1. Searching for Majorana fermions in semiconducting nano-wires Pedram Roushan Peter O’Malley John Martinis Department of Physics, UC Santa Barbara Borzoyeh Shojaei Chris Palmstrøm Materials Department, UC Santa Barbara Roman Lutchyn Microsoft Station Q The 8th Capri Spring School on Transport in Nanostructures April 2012, Capri, Italy

2. Fu & Kane, PRL (2008)Sau et al., PRL (2010) And more… for a review see: Alicea, arXiv:1202.1293v1 Kitaev, Phys.-Usp. (2001) Theoretical proposals on Majorana fermions

3. Josephson Current Flux (  ) π 4π4π Majorana fermions in Josephson junctions Lutchyn et al., PRL (2010) 2π2π3π3π Topological Trivial

4. Josephson Current Flux (  ) π 4π4π Frequency Resonance Amplitude Majorana fermions in Josephson junctions Lutchyn et al., PRL (2010) 2π2π3π3π Topological Trivial

5. 2DEG Parameters Device parameterstuneable parameters α,  spin orbit coupling L, W geometry Bmagnetic field g magnetic moment Δ ind induced SC gapμchemical potential m* effective mass Ttemperature μeμe electron mobility nene carrier concentration The parameter space

6. 2DEG Parameters Device parameterstuneable parameters α,  spin orbit coupling L, W geometry Bmagnetic field g magnetic moment Δ ind induced SC gapμchemical potential m* effective mass Ttemperature μeμe electron mobility nene carrier concentration The parameter space Non-helical E Fermi Spin-orbit splitting

7. 2DEG Parameters Device parameterstuneable parameters α,  spin orbit coupling L, W geometry Bmagnetic field g magnetic moment Δ ind induced SC gapμchemical potential m* effective mass Ttemperature μeμe electron mobility nene carrier concentration The parameter space Spin-orbit splitting Non-helical E Fermi Non-helical E Fermi

8. S.I. (100) GaAs Substrate 500 nm GaAs 1000 nm GaSb 2000 nm AlSb 10 x 2.5 nm GaSb / 2.5 nm AlSb S.L. 100 nm AlSb 15 nm InAs QW 50 nm Al 0.5 Ga 0.5 Sb 5 nm GaSb Cap S.I. (100) GaAs Substrate 100 nm GaAs 10 x 2.5 nm GaSb / 2.5 nm AlSb S.L. 20 nm AlSb 15 nm InAs QW 5 nm GaSb Cap 10 nm AlAs 100 nm AlSb 2000 nm GaSb 50 nm AlSb S.I. (100) GaAs Substrate 500 nm GaAs 1000 nm GaSb 2000 nm AlSb 10 x 2.5 nm GaSb / 2.5 nm AlSb S.L. 100 nm AlSb 15 nm InAs QW 5 nm Al 0.5 Ga 0.5 Sb 5 nm GaSb Cap Molecular Beam Epitaxy grown quantum wells

9. T = 60 mK  sheet = 10 to 150  /□ μ e = 74,000 to 210,000cm 2 / V∙s n e = 5 x 10 11 to 3 x 10 12 to cm 2 l = 0.9 to 6  m Measuring 2DEG parameters: mobility and concentration  =8  =6  xx = V xx / I I in I out  xy =V xy / I

10. Measuring 2DEG parameters: Effective mass Theory: D. Shoenberg, Magnetic oscillations in metals. Cambridge university press (1984). Temperature (K) m*=0.039m e

11. Magneto-resistance feasurement: Weak anti-localization Asymmetric quantum well Spin-orbit coupling Rashba (  ) Dresselhaus (  ) Lack of inversion symmetry

12. Measuring 2DEG parameters: Spin-orbit coupling Theory: Iordanskii et al., JETP Lett. (1994), Knap et al. PRB (1996), Lyanda-Geller PRL (1998) Experiment: Miller et al., PRL (2003). Kallaher et al., PRB (2010). …   13±1 meV.Å  425±6 eV.Å 3

13. 2DEG Band structure parameters: E Fermi k F =0.018 Å -1

14. 2DEG Band structure parameters: E Fermi k F =0.018 Å -1

15. 2DEG Band structure parameters: E Fermi k F =0.018 Å -1

16. ParameterValue α,  spin orbit coupling 10 to 30 meV.Å, 400 to 450 meV.Å 3 gmagnetic moment 15 (from literature) m*effective mass 0.03 to 0.07 m e μeμe electron mobility 60,000 to 210,000 cm 2 / V∙s nene carrier concentration 5x10 11 to 3x10 12 / cm 2 Δ ind induced gap L, W,...geometry Bmagnetic field Conclusion and outlook Come to UC Santa Barbara and visit us