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Spontaneous Time Reversal Breaking of Majorana Fermions in Dipolar Systems

Spontaneous Time Reversal Breaking of Majorana Fermions in Dipolar Systems. Yi Li and Congjun Wu University of California, San Diego. APS March Meeting Dallas, TX; Mar. 22, 2011. Ultracold Dipolar Fermion Molecules. Head to Tail. Shoulder by Shoulder.

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Spontaneous Time Reversal Breaking of Majorana Fermions in Dipolar Systems

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  1. Spontaneous Time Reversal Breaking of Majorana Fermions in Dipolar Systems Yi Li and Congjun Wu University of California, San Diego APS March Meeting Dallas, TX; Mar. 22, 2011

  2. Ultracold Dipolar Fermion Molecules Head to Tail Shoulder by Shoulder Anisotropy channel dominant pairing [Baranov et. al. 2002] Anisotropy Repulsive Attractive • Experiments40K87Rb polar molecules [Ni et. al, 2008,etc …] • Unconventional Single component p-wave Cooper pairing

  3. Majorana Fermions in the Tube Lattices of Dipolar Fermion Molecules z-direction: 1D tube of pz pairing fermions Andreev bound states localized at ends z0 with energy zero. Kitaev, 2000; Tewari, et al, 2007; Alicea, et al, 2010; etc ... z y x Dispersionless in kx and ky Each x-y plane: Andreev Bound States → 1D or 2D Majorana fermions lattices.

  4. z Josephson Coupling between Parallel Dipolar Molecule Tubes L>>ξ L>>ξ L>>ξ leading order [Kitaev, 2000; Yakovenko et al, 2004; Fu and Kane, 2009; Xu and Fu, 2010]

  5. CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH 1D Su-Schrieffer-Heeger Model Electron-phonon interaction → Dimerization (modulation of the lattice distortion)

  6. 1D Chain of Majorana States Majorana - Superfluid phase coupling → (modulation of the phases)

  7. 2D Majorana Honeycomb Lattice = Assuming constant superfluid phase difference |Δθ|, the system prefers a vortex free state. [Lieb, 1994; Kitaev, 2006]

  8. 2D Majorana Square Lattice θ=π/2 θ=0 θ=π θ=3π/2 Fermion vortex state (vorticity =1 ) Majorana π-flux state

  9. Conclusion • pz-wave Cooper pairing in dipolar Fermion molecule systemsMajorana fermions at z-direction ends of the dipolar tubelattices • Interaction between Majorana fermions and fermion superfluid phasesSpontaneous TR breaking phases on Majoranalattices • Theoretical Challenges Further numerical simulation of the TR breaking Phases of Majoranalattices • Experimental Challenges Stability and manipulation of dipolar tube lattices Thank you!

  10. CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH CH 1D Chain of Majorana States 1D Majorana Chain with current majorana - superfluid phase coupling → (modulation of the phases) c.f. 1D Su Schrieffer Heeger Model electron-phonon interaction → dimerization (modulation of the lattice distortion)

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