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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