Sergey FrolovUniversity of Pittsburgh

Majorana in

nanowiresLecture II (zero-bias peaks)

InSb nanowires: length 3 mm, diameter 100 nm

Plissard et al, Nano Letters 2012

Majorana recipe:

1. Nanowire

2. Spin-orbit interaction

3. Superconductivity

4. Magnetic field

Lutchyn, Sau, Das Sarma, PRL 2010

Oreg, Refael, von Oppen, PRL 2010

InSb nanowires: length 3 mm, diameter 100 nm

Plissard et al, Nano Letters 2012

Majorana recipe:

1. Nanowire

2. Spin-orbit interaction

3. Superconductivity

4. Magnetic field

Lutchyn, Sau, Das Sarma, PRL 2010

Oreg, Refael, von Oppen, PRL 2010

V (mV)

dI/

dV

(2e

2/h

)

B = 0

490 mT

D = 250 meV

Mourik et al. Science 2012

Tunneling Spectroscopy: a powerful technique

B(T)1 2 3

0

-700

700

0.16

0.10

Vsd (

uV

)

Data: Peng Yu (unpublished)

B

B(T)0.60

V(m

V)

0

1

-1

(2e2/h)

0.1

0.4

(2e2/h)

G(2

e2/h

)

0

0.3

-1 0 1

V(mV)

Tunneling Spectroscopy: a powerful technique

B(T)1 2 3

0

-700

700

0.16

0.10

Vsd (

uV

)

Data: Peng Yu (unpublished)

B(T)0.60

V(m

V)

0

1

-1

(2e2/h)

0.1

0.4

G(2

e2/h

)

0

0.3

-1 0 1

V(mV)

(2e2/h)

0-700 700

Vsd (uV)

What are the basic properties of

Majorana Bound States?

• Pinned to (or near) zero energy

• Exist in a limited parameter space of m, Ez

• Require spin-orbit interaction

• Come in pairs

Field orientation dependence

B=0.5T

-0.2π 0 0.2π 0.4π 0.6π

1

-1

0

(2e2/h)

Angle

0.03

0.09

V(m

V)

π/60

π/2 π

1

-1

0

V(m

V)

1

-1

0

B(T)

0 0.5 0 0.5

0.05

0.1

(2e2/h)

How are we finding Majoranas, actually?

V (mV)

dI/

dV

(2e

2/h

)

Black

box

Topological Transition

EZ < D EZ = D EZ > D

Trivial Superconductor“positive gap”

Majorana“zero gap”

Topological Superconductor“negative gap”

Stanescu, Lutchyn, Das Sarma; Phys Rev B 2011

Stanescu, Lutchyn, Das Sarma; Phys Rev B 2011

B(q)

Vgate1

Vgate2

Vgate3

Vgate…

Phase diagram of Zero Bias Peaks – Mapping out the Topological Condition

BG1=-0.53V BG1=-0.42V BG1=-0.31V

1-0.1

1

0

-1

V(m

V)

B(T)1-0.1 1-0.1

(2e2/h)

0.02

0.08

J. Chen et al, Science Advances (2017)

EZ > (D2+m2)0.5

Numerics : Stanescu Group

Where is the second Majorana?

FG2BGFG1

NbTiNPdPd

N1 N2S

BGFG1 FG2

g1 g2

400 nm

Quiz

V (μ

V)

300

-300

150B (mT)0

0

0.006

(2e2/h)(2e2/h)

0.75

0

0.05

0.1

V(m

V)

B(T)0 0.750.5

-0.75

0.25

ГS

S

GS(N)

ES(N+1)

Andreev Bound States in Single Quantum Dots

U

0

EJH Lee, NatNano 2014

0.20.1

0T

0.25T

0.35T

(2e2/h)

BG1(V)0.80.75

V(m

V)

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

Su et al, arXiv:1904.05354

2019

Magnetic field evolution of Andreev bound states

0.20.1

0T

0.25T

0.35T

(2e2/h)

BG1(V)0.80.75

V(m

V)

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

(2e2/h)0.10.05 0.15

B(T)

10 0.5 10 0.5 10 0.5

V(m

V)

BG1=0.76V BG1=0.77V BG1=0.775V

BG1=0.78V BG1=0.785V BG1=0.79V

B

|S >

|D >

Magnetic field evolution of Andreev bound states

0.20.1

0T

0.25T

0.35T

(2e2/h)

BG1(V)0.80.75

V(m

V)

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

(2e2/h)0.10.05 0.15

B(T)

10 0.5 10 0.5 10 0.5

V(m

V)

BG1=0.76V BG1=0.77V BG1=0.775V

BG1=0.78V BG1=0.785V BG1=0.79V

Single dot: Andreev Bound States

0.20.1

0T

0.25T

0.35T

(2e2/h)

BG1(V)0.80.75

V(m

V)

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

0.4

-0.4

0

(2e2/h)0.10.05 0.15

B(T)

10 0.5 10 0.5 10 0.5

V(m

V)

BG1=0.76V BG1=0.77V BG1=0.775V

BG1=0.78V BG1=0.785V BG1=0.79V

BG1

0.0 0.2 0.4 0.6 0.8

0.76

0.77

0.78

0.79

BG

1(V

)

B(T)

onset

outset

onset outset

Majorana vs. Andreev

Phase diagram of ZBPs:

J. Chen et al, arXiv:1611.00727

Vbias = 0

Possible way to distinguish Majorana and Andreev: zero-bias conductance

“Andreev”

“Majorana”

Trivial (Non Topological) Andreev States

Ubiquitous non-Majorana zero-bias peaks:

J. Chen et al, arXiv:1902.02773BG1 FG

Pd

NbTiN

200 nm

B (T)

BG1=0.137 V

V (

mV

)

-0.5

0.5

0

0 10.5

BG1=0.1375 V

0 10.5

BG1=0.1365 V

-0.5

0.5

0

0 10.5

BG1(V)1.3 1.71.51.4 1.6

-200

V(μ

V)

200

200-200

V(μ

V)

0.1

0.5

(2e2/h)

0T

0.3T

ZBP ubiquitous in gate space – at finite field

B= 0T B= 0.3T B= 0.5T

BG1(V)

1.60 1.621.61 1.60 1.621.61 1.60 1.621.61

V(m

V)

0.3

-0.3

0

0.2

(2e2/h)

0.4

BG1(V)1.3 1.71.51.4 1.6

-200

V(μ

V)

200

200-200

V(μ

V)

0.1

0.5

(2e2/h)

0T

0.3T

Conclusions

• Theory is solid, so Majorana must be there

• But! Zero bias peaks are way to easy to find

• Trivial Andreev Bound States hard to distinguish

from Majorana

• Need to see MANY (ideally all)

basic Majorana signatures

in a single device!

(otherwise fine-tuning must be

assumed)