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Fabio Cavaliere Anomalous Friedel oscillations i n a quasi-helical quantum dot Filippo Maria Gambetta, Giacomo Dolcetto, Matteo Biggio – Uni Genova (IT) Dario Ferraro – Uni Geneva (CH) Niccolò Traverso Ziani – Uni Würzburg (DE) Simone Barbarino – SNS Pisa (IT) Roberta Citro, Francesco Romeo – Uni Salerno (IT)
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  • Fabio Cavaliere

    Anomalous Friedel oscillationsin a quasi-helical quantum dot

    Filippo Maria Gambetta, Giacomo Dolcetto, Matteo Biggio Uni Genova (IT)Dario Ferraro Uni Geneva (CH)Niccol Traverso Ziani Uni Wrzburg (DE)Simone Barbarino SNS Pisa (IT)Roberta Citro, Francesco Romeo Uni Salerno (IT)

  • Outline

    Introduction

  • Outline

    Introduction

    Helical 1D quantum dotsSpin textures and correlations

  • Outline

    Introduction

    Helical 1D quantum dotsSpin textures and correlations

    Quasi-helical 1D quantum dots

    Anomalous Friedel oscillations

  • standard 1D quantum wire

  • standard 1D quantum wire

    Spin-momentum locking!

    helical 1D system

  • Two-dimensional topological insulators

    [B.A.Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006); B.A. Bernevig, SC Zhang PRL 96 106802 (2006); L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)]

    CdTe

    CdTe

    HgTe

  • Two-dimensional topological insulators

    [B.A.Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006); B.A. Bernevig, SC Zhang PRL 96 106802 (2006); L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)]

    CdTe

    CdTe

    HgTe

  • Two-dimensional topological insulators

    [B.A.Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006); B.A. Bernevig, SC Zhang PRL 96 106802 (2006); L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)]

    Insulating bulk states, gapless counterpropagating edge statesProtected by TRS, with spin-momentum locking

    CdTe

    CdTe

    HgTe

  • Protected by TRS

  • Protected by TRS

    Magnetic barriers break TRS and allow back-scattering

  • Protected by TRS

    Magnetic barriers break TRS and allow back-scattering

  • Protected by TRS

    Magnetic barriers break TRS and allow back-scattering

  • Helical quantum dot

  • C. Timm, Phys. Rev. B 86, 155456 (2012), G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Phys. Rev. B 87, 235423 (2013)

    Towards a helical dot

  • C. Timm, Phys. Rev. B 86, 155456 (2012), G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Phys. Rev. B 87, 235423 (2013)

    Towards a helical dot

  • C. Timm, Phys. Rev. B 86, 155456 (2012), G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Phys. Rev. B 87, 235423 (2013)

    dependent constraints between Left ( spin down) and Right (spin up) fields

    Towards a helical dot

  • dependent boundaries over a double length 2L

  • dependent boundaries over a double length 2L

  • Spin density

  • Spin density

    Quantum averages

  • Spin density

    Quantum averages

  • spin-density oscillations in the x-y plane with wave number

    G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Phys. Rev. B 87, 235423 (2013)

  • -controlledspin textures

    G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Physica Status Solidi RRL 7, 1059 (2013)F. M. Gambetta, N. T. Ziani, F. C., and M. Sassetti, Europhys. Lett. 107, 47010 (2014)

  • -controlledspin textures

    Interactions enhancethe spin oscillations

    G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Physica Status Solidi RRL 7, 1059 (2013)F. M. Gambetta, N. T. Ziani, F. C., and M. Sassetti, Europhys. Lett. 107, 47010 (2014)

  • -controlledspin textures

    Interactions enhancethe spin oscillations

    Probability of finding given spins at distance x

    Enhanced spin correlations!

    G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Physica Status Solidi RRL 7, 1059 (2013)F. M. Gambetta, N. T. Ziani, F. C., and M. Sassetti, Europhys. Lett. 107, 47010 (2014)

  • Quasi-helical quantum dot

  • InSb, In As, Pt@Si

  • A non-helical LL withtwo spin channels

    InSb, In As, Pt@Si

  • InSb, In As, Pt@Si

  • Within the gap:a quasi-helical LL!

    InSb, In As, Pt@Si

  • Quasi-helical regime:

    F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    A Luttinger theory in the gap

  • Quasi-helical regime:

    F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    A Luttinger theory in the gap

  • Quasi-helical regime:

    F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    A Luttinger theory in the gap

  • Quasi-helical regime:

    F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    A Luttinger theory in the gap

  • The quasi-helical LL statesexist near the Fermi surface

    Physics in the gap, near the Fermi surface

  • The quasi-helical LL statesexist near the Fermi surface

    Physics in the gap, near the Fermi surface

  • The quasi-helical LL statesexist near the Fermi surface

    Physics in the gap, near the Fermi surface

  • The quasi-helical LL statesexist near the Fermi surface

    Physics in the gap, near the Fermi surface

    Linear transport!

  • Anomalous Friedel oscillations

    N=50, expecting 50 peaks. Only 25 are found!

    F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)[See: J. Klinovaja and D. Loss, Phys. Rev. B 86, 085408 (2012)]

  • Anomalous Friedel oscillations

    Towards the conventional Friedel oscillations

    F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

  • Conclusions

    G. Dolcetto, F. C., D. Ferraro, and M. Sassetti, Phys. Rev. B 87, 085425 (2013)G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Phys. Rev. B 87, 235423 (2013)

    G. Dolcetto, N. T. Ziani, M. Biggio, F. C., and M. Sassetti, Physica Status Solidi RRL 7, 1059 (2013)G. Dolcetto, F. C., and M. Sassetti, Phys. Rev. B 89, 125419 (2014)

    F. M. Gambetta, N. T. Ziani, F. C., and M. Sassetti, Europhys. Lett. 107, 47010 (2014)F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    Helical 1D quantum dotsSpin textures can be controlled by tuningmagnetic impurities either in DC or in AC.True spin correlations develop for strong intractions.

    Quasi-helical 1D quantum dots

    Evanescent states develop at the Fermi surface,inducing anomalous Friedel oscillations (and peculiarspin textures) in the TDOS.

  • 18

  • The quasi-helical LL statesexist near the Fermi surface

    Physics near the Fermi surface

  • Non-helical physics

    Physics near the Fermi surface

  • The quasi-helical LL statesexist near the Fermi surface

    Physics near the Fermi surface

  • The quasi-helical LL statesexist near the Fermi surface

    Physics near the Fermi surface

  • The quasi-helical LL statesexist near the Fermi surface

    Physics near the Fermi surface

    Collective excitation wavefunction

  • The quasi-helical LL statesexist near the Fermi surface

    Physics near the Fermi surface

    Collective excitation wavefunction

    CE magnetization

  • The quasi-helical LL statesexist near the Fermi surface

    Physics near the Fermi surface

    Collective excitation wavefunction

    CE magnetization

  • F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    Peculiar spin textures

  • F. M. Gambetta, N. T. Ziani, S. Barbarino, F.C., and M. Sassetti, Submitted (2015)

    Peculiar spin textures

  • 21

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