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SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE George I. Japaridze

SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE George I. Japaridze. Ilia state University and Andronikashvili Institute of Physics. SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE. What is a helical liquid (HL)? Unconventional State of matter with spin-momentum locking.

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SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE George I. Japaridze

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  1. SYNTHETIC HELICAL LIQUID IN A QUANTUM WIREGeorge I. Japaridze Ilia state University and Andronikashvili Institute of Physics

  2. SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE • What is a helical liquid(HL)? • Unconventional State of matter with spin-momentum locking

  3. SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE • What is a helical liquid(HL)? • Unconventional State of matter with spin-momentum locking

  4. Insulators with Strong Spin-OrbitInteraction:Spin-Hall Effect: Edge states • L. Fu, C. L. Kane and E. J. MelePRL 98, 106803(2007). • J. E. Moore and L. Balents, PRB 75, 121306(R)(2007). • S.-C. Zhang, Nature Physics 1, 6 (2008).

  5. Exotic quantum states Majorana Fermions in 1d • Alicea, PRB 81, 125318 (2010) • Oreg, Refael, and von Oppen, PRL 105, 177002 (2010) • Lutchyn, Sau, and Das Sarma, PRL 105, 077001 (2010) • Kitaev, Phys.-­‐Usp. 44, 313 (2001) • Alicea, Oreg, Refael, v.Oppen, Fisher, Nature Phys.7,412 (2011) • Gangadharaiah, Braunecker, Simon, DL, PRL 107, 036801 (2011)

  6. Part I:Magnetic field induced quasi-helical liquid state in a disordered 1D electron system with strong spin-orbit interaction • Anders Ström, Bernd Braunecker and G.J. • PRB 87, 075151 (2013).

  7. Band structures Spins look anti-parallell for opposite velocities. Helical? Corrupted by the magnetic field HS! Let’s calculate the spin overlaps!

  8. Band structures Spin Overlaps Limits:

  9. Band structures Spin Overlaps Detail for aa overlap. 0.3 meV (ca 1 T) yields overlap squared of about 0.01.

  10. Disorder: Anderson Localization in 1D !!(absent in the Helical Liquid State!!) Overlaps: Limits:

  11. Disorder RG Scaling equations! For full Luttinger liquid with spin: For spinless or helical Luttinger liquid: Above gap Below gap

  12. Disorder Localisation length Can have loc. from ab disorder, if gap is smaller than ca 6ehjhjhjee5 eV, almost 1 K. Below the gap, we only need to consider disordered aa backscattering.

  13. Part II: SYNTHETIC HELICAL LIQUID IN A QUANTUM WIRE Mariana Malard, Henrik Johannesson and GJ PRB 89, 201403(R)  (2014).

  14. Band picture _ _ insulating phase + + branch 2

  15. Band picture conductinghelicalelectronliquid _ _ + + branch 2

  16. Our proposal modulation of the spin-orbit Rashba interaction HL in a quantum wire using electrical fields only and standard nanoscale semiconductor technology! top nanogates + spin-orbit Dresselhaus + e-e interactions Semiconductor heterostructure quantum wire

  17. The MODEL hopping and chemical potential + modulated Rashba interaction + + e-e interaction uniform Rashba and Dresselhaus interactions

  18. Effective theory sine-Gordon potential relevant for K < ½ gap helical Dirac hamiltonian branch-mixing potential

  19. For future success in building of German-Georgian Science Bridge Thank you for your attention!

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