Spontaneous breaking of time-reversal symmetry in the pseudogap state of a high-Tc superconductor

A change in 'symmetry' is often observed when matter undergoes a phase transition-the symmetry is said to be spontaneously broken. The transition made by underdoped high-transition-temperature (high-Tc) superconductors is unusual, in that it is not a mean-field transition as seen in other superconductors. Rather, there is a region in the phase diagram above the superconducting transition temperature Tc (where phase coherence and superconductivity begin) but below a characteristic temperature T* where a 'pseudogap' appears in the spectrum of electronic excitations. It is therefore important to establish if T* is just a cross-over temperature arising from fluctuations in the order parameter that will establish superconductivity at Tc (refs 3, 4), or if it marks a phase transition where symmetry is spontaneously broken. Here we report that, for a material in the pseudogap state, left-circularly polarized photons give a different photocurrent from right-circularly polarized photons. This shows that time-reversal symmetry is spontaneously broken below T*, which therefore corresponds to a phase transition.     

多项式微分系统的不变直线的不同斜率的最大个数

本文证明了公式β（ｎ）＝σ（ｎ－１）＋１其中α（ｎ－１）是ｎ－１次多项式微分系统的不为直线的最多条数，βｎ）是ｎ次多项式微分系统的不变直线的不同斜率的最大个数。这里假设所讨论的多项式系统只有限条不变直线。     

The origin of multiple superconducting gaps in MgB2

Magnesium diboride, MgB2, has the highest transition temperature (T(c) = 39 K) of the known metallic superconductors. Whether the anomalously high T(c) can be described within the conventional BCS (Bardeen-Cooper-Schrieffer) framework has been debated. The key to understanding superconductivity lies with the 'superconducting energy gap' associated with the formation of the superconducting pairs. Recently, the existence of two kinds of superconducting gaps in MgB2 has been suggested by several experiments; this is in contrast to both conventional and high-T(c) superconductors. A clear demonstration of two gaps has not yet been made because the previous experiments lacked the ability to resolve the momentum of the superconducting electrons. Here we report direct experimental evidence for the two-band superconductivity in MgB2, by separately observing the superconducting gaps of the sigma and pi bands (as well as a surface band). The gaps have distinctly different sizes, which unambiguously establishes MgB2 as a two-gap superconductor.