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BCS Theory on Lasing ZnO Nanowires A.J. van Lange 1 , M.A.M. Versteegh 1 , J.I. Dijkhuis 1 , H.T.C. Stoof 2 1  Debye Institute for Nanomaterials Science, Utrecht 2  Institute for Theoretical Physics, Utrecht ,[object Object],[object Object],[object Object],Luminescence Spectra Gain calculations CCD images of a single lasing nanowire with increasing distance from the microscope objective. ZnO nanowires are among the smallest known lasers. In an effort to explain their UV laser action, we have developed a many body theory of the electron hole (e-h) plasma in ZnO. In experiment ZnO nanowires are excited by intense 800-nm 120-fs pulses to create an e-h plasma with high carrier densities. For low carrier densities laser action in ZnO is described by exciton polaritons.  In our experiment lasing occurrs above the Mott density, where excitons no longer exist. We study the possibility of a new bound state at high densities: the Cooper pair of an electron and a hole.  Our goal is to extract the optical response from the theory and to compare those results to our experiments on ZnO nanowires. Although the theory does not incorporate any finite size effects, nanowires are preferable over bulk in experiment, because their crystalline structure shows very little defects. Introduction BCS theory in an e-h plasma ,[object Object],[object Object],[object Object],[object Object],Angle Averaged Gap Equation This equation can be discretized to  , with   Assumptions Gallery ,[object Object],[object Object],[object Object],[object Object],[object Object],Future work Screened Coulomb Interaction   Figure 1:  Angle averaged  screened potential at n e = 10 25  m -3  .  Value of V0  ≈ 10 -46  Jm -3 . The gap equation is integrated over the angles to yield where  is the angle averaged Coulomb interaction . As we lower the temperature, the eigenvalue of U becomes one at the critical temperature. In statistical field theory screening is described by the Bethe-Salpeter equation: Because we are looking at  with long wavelength behaviour, we set  ω  =  0. To find the angle averaged potential  , we write  and perform the integrals over the angles. In the evaluation of the bubble diagram Fermi-Dirac distributions are approximated by stepfunctions.  Here,  is the bare Coulomb interaction and the amplitude of the bubble diagram is called  .  The effective screened interaction is: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Pump-probe measurement Acknowledgements We thank P. Jurrius and C.R. de Kok for technical support and D.H. van Dorp and D.A.M. Vanmaekelbergh for the nanowire samples.

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