Robustness of majorana induced fractional josephson effect
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Robustness of Majorana induced Fractional Josephson Effect. Kam Tuen Law HKUST July 9 , 2011 QC11. Outline. Majorana Fermions -Properties -In condensed matter systems -Probing Majorana fermions Fractional Josephson Effect Single Channel Case Multi-Channel Case

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Robustness of Majorana induced Fractional Josephson Effect

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Robustness of majorana induced fractional josephson effect

Robustness of Majorana induced Fractional Josephson Effect

KamTuen Law HKUST

July 9, 2011 QC11


Outline

Outline

Majorana Fermions

-Properties

-In condensed matter systems

-Probing Majorana fermions

Fractional Josephson Effect

  • Single Channel Case

  • Multi-Channel Case

  • Chiral Topological Superconductors


Properties of majorana fermions

Properties of Majorana Fermions

Non-locality

3) Satisfy non-Abelian Statistics

Abelian Statistics

Non-Abelian Statistics

1

0

0

1

D. Ivanov PRL (2001)


Properties of majorana fermions1

Properties of Majorana Fermions

Read,Green PRB 2000


Robustness of majorana induced fractional josephson effect

Topological Insulator and Majorana Fermions

How to create Majarana Fermions on topological insulator surface?

By proximity effect induced by a superconductor

Vortex hosts MajoranaFermion

Fu, Kane PRL 2008


Robustness of majorana induced fractional josephson effect

Spin-Orbit Coupled Semiconductors

Alicea PRB 2010


Robustness of majorana induced fractional josephson effect

Spin-Orbit Coupled Semiconductors


Robustness of majorana induced fractional josephson effect

  • Majorana Fermion Induced Resonant Andreev Reflection


Majorana fermions at sc ti interface

Majorana Fermions at SC/TI interface

TI

SC

M

Charge Transport Through Neutral Mode

Fu, Kane PRL 2009

Akhmerov , etc. PRL 2009


Resonant andreev reflection

Resonant Andreev Reflection

Andreev Reflection

e

2e

h

NM Lead

Sc

Even number of flux Quantum

Odd number of flux Quantum

KTL, Lee, Ng PRL 2009


Resonant andreev reflection1

Resonant Andreev Reflection

Cross Andreev

reflection

electron

hole

Superconductor

Even number of vortices

Local Andreev

reflection

Cross Andreev

reflection


Robustness of majorana induced fractional josephson effect

Fractional Josephson Effect 1

E

E

Kitaev 2000

Kwon etc. 2004


Robustness of majorana induced fractional josephson effect

Fractional Josephson Effect 2

E

Why changes sign?

Can the crossing survives

in the multi-channel case?

Robust because for any V

which preserve fermion parity


Fractional josephson effect 3

Fractional Josephson Effect 3

Potter, Lee PRL 2010

KTL,LEE Arxiv:1103.5013


Fractional josephson effect 4

Fractional Josephson Effect 4

Change by 2


Fractional josephson effect 5

Fractional Josephson Effect 5


Fractional josephson effect 6

Fractional Josephson Effect 6

To be published KLT, LEE


Conclusion

Conclusion

1.Fractional Josephson effect is robust in the multi-channel case

2.It survives also at finite temperatures

3.It can be used to probe the fermion parity of the Josephson current

4. FJE is immune to disorder in the chiral superconductor case

5.Current phase relation in the chiral superconductor case

shows distinctive features

Thank you


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