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 Anisotropy channel dominant pairing [Baranov et. al. 2002] Unconventional Single component p-wave Cooper pairing Anisotropy Repulsive Attractive Shoulder by Shoulder Head to Tail Experiments 40 K 87 Rb polar molecules [Ni et. al, 2008, etc …]

3. x y z Majorana Fermions in the Tube Lattices of Dipolar Fermion Molecules Each x-y plane: Andreev Bound States → 1D or 2D Majorana fermions lattices. Dispersionless in k x and k y Kitaev, 2000; Tewari, et al, 2007; Alicea, et al, 2010; etc... z-direction: 1D tube of p z pairing fermions Andreev bound states localized at ends z 0 with energy zero.

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

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

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 Fermion vortex state (vorticity =1 ) Majorana π-flux state θ=0 θ=π/2 θ=π θ=3π/2

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

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