majorana in nanowires
TRANSCRIPT
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Data: Peng Yu (unpublished)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Data: Peng Yu (unpublished)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)