circular dichroism is due to the 5ǂ1 superstructure replica of the electronic bands and therefore cannot be considered as evidence for spontaneous time-reversal symmetry breaking in cuprates. The main conclusions of Kaminski et al. are based on the temperature-dependent circular dichroism observed in a ‘mirror’ plane of the underdoped Bi2212 thin films. However, Bi2212 samples possess a 5ǂ1 superstructure that breaks reflection sym- metry in these planes, as demonstrated by electron diffraction and angle-resolved photo- emission (ARPES) experiments (Fig. 1a,b). The 5ǂ1 superstructure is suppressed by doping pristine Bi2212 with lead. We per- formed ARPES experiments similar to those reported by Kaminski et al. 1 on both systems. At room temperature (Fig. 1c), the influence of the superstructure is already obvious: for pristine Bi2212, the dichroic signal is non- zero in the Ǵ–(Ț,0) plane. This result can readily be explained. The superstructure results in diffraction replicas of the electronic structure seen in the momentum-distribution map (Fig. 1b) as green and blue dashed curves. Because of the pronounced inequivalence of the matrix elements in the first and second Brillouin zones, the spectral weight of these replicas is always different near the (Ț,0) point. Recording the dichroism as a function of momentum k along the white double- headed arrow in Fig. 1b, one effectively measures the superposition of the three signals originating from the main band and two non-equivalent diffraction replicas. A systematic investigation of the 5ǂ1 super- structure-free Pb-Bi2212 samples that have a large pseudogap (Fig. 1d) reveals that the dichroism in the mirror plane remains zero within the experimental error bars, indepen- dent of temperature (Fig. 1c) and doping 2 . The finite superstructure-induced room- temperature dichroism in the mirror plane must also be present in the thin films, which do exhibit a superstructure signal. The energy-distribution curves (EDCs),which are brief communications arising NATURE | 2 SEPTEMBER 2004 | www.nature.com/nature 1 identical to an accuracy of 0.06% (see Fig. 2e of ref. 1), therefore indicate that they cannot be taken at the (Ț,0) point and that the zero momentum in Fig. 3g of ref. 1 probably does not correspond to the mirror plane. The large uncertainty in locating the actual position in the k-space (not specified by Kaminski et al.) is also evident from data shown in their Fig. 3d,h. Presented EDCs for the overdoped sample are claimed to be k f EDCs. However, it is known that, at finite temperature at k f , the spectral function has a peak at the chemical potential and so multiplication by the Fermi function would result in the leading-edge midpoint being located at negative binding energies, which is not the case. Provided that the zero momentum in Fig. 3g of ref. 1 does not correspond to the (Ț,0) point, the temperature dependence of the dichroism is not surprising. Away from the mirror plane, the dichroism correspond- ing to the main band is temperature depen- dent, as can be seen by comparing the slopes of the dichroism in their Fig. 3c (note that the lines shown in Fig. 3c,g of ref. 1 are not always linear fits to the 11 data points, as is evident from the data collected at 150 K) and in Fig. 3d of ref. 2. The absence of full-range curves 2 in Fig. 3c, g of ref. 1 does not allow the exact location in momentum space from which the presented data are taken to be determined; neither can we determine whether this is Superconductors Time-reversal symmetry breaking? Arising from: Kaminski, A. et al. Nature 416, 610–613 (2002) φ (π,0) a c b d Bi2212 Pb-Bi2212 6 4 2 0 –2 Dichroism (%) 40 30 20 10 0 Relative LEM (meV) –4 –6 –0.10 0.00 Momentum (Å –1 ) 0 20 40 60 80 Fermi surface angle (degrees) 0.10 Not mirror planes Mirror planes Figure 1 Features of superstructure in superconducting cuprates. a, b, Electron diffraction (a) and angle-resolved photoemission (b), showing angular distributions of the electrons in pristine (left) and Pb-doped (right) Bi2212. White dotted lines, crystallographic planes; green and blue dashed lines, diffraction replicas; white dashed line, first Brillouin zone. c, Dichroism near (Ț, 0) in Bi2212 (red triangles) and Pb-Bi2212 (blue diamonds; filled, 300 K; open, 100 K). d, Anisotropic pseudogap in Pb-Bi2212 measured at 120 K as binding energy of the leading-edge midpoints (LEM) for all spectra within the quadrant of the Brillouin zone as a function of Fermi surface angle Ƞ (white arrow in b, right). ©2004 Nature Publishing Group