Searching for Majorana Modes in Semiconductor Nanowires

Report
Searching for Majorana fermions in
semiconducting nano-wires
Pedram Roushan
Peter O’Malley
John Martinis
Department of Physics, UC Santa Barbara
Borzoyeh Shojaei
Chris Palmstrøm
Materials Department , UC Santa Barbara
Roman Lutchyn
Microsoft Station Q
The 8th Capri Spring School on Transport in Nanostructures
April 2012, Capri, Italy
Theoretical proposals on Majorana fermions
Kitaev, Phys.-Usp. (2001)
Fu & Kane, PRL (2008)
And more…
for a review see: Alicea, arXiv:1202.1293v1
Sau et al., PRL (2010)
Majorana fermions in Josephson junctions
Josephson Current
Lutchyn et al., PRL (2010)
Trivial
Topological
π
2π
3π
Flux (F)
4π
Majorana fermions in Josephson junctions
Trivial
Topological
π
2π
3π
Flux (F)
Resonance
Amplitude
Josephson Current
Lutchyn et al., PRL (2010)
4π
Frequency
The parameter space
2DEG Parameters
α, g spin orbit coupling
g
magnetic moment
m*
effective mass
μe
electron mobility
ne
carrier concentration
Device parameters
L, W geometry
Δind
induced SC gap
tuneable parameters
B
magnetic field
μ
chemical potential
T
temperature
The parameter space
2DEG Parameters
α, g spin orbit coupling
g
magnetic moment
m*
effective mass
μe
electron mobility
ne
carrier concentration
Device parameters
L, W geometry
Δind
induced SC gap
tuneable parameters
B
magnetic field
μ
chemical potential
T
temperature
Non-helical
EFermi
Spin-orbit splitting
The parameter space
2DEG Parameters
α, g spin orbit coupling
g
magnetic moment
m*
effective mass
μe
electron mobility
ne
carrier concentration
Device parameters
L, W geometry
Δind
induced SC gap
tuneable parameters
B
magnetic field
μ
chemical potential
T
temperature
Non-helical
Non-helical
EFermi
EFermi
Spin-orbit splitting
Molecular Beam Epitaxy grown quantum wells
5 nm GaSb Cap
5 nm GaSb Cap
50 nm Al0.5Ga0.5Sb
50 nm AlSb
15 nm InAs QW
15 nm InAs QW
20 nm AlSb
5 nm GaSb Cap
5 nm Al0.5Ga0.5Sb
15 nm InAs QW
100 nm AlSb
100 nm AlSb
10 x 2.5 nm GaSb / 2.5
nm AlSb S.L.
10 x 2.5 nm GaSb /
2.5 nm AlSb S.L.
2000 nm GaSb
10 x 2.5 nm GaSb / 2.5
nm AlSb S.L.
2000 nm AlSb
2000 nm AlSb
1000 nm GaSb
500 nm GaAs
S.I. (100) GaAs
Substrate
100 nm AlSb
10 nm AlAs
100 nm GaAs
S.I. (100) GaAs Substrate
1000 nm GaSb
500 nm GaAs
S.I. (100) GaAs
Substrate
Measuring 2DEG parameters:
mobility and concentration
Iin
Iout
rxx = Vxx / I
n =6
rxy=Vxy / I
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
n =8
T = 60 mK
Measuring 2DEG parameters:
Effective mass
2 2k B m*
log( A / T )  Const.  log[sinh(
T )]
eB
m*=0.039me
Temperature (K)
Theory: D. Shoenberg, Magnetic oscillations in metals. Cambridge university press (1984).
Magneto-resistance feasurement:
Weak anti-localization
Spin-orbit coupling
•Rashba(a)
Asymmetric
quantum well
• Dresselhaus(g)
Lack of inversion symmetry
Measuring 2DEG parameters:
Spin-orbit coupling
a 13±1 meV.Å
g 425±6 eV.Å3
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). …
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
Conclusion and outlook
Parameter
Value
α, 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 gap
L, W, ...
B
geometry
magnetic field
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