Robustness of Majorana induced Fractional Josephson Effect

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Presentation transcript:

Robustness of Majorana induced Fractional Josephson Effect Kam Tuen Law HKUST July 9, 2011 QC11

Outline Majorana Fermions Fractional Josephson Effect -Properties -In condensed matter systems -Probing Majorana fermions Fractional Josephson Effect Single Channel Case Multi-Channel Case Chiral Topological Superconductors

Properties of Majorana Fermions 𝛾= 𝛾 + Non-locality 𝜓= 𝛾 1 + 𝑖𝛾 2 3) Satisfy non-Abelian Statistics Abelian Statistics Non-Abelian Statistics 1 1 D. Ivanov PRL (2001)

Properties of Majorana Fermions 𝑆𝑟 2 𝑅𝑢 𝑂 4 Read,Green PRB 2000 𝛾 2 𝛾 1

Topological Insulator and Majorana Fermions How to create Majarana Fermions on topological insulator surface? By proximity effect induced by a superconductor Vortex hosts Majorana Fermion Fu, Kane PRL 2008

Spin-Orbit Coupled Semiconductors Alicea PRB 2010

Spin-Orbit Coupled Semiconductors

Majorana Fermion Induced Resonant Andreev Reflection

Majorana Fermions at SC/TI interface Charge Transport Through Neutral Mode Fu, Kane PRL 2009 Akhmerov , etc. PRL 2009

Resonant Andreev Reflection h NM Lead Sc Even number of flux Quantum Odd number of flux Quantum KTL, Lee, Ng PRL 2009

Resonant Andreev Reflection Cross Andreev reflection Superconductor electron hole Even number of vortices Local Andreev reflection Cross Andreev reflection

Fractional Josephson Effect 1 𝜙=0 𝜙 E E 𝜙 𝜙 Kitaev 2000 Kwon etc. 2004

Fractional Josephson Effect 2 𝛾 1 𝛾 2 E |1> Why 𝜀 0 changes sign? Can the crossing survives in the multi-channel case? |0> 𝜙 Robust because <0 𝑉 1> =0 for any V which preserve fermion parity

Fractional Josephson Effect 3 Potter, Lee PRL 2010 KTL,LEE Arxiv:1103.5013

Fractional Josephson Effect 4 Change 𝜙 by 2𝜋

Fractional Josephson Effect 5

Fractional Josephson Effect 6 To be published KLT, LEE

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