1. Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator Nanoribbons Tudor D. Stanescu West Virginia University Collaborators: Piyapong Sitthison (WVU) Brasov September, 2014

2. Outline  Majorana fermions in solid state structures: status and challenges  Proximity-coupled topological insulator nanoribbons Modeling Low-energy states Phase diagram Proximity-induced gap

3. I Majorana fermions in solid state structures

4. Experimental status: NOT observed Majorana (1937): neutral spin-1/2 particles can be described by a real wave equation: Question: Are the spinors representing spin-1/2 particles necessarily complex ? Relevance: particle physics (neutrinos ?) 2000s: Majorana fermions can emerge as quasi- particle excitations in solid-state systems Majorana fermion – an electrically neutral particle which is its own antiparticle What is a Majorana fermion?

5. electron (-e) hole (+e) Cooper pair (-2e)  charge is not an observable  the elementary excitations are combinations of particles and holes (Bogoliubov quasiparticles) Superconductors – the natural hosts for Majoranas Particle-hole symmetry Zero energy state (Majorana fermion) Spinless fermions + particle-hole symmetry Majoranas at E=0

6. 1D spinless p-wave superconductor Kitaev, Physics-Uspekhi, 01 Sau et al., PRL’10 Alicea PRB’10 Semiconductor nanowire Superconductor Lutchyn et al., PRL’10 Oreg et al., PRL’10 Spin-orbit coupling Zeeman splitting Proximity-induced superconductivity Single-channel nanowire Practical route to realizing Majorana bound states

7. Probing Majorana bound states: tunneling spectroscopy Sau et al., PRB 82, 214509 (2010) TDS et al., PRB 84, 144522 (2011)

8. Experimental signatures of Majorana physics Mourik et al., Science 336, 1003 (2012)

9. TDS et al., PRB 84, 144522 (2011) Suppression of the gap-closing signature TDS et al., PRL 109, 266402 (2012)

10. Low-energy spectra in the presence of disorder TDS et al., PRB 84, 144522 (2011) Static disorder Interface inhomogeneity Takei et al., PRL 110, 186803 (2013)

11. What is responsible for the selective qp broadening?

12. Proximity effect in a NM-SM-SC hybrid structure TDS et al., PRB 90, 085302 (2014)

13. The soft gap in dI/dV and LDOS TDS et al., PRB 90, 085302 (2014)

14. II Proximity-Coupled Topological Insulator Nanoribbons

15. The topological insulator Majorana wire Cook & Franz, PRB 86, 155431 (2012)

16. Theoretical modeling Low-energy TI states Effective TI Hamiltonian SC Hamiltonian Local potential TI-SC coupling

17. Effective Green function BdG equation

18. Low-energy TI spectrum (3D) Sitthison & TDS, PRB 90, 035313 (2014)

19. Low-energy TI spectrum (2D) Sitthison & TDS, PRB 90, 035313 (2014)

20. Low-energy TI spectrum (1D) Sitthison & TDS, PRB 90, 035313 (2014) V=0;  =0V=0;  =0.5V=0.05;  =0.5

21. Low-energy states Sitthison & TDS, PRB 90, 035313 (2014) V=0;  =0.5 V=0.05;  =0.5

22. Proximity-induced quasiparticle gap Sitthison & TDS, PRB 90, 035313 (2014)  eV  eV

23. Phase diagram Sitthison & TDS, PRB 90, 035313 (2014)

24. Induced qp gap as function of  and  Sitthison & TDS, PRB 90, 035313 (2014)

25. Single interface structures Sitthison & TDS, PRB 90, 0000 (2014) V=0 V=0.03 eV V=0.06 eV

26. Tuning the chemical potential using gates Sitthison & TDS, PRB 90, 0000 (2014)

27. Conclusions  Details matter; the unambiguous demonstration of Majorana bound states  realistic modelling & controlled exp. conditions  TI-SC structures; the realization of robust topological SC phases (and Majorana bound states) over a wide range of  is not a straightforward task  Main problem: intrinsic or applied bias potentials may push some of the low-energy states away from the interface  Possible solution: symmetric TI-SC structures