robustness of majorana induced fractional josephson effect kam tuen law hkust july 9, 2011 qc11
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Robustness of Majorana induced Fractional Josephson Effect
Kam Tuen Law HKUSTJuly 9, 2011 QC11
a)
b)
ππΏ ππ
ππΏ0 ππ 0
β0πππ
β0πππ
β0
β0
Single-band superconducting wires
Multi- band superconducting wires
πΎπΏπ
βπΎπΏπ
πΎπ π
βπΎπ π
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
1) Non-locality 3) Satisfy non-Abelian Statistics
Abelian Statistics Non-Abelian Statistics
1|||| ii B 1|||| ii B
1 0
0 1
D. Ivanov PRL (2001)
Properties of Majorana Fermions
ππ 2π π’π4
Read,Green PRB 2000
πΎ1
πΎ 2
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
..2211 chttH DDT
)]0()0()[(1 aitHT
Majorana Fermions at SC/TI interface
Fu, Kane PRL 2009Akhmerov , etc. PRL 2009
Charge Transport Through Neutral Mode
TI
SC
M
)()(0 yxyx iiviivH
*
sH
MMHm
h
eG
2
2121 ii
Resonant Andreev Reflection
TML HHHH
dxxxivH xfL )()(
)]0()0()[(1 aitHT
dxxxivH xmM )()(
KTL, Lee, Ng PRL 2009
2e
e
h
NM Lead Sc
Andreev Reflection
Even number of flux Quantum 0G
Odd number of flux Quantumh
eG
22
Resonant Andreev Reflection
Superconductorelectron hole
Cross Andreevreflection
Even number of vortices
IedtItIIP *2)0(Λ)(Λ)0(Λ
IeP 2
IeP
Local Andreev reflection
Cross Andreevreflection
Fractional Josephson Effect 1
0 2 3
2 2 1 .0
0 .5
0 .0
0 .5
1 .0E
π
π
E
0 2 3
2 2 1
0 .5
0
0 .5
1
π=0
π
Kitaev 2000Kwon etc. 2004
Fractional Josephson Effect 2
πΎ1 πΎ 2
0 2 3
2 2 1
0 .5
0
0 .5
1E
π
ΒΏ1>ΒΏ
ΒΏ0>ΒΏ
Robust because for any Vwhich preserve fermion parity
1. Why changes sign?2. Can the crossing survives in the multi-channel case?
Fractional Josephson Effect 3
Potter, Lee PRL 2010
a)
b)
ππΏ ππ
ππΏ0 ππ 0
β0πππ
β0πππ
β0
β0
Single-band superconducting wires
Multi- band superconducting wires
πΎπΏπ
βπΎπΏπ
πΎπ π
βπΎπ π
KTL,LEE Arxiv:1103.5013
Fractional Josephson Effect 4
Change by 2
0 2 3
2 2 1
0 .5
0
0 .5
1
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
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