Searching for Majorana fermions in semiconducting nano-wires
Pedram RoushanPeter O’MalleyJohn Martinis
Department of Physics, UC Santa Barbara
Borzoyeh ShojaeiChris Palmstrøm
Materials Department , UC Santa Barbara
Roman LutchynMicrosoft Station Q
The 8th Capri Spring School on Transport in NanostructuresApril 2012, Capri, Italy
Fu & Kane, PRL (2008) Sau et al., PRL (2010)
And more…for a review see: Alicea, arXiv:1202.1293v1
Kitaev, Phys.-Usp. (2001)
Theoretical proposals on Majorana fermions
Jose
phso
n Cu
rren
t
Flux (F) π 4π
Majorana fermions in Josephson junctions
Lutchyn et al., PRL (2010)
2π 3π
Topological
Trivial
Jose
phso
n Cu
rren
t
Flux (F) π 4π
Frequency
Reso
nanc
e Am
plit
ude
Majorana fermions in Josephson junctions
Lutchyn et al., PRL (2010)
2π 3π
Topological
Trivial
2DEG Parameters Device parameters tuneable parameters
α, g
spin orbit coupling L, W geometry B magnetic field
g magnetic moment Δind induced SC gap μ chemical potentialm* effective mass T temperatureμe electron mobility
ne carrier concentration
The parameter space
2DEG Parameters Device parameters tuneable parameters
α, g
spin orbit coupling L, W geometry B magnetic field
g magnetic moment Δind induced SC gap μ chemical potentialm* effective mass T temperatureμe electron mobility
ne carrier concentration
The parameter space
Non-helicalEFermi
Spin-orbit splitting
2DEG Parameters Device parameters tuneable parameters
α, g
spin orbit coupling L, W geometry B magnetic field
g magnetic moment Δind induced SC gap μ chemical potentialm* effective mass T temperatureμe electron mobility
ne carrier concentration
The parameter space
Spin-orbit splitting
Non-helical
EFermi
Non-helicalEFermi
S.I. (100) GaAs Substrate
500 nm GaAs
1000 nm GaSb
2000 nm AlSb
10 x 2.5 nm GaSb / 2.5 nm AlSb S.L.
100 nm AlSb
15 nm InAs QW
50 nm Al0.5Ga0.5Sb
5 nm GaSb Cap
S.I. (100) GaAs Substrate
100 nm GaAs
10 x 2.5 nm GaSb / 2.5 nm AlSb S.L.
20 nm AlSb15 nm InAs QW
5 nm GaSb Cap
10 nm AlAs100 nm AlSb
2000 nm GaSb
50 nm AlSb
S.I. (100) GaAs Substrate
500 nm GaAs
1000 nm GaSb
2000 nm AlSb
10 x 2.5 nm GaSb / 2.5 nm AlSb S.L.
100 nm AlSb
15 nm InAs QW5 nm Al0.5Ga0.5Sb5 nm GaSb Cap
Molecular Beam Epitaxy grown quantum wells
T = 60 mK
rsheet = 10 to 150 W/□
μe = 74,000 to 210,000cm2 / V∙s
ne = 5x1011 to 3x1012 to cm2
l = 0.9 to 6 mm
Measuring 2DEG parameters:mobility and concentration
n =8
n =6rxx = Vxx /
I
Iin Iout rxy=Vxy / I
Measuring 2DEG parameters:Effective mass
Theory: D. Shoenberg, Magnetic oscillations in metals. Cambridge university press (1984).
Temperature (K)
m*=0.039me
)]2log[sinh(.)/log(*2
TBemkConstTA B
Magneto-resistance feasurement: Weak anti-localization
Asymmetric quantum well
Spin-orbit coupling
•Rashba(a)
• Dresselhaus(g)Lack of inversion symmetry
Measuring 2DEG parameters:Spin-orbit coupling
Theory: Iordanskii et al., JETP Lett. (1994), Knap et al. PRB (1996), Lyanda-Geller PRL (1998)Experiment: Miller et al. , PRL (2003). Kallaher et al., PRB (2010). …
a 13±1 meV.Åg 425±6 eV.Å3
2DEG Band structure parameters:
EFermi
kF=0.018 Å-1
2DEG Band structure parameters:
EFermi
kF=0.018 Å-1
2DEG Band structure parameters:
EFermi
kF=0.018 Å-1
Parameter Valueα, g spin orbit coupling 10 to 30 meV.Å, 400 to 450 meV.Å3
g magnetic moment 15 (from literature)m* effective mass 0.03 to 0.07 me
μe electron mobility 60,000 to 210,000 cm2 / V s∙ne carrier concentration 5x1011 to 3x1012 / cm2
Δind induced gapL, W, ... geometry
B magnetic field
Conclusion and outlook
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