Physikalisches Institut, EP3 Universität Würzburg · PDF fileband structure D.J....
Transcript of Physikalisches Institut, EP3 Universität Würzburg · PDF fileband structure D.J....
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Laurens W. Molenkamp
Physikalisches Institut, EP3Universität Würzburg
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Overview
- HgTe/CdTe bandstructure, quantum spin Hall effect- HgTe as a Dirac system- Dirac surface states of strained bulk HgTe- QAHE and Josephson junctions
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5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.76.6
1.0
1.5
0.5
0.0
-0.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
6.0
5.5
Bandgap vs. lattice constant(at room temperature in zinc blende structure)
Ban
dgap
ene
rgy
(eV
)
lattice constant a [Å]0 © CT-CREW 1999
MBE-Growth
HgTe-Quantum Wells
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band structure
D.J. Chadi et al. PRB, 3058 (1972)
fundamental energy gap
meV 30086 EE meV 30086 EE
semi-metal or semiconductor
HgTe
-1.0 -0.5 0.0 0.5 1.0k (0.01 )
-1500
-1000
-500
0
500
1000
E(m
eV) 8
6
7
-1.0 -0.5 0.0 0.5 1.0k (0.01 )
-1500
-1000
-500
0
500
1000
E(m
eV) 8
6
7
Eg
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Type-III QW
VBO = 570 meV
HgCdTeHgCdTeHgTe
HgCdTe
HH1E1
QW < 63 Å
HgTe
inverted normal
band structure
conduction band
valence band
HgTe-Quantum Wells
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Layer Structure
gate
insulator
cap layer
doping layer
barrier
barrierquantum well
doping layer
buffer
substrate
Au
100 nm Si N /SiO
3 4 2
25 nm CdTe
CdZnTe(001)
25 nm CdTe10 nm HgCdTe x = 0.79 nm HgCdTe with I10 nm HgCdTe x = 0.74 - 12 nm HgTe10 nm HgCdTe x = 0.7 9 nm HgCdTe with I10 nm HgCdTe x = 0.7
symmetric or asymmetricdoping
Carrier densities: ns = 1x1011 ... 2x1012 cm-2
Carrier mobilities: = 1x105 ... 1.5x106 cm2/Vs
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 80
100
200
300
400
500
µ=1.06*106cm2(Vs)-1
nHall=4.01*1011cm-2
Q2134a_Gate
B[T]
Rxx
[]
-15000
-10000
-5000
0
5000
10000
15000
Graph2
Rxy
[]
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123456
k (0.01 -1)
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Ener
gyE(
k)(e
V)
k || (1,1)k || (1,0)k = (kx,ky)
k || (1,1)k || (1,0)k = (kx,ky)
4 nm QW 15 nm QW
normal
semiconductor
inverted
semiconductor
1 2 3 4 5 6
k (0.01 -1)
-0.20
-0.15
-0.10
-0.05
0.00
0.50
0.10
0.15
0.20
E2
H1H2
E1L1
0.6 0.8 1.0 1.2 1.4
dHgTe (100 )
E2E2
E1E1H1H1
H2H2H3H3
H4H4 H5H5
H6H6L1L1
Band Gap Engineering
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Bandstructure HgTe
E
k
E1
H1
invertedgap
4.0nm 6.2 nm 7.0 nm
normalgap
H1
E1
B.A Bernevig, T.L. Hughes, S.C. Zhang, Science 314, 1757 (2006)
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Topological Quantization
C.L.Kane and E.J. Mele, Science 314, 1692 (2006)
C.L.Kane and E.J.Mele, PRL 95, 146802 (2005)C.L.Kane and E.J.Mele, PRL 95, 226801 (2005)A.Bernevig and S.-C. Zhang, PRL 96, 106802 (2006)
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QSHE, Simplified Picture
normalinsulator
bulk
bulkinsulating
entire sampleinsulating
m > 0 m < 0
QSHE
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Experimental Signature
normal insulator state
QSHI
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Need small Samples
L
W
(L x W) m
2.0 x 1.0 m1.0 x 1.0 m1.0 x 0.5 m
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Observation of QSHI state
M. König et al., Science 318, 766 (2007).
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-1.0 -0.5 0.0 0.5 1.0 1.5 2.0103
104
105
106
G = 2 e2/h
Rxx
/
(VGate- Vthr) / V
Observation of QSH Effect
(1 x 0.5) m2
(1 x 1) m2(2 x 1) m2
(1 x 1) m2
non-inverted
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1 m 2 m
1 2 3
6 5 4
1 m
1 m
5 m
1 2
34
(a) (b)
Verify helical edge state transport
Multiterminal /Non-local transport samples
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Multi-Terminal Probe
210001121000012100001210000121100012
T
heIG
heIG
t
t
2
23
144
2
14
142
232
generally
22 2)1(
ehnR t
3exp4
2 t
t
RR
heG t
2
exp,4 2
Landauer-Büttiker Formalism normal conducting contacts no QSHE
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0.0 0.5 1.0 1.5 2.00
5
10
15
20
25
R (k
)
V* (V)
I: 1-4V: 2-3
1
3
2
4
R14,23=1/4 h/e2
R14,14=3/4 h/e2
Non-Local data on H-bar
A. Roth et al., Science 325, 294 (2009).
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Configurations would be equivalent in quantum adiabatic regime
-1 0 1 2 30
5
10
15
20
25
30
35
40
R (k
)
V* (V)
I: 1-4V: 2-3
R14,23=1/2 h/e2
R14,14=3/2 h/e2
I: 1-3V: 5-6
R13,13=4/3 h/e2
R13,56=1/3 h/e2
-1 0 1 2 3 4
V* (V)
Multi-Terminal Measurements
A. Roth et al., Science 325, 294 (2009).
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Spin-Hall Effect
Intrinsic SHE
Rashba effect
J.Sinova et al.,Phys. Rev. Lett. 92, 126603 (2004)
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H-bar for detection of Spin-Hall-Effect
(electrical detection through inverse SHE)
E.M. Hankiewicz et al ., PRB 70, R241301 (2004)
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200 nm 200 nm
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.00
100
200
300
400
500
0
2
4
6
8
10
12
R12
,36
()
Vg (V)
I (n
A)
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.00.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
T = 2 K
Rno
nloc
al /
k
VGate / V
I / n
A
n-conductingp-conducting
insu
latin
g
– Suppress non-local QSHE using long leads or narrow wires
– Intrinsic metallic SHE only shows up for holes: larger spin-orbit
– Amplitude in agreement with modeling (E. Hankiewicz, J. Sinova)
H-bar experiments
C. Brüne et al., Nature Physics 6, 448 (2010).
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-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,00
100
200
300
400
500
R21
,36
()
Vg* (V)
-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,00
100
200
300
400
500
R36
,21
()
Vg* (V)-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0
0,0
0,5
1,0
1,5
2,0
R45
,21
(k
)
Vg* (V)
-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,00,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
R21
,45
(k
)
Vg* (V)
Q2197(a)
p-cond. insul. n-cond.
p-cond. insul. n-cond.
p-cond. insul. n-cond.
Q2198(b)
p-cond. insul. n-cond.
I
V
I
V
I
V
I
V
C. Brüne et al., Nature Physics 6, 448 (2010).
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QSHE and iSHE as spin injector and detector
Split-gated H-bar
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Detect iSHE through QSHI edge channels
I
U
Gate in 3-8 leg is scanned, 2-9 leg is n-type metallic,
current passed between contacts 2 and 9.
C. Brüne et al., Nature Physics 8, 486–491 (2012)
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Detect QSHI throughinverse iSHE
I
U
Gate in 3-8 leg is scanned, 2-9 leg is n-type metallic,
current passed between contacts 3 and 8 C. Brüne et al., Nature Physics 8, 486–491 (2012).
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Scanning SQUID
Katja Nowack et al., (Kam Moler group, Stanford)
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Scanning Microwave Impedance
Yue Ma et al., (Z.X. Shen group, Stanford).
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Bulk HgTe as a 3-D Topological ‚Insulator‘
-1.0 -0.5 0.0 0.5 1.0k (0.01 )
-1500
-1000
-500
0
500
1000
E(m
eV) 8
6
7
-1.0 -0.5 0.0 0.5 1.0k (0.01 )
-1500
-1000
-500
0
500
1000
E(m
eV) 8
6
7
Bulk HgTe is semimetal,
topological surface state overlaps w/ valenceband.
k(1/a)
E-E
F(eV
)
ARPES: Yulin Chen, ZX Shen,
StanfordC. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).
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70 nm layer on CdTe substrate:coherent strain opens gap
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0 2 4 6 8 10 12 14 160
2000
4000
6000
8000
10000
12000
14000
16000
0
2000
4000
6000
8000
10000
12000
14000
Rxx (SdH)
R
xx in
Ohm
B in Tesla
Rxy (Hall)
Rxy
in O
hm
Bulk HgTe as a 3-D Topological ‚Insulator‘
@ 20 mK: bulk conductivity almost frozen out - Surface state mobility ca. 35000 cm2/Vs
C. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).
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3D HgTe-calculations
2 4 6 8 10 12 14 160
2000
4000
6000
8000
10000
2.73.54.45.67.69.711 33.94.96.78.510.112
experiment
Rxx
in O
hm
B in Tesla
n=3.7*1011 cm-2
n=4.85*1011 cm-2
n=(4.85+3.7)*1011 cm-2
DO
S
Red and blue lines : DOS for each of the Dirac-cones with the corresponding fixed 2D-density,Green line: the sum of the blue and red lines
C. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).
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Experiments on a gatedHallbar
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0 2 4 6 8 10 12 14 16
-10
12
34
5 0
5
10
15
20
25
Vgate [V]
B [T]
Rxy
[k
]
Rxy from -1.5V to 5V
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Superconducting contacts on strained HgTe
L. Maier et al., Phys. Rev. Lett. 109, 186806 (2012).
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dV/dI (Vbias, B) at 20 mK
dV/dI (Ibias, B) at 20 mK
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L. Maier et al., Phys. Rev. Lett. 109, 186806 (2012).
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L. Maier et al., Phys. Rev. Lett. 109, 186806 (2012).
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Sample "Quad", device ADevice with improved HgTe-Nb interfaces.
Nb Nb
CdTe
70 nm strained HgTe
I
V
W=
2 m
stra
ined
HgT
e
Nb Nb
L = 1000 nm
D=
200
nm
V
I
J. Oostinga et al., Phys. Rev. X 3, 021007 (2013).
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At T = 25 mK, 200 mK, 500, 800 mK
Subgap regime
Decrease of differential conductance in subgap regime in the range |eV| < 2Nbis due to strongly enhanced probability of Andreev reflection
(corresponding to improved transparency of the HgTe-Nb interfaces).
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10-3
0
10
20
30
40
50
60
70
80dV/dI at B = 0 mT
Usample / V
dV/d
I /
800 mK500 mK200 mK25 mK (scaled)
eV /2 Nb
eV /2 Nb
supercurrent(V 0)
meV 1Nb
subgap regime:Nb2eV
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5
x 10-4
20
30
40
50
60
70comparison - left side
dV/d
I /
1 2 3 4
x 10-4
20
30
40
50
60
70comparison - right side
Usample / V
dV/d
I /
Reproducible oscillations
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Supercurrent regimeAt T = 25 mK, 200 mK, 500, 800 mK
-6 -4 -2 0 2 4 6
x 10-6
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
x 10-4 I-V at different temperatures
I / A
Usa
mpl
e / V
800 mK500 mK200 mK
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x 10-5
-5
-4
-3
-2
-1
0
1
2
3
4
5x 10-4 I - V at B = 0 mT, T = 25 mK
I / A
Usa
mpl
e / V
20120411_004 (<-)20120412_001 (<-)20120412_002 (->)
sI
sIrI
rI
Switching current depends on sweeping direction (origin unknown):
Retrapping current does not depend on sweeping direction:
ss II rr II
IcRN 0.15-0.2 mV
At T = 25 mK:Ic Is 3-4 A
RN 50
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T 25 mKJust DC
Sample with two contacts also shows somewhat irregular ‚Fraunhofer‘ pattern.
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T 25 mKJust DC
IC = 3.78 µABp = 1.09 mT
Could of course just be inhomogeneouscurrent injection.
Next steps:- build SQUID- go for 2D samples
J. Oostinga et al., Phys. Rev. X 3, 021007 (2013).
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Conclusions– HgTe quantum wells: normal and inverted gap, linear (Dirac) dispersion
– show Quantum Spin Hall Effect and Quantum Anomalous Hall Effect
– demonstrated helical edge channels and spin polarization
– strained 3D layers show QHE of topological surface states
– In which a supercurrent can be induced
Collaborators:Bastian Büttner, Christoph Brüne, Hartmut Buhmann, Markus König, Luis Maier, Matthias Mühlbauer, Jeroen Oostinga, Cornelius Thienel
Theory: Alena Novik, Ewelina Hankiewicz , Grigory Tkachov, BjörnTrauzettel (all @ Würzburg), Jairo Sinova (TAMU), Shoucheng Zhang, Xiaoliang Qi (Stanford), Chaoxing Liu (Penn State)
Funding: DFG (SPP Spintronics, DFG-JST FG Topotronics), Humboldt Stiftung, EU-ERC AG “3-TOP”, DARPA