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Rare gas bubble in aluminum is an interesting embedded nanosystem, where the bubble radii have been reported to vary from fraction of a nm to less than 10 nm. Depending on implantation conditions. The repulsive pseudopotential of the rare gas atoms in A1 makes bubble formation energetically favourable. Because of their small size and proximity to the A1 surface, these bubbles exhibit quantum confinement and interference. In our laboratory, we have studied consequences of photoelectron emission from the rare gas bubbles using x-ray photoelectron spectroscopy. As a consequence of the nanometer size, the photo-hole formed by Xe 3d or Ar 2p photoemission is screened by the A1 conduction electrons, which substantially lowers their binding energy compared to the gas phase [1,2]. As the bubble size increases, the A1 conduction electron screening decreases and the binding energy increases. Ne 1s spectra unexpectedly exhibits two beaks, that we ascribe to the existence of a bimodal depth and size distribution of Ne bubbles [3]. Another interesting observation is existence of aluminum bulk and surface plasmon collective excitations in the core-level spectra of the rare gas bubbles, whose intensities are even higher than those of A1 metal [4]. Both intrinsic and extrinsic bulk plasmons are detected, but they exhibit diametrically opposite intensity variation due to change in the size and implantation depth. The intrinsic plasmon in 1ÏŽp is observed because of their nano-meter size, and its intensity decreases with increasing size as the A1 conduction electron screening becomes weaker. On the other hand, the extrinsic plasmon contribution increases with implantation depth. Furthermore, evidence of bubble surface plasmon is obtained.References[1] C.Biswas, A.K. Shukla, S. Banik, S.R. Barman and A.Chakrabarti, Phys. Rev. Lett. 92, 115506 (2004)[2] R.S. Dhaka, C.Biswas, A.K. Shukla, S.R. Barman and A.Chakrabarti, Phys. Rev. B77, 104119 (2008).[3] R.S. Dhaka and S.R. Barman, Phys. Rev. B79, 125409 (2009)[4] R.S. Dhaka and S.R. Barman, Phys. Rev. Lett. 104, 036803 (2010)

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In this talk I will review some recent articles in Kitaev model. Kitaev model was introduced by Alexei Kitaev in 2008. It is a quantum spin model with anisotropic couplings, which can be solved exactly in two dimensions.

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