search for topological superconductivity in hgte josephson
TRANSCRIPT
Paris — 25/05/2018
Physikalisches Institut (EP3) Universität Würzburg, Am Hubland, D-97074 Würzburg
http://www.physik.uni-wuerzburg.de/EP3/
Erwann Bocquillon
Search for topological superconductivity in HgTe Josephson junctions
Laboratoire Pierre Aigrain Ecole Normale Supérieure
24 rue Lhomond, 75231 Paris Cedex 05 France www.lpa.ens.fr
Paris — 25/05/2018
Physikalisches Institut (EP3) Universität Würzburg, Am Hubland, D-97074 Würzburg
http://www.physik.uni-wuerzburg.de/EP3/
Erwann Bocquillon
Search for topological superconductivity in HgTe Josephson junctions
Erwann Bocquillon Paris - 25/05/2018
Topology
�2
▻ topology: study of « the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. »
POW
POW
0 holes
1 hole
2 holes
3 holeselectricalconductance
Illustration: ©Johan Jarnestad/The Royal Swedish Academy of Sciences
Wikipedia, article on « topology »
Erwann Bocquillon Paris - 25/05/2018
Topology
�2
▻ topology: study of « the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. »
Z
SKdS = 2(1� g)
Gauss-Bonnet theorem K: (Gauss) curvature
▻ topological invariants ex: genus g
POW
POW
0 holes
1 hole
2 holes
3 holeselectricalconductance
Illustration: ©Johan Jarnestad/The Royal Swedish Academy of Sciences
Wikipedia, article on « topology »
Erwann Bocquillon Paris - 25/05/2018
Topology & band structure
�3
▻ Brillouin zone ⇔ torus
BZ
kx
ky
⇔
Erwann Bocquillon Paris - 25/05/2018
Topology & band structure
�3
▻ Brillouin zone ⇔ torus
BZ
kx
ky
⇔
C1 =1
2⇡
X
n
Z
BZBn(k) · d2k
Bn(k) = �ihrkunk| ^ |rkunk|i
|unki Bloch waves
▻ topological invariant: Chern number and Berry phase
Erwann Bocquillon Paris - 25/05/2018
Topology & band structure
�3
▻ Brillouin zone ⇔ torus
⇒ defines trivial and topological phases ⇒ enforces robust states at their interfaces
BZ
kx
ky
⇔
C1 =1
2⇡
X
n
Z
BZBn(k) · d2k
Bn(k) = �ihrkunk| ^ |rkunk|i
|unki Bloch waves
▻ topological invariant: Chern number and Berry phase
Erwann Bocquillon Paris - 25/05/2018
Topological insulators in HgTe
�4
CdTe
�8
�6
1 eV
HgTe
�6
�8
�0.3 eV
k k
"(k)"(k)
▻ Band inversion ⇒ conducting states at interfaces
▻ 2D confinement ⇒ insulating state in 2D plane
Bernevig et al., Science 314, 1757 (2006) König et al., Science 318, 766 (2007)
Erwann Bocquillon Paris - 25/05/2018
Topological insulators in HgTe
�4
Quantum Spin Hall effect
HgCdTe ~ 25 nmHgTe ~ 7-10 nm
HgCdTe ~ 100 nm
CdZnTe (substrate)
▻ Band inversion ⇒ conducting states at interfaces
▻ 2D confinement ⇒ insulating state in 2D plane
"(k)
kBernevig et al., Science 314, 1757 (2006) König et al., Science 318, 766 (2007)
Erwann Bocquillon Paris - 25/05/2018
Topology and Majoranas
�5
J. Alicea, Rep. Prog. Phys. 75, 076501 (2012) C.W.J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013)
V. Mourik et al., Science 336, 1003 (2012) … S. M. Albrecht et al., Nature 531, 206 (2016)
k ?"k ",�k #
+Cooper pair of helical Dirac fermions
⇒ helical pairing ⇒ p-type correlations
=
Erwann Bocquillon Paris - 25/05/2018
Topology and Majoranas
�5
J. Alicea, Rep. Prog. Phys. 75, 076501 (2012) C.W.J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013)
V. Mourik et al., Science 336, 1003 (2012) … S. M. Albrecht et al., Nature 531, 206 (2016)
k ?"k ",�k #
+Cooper pair of helical Dirac fermions
⇒ helical pairing ⇒ p-type correlations
=
=
†
� =1
2(c+ c†)
Erwann Bocquillon Paris - 25/05/2018
Topology and Majoranas
�5
J. Alicea, Rep. Prog. Phys. 75, 076501 (2012) C.W.J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013)
V. Mourik et al., Science 336, 1003 (2012) … S. M. Albrecht et al., Nature 531, 206 (2016)
k ?"k ",�k #
+Cooper pair of helical Dirac fermions
⇒ helical pairing ⇒ p-type correlations
=
N
ST
=
†
� =1
2(c+ c†)
Erwann Bocquillon Paris - 25/05/2018
Topology and Majoranas
�5
J. Alicea, Rep. Prog. Phys. 75, 076501 (2012) C.W.J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013)
V. Mourik et al., Science 336, 1003 (2012) … S. M. Albrecht et al., Nature 531, 206 (2016)
k ?"k ",�k #
+Cooper pair of helical Dirac fermions
⇒ helical pairing ⇒ p-type correlations
=
N
ST
Erwann Bocquillon Paris - 25/05/2018
Topological Josephson junctions
�6
Gapless Andreev bound states
▻ hybridized Majoranas ⇒ new mode
▻ 4π-periodic gapless Andreev bound state
� �ei�
Kwon et al., JLTP 30, 613 (2004) Fu et al., PRL 100, 096407 (2008) Badiane et al., CRP 14, 840 (2013)
Erwann Bocquillon Paris - 25/05/2018
Topological Josephson junctions
�6
Gapless Andreev bound states
▻ hybridized Majoranas ⇒ new mode
▻ 4π-periodic gapless Andreev bound state
� �ei�
Kwon et al., JLTP 30, 613 (2004) Fu et al., PRL 100, 096407 (2008) Badiane et al., CRP 14, 840 (2013)
Erwann Bocquillon Paris - 25/05/2018
Topological Josephson junctions
�6
Gapless Andreev bound states
▻ hybridized Majoranas ⇒ new mode
▻ 4π-periodic gapless Andreev bound state
� �ei�
Kwon et al., JLTP 30, 613 (2004) Fu et al., PRL 100, 096407 (2008) Badiane et al., CRP 14, 840 (2013)
(Fractional) Josephson effect
▻ conventional junction
▻ topological contribution
sin�/2
π0 2π 3π 4π
Energy
"[�
]
-1.0
-0.5
0.0
0.5
1.0
Phase di↵erence �
IS(�) = Ic sin�
d�
dt=
2eV
~ ⇒
sin� ! sin�/2 fJ ! fJ/2⇒
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Erwann Bocquillon Paris - 25/05/2018
Quantum spin Hall junctions
�7
HgTe Josephson junctions
▻ Al contacts (in situ)
▻ Au top gate
Hart et al., Nat. Phys. 10, 638 (2014) Bocquillon et al., Nat. Nano. 12, 137 (2017)
HgTeHg0.3Cd0.7Te
2μm
AlHfO2/Au
L ' 400 nm
W ' 4 µm
Erwann Bocquillon Paris - 25/05/2018
Quantum spin Hall junctions
�7
HgTe Josephson junctions
▻ Al contacts (in situ)
▻ Au top gate
Hart et al., Nat. Phys. 10, 638 (2014) Bocquillon et al., Nat. Nano. 12, 137 (2017)
HgTeHg0.3Cd0.7Te
2μm
AlHfO2/Au
Erwann Bocquillon Paris - 25/05/2018
Detection setup
�8
▻ voltage bias shunt resistance Rs
current resistance R
T≃ 300 K
T≃ 4 K
T≃ 150 mK
T≃ 25 mK
rf exc.
spectrum analyzer
c
from bias-T
Vg to rf amp.
exc. current
VR
V
b
2 μm
I
RS
R
HEMT amp.
a
Superconducting phase ! π 2π 3π 4π
Ener
gy
0
0
Δi
-Δi
EJ
topological state
conv. state
bias-T
▻ rf amplification setup 1 cryo amp. (+ 2 amps at RT) 0.1 fW (-130 dBm) in 8 MHz
a
Superconducting phase ! π 2π 3π 4π
Ener
gy
0
0
Δi
-Δi
EJ
topological state
conv. state
T≃ 300 K
T≃ 4 K
T≃ 150 mK
T≃ 25 mK
rf exc.
spectrum analyzer
c
from bias-T
Vg to rf amp.
bias current
RI I
V
2 μm
I
RS
RI
to voltage meas.
b
HEMT amp.
Erwann Bocquillon Paris - 25/05/2018
Emission spectra
�9
▻ voltage V swept
▻ integrated power at fd=3 GHz (in 8 MHz bandwidth)
▻ trivial QW : signal at fd=fJ
▻ topological QW : at fd=fJ and fJ/2
Deacon et al., Phys. Rev. X 7, 021011 (2017)dc v
olta
ge V
[μV
]
dc voltage V [μV]
frequency fd [GHz]
dc c
urre
nt I
[μA] rf am
p. A [a.u.]
a b c
d e f
dc v
olta
ge V
[μV
]
dc voltage V [μV]
frequency fd [GHz]
dc c
urre
nt I
[μA] rf am
p. A [a.u.]
dc v
olta
ge V
[μV
]
dc voltage V [μV]
frequency fd [GHz]
dc c
urre
nt I
[μA] rf am
p. A [a.u.]
fJ2fJ
fJ
fJ/2
2fJ
fJ/2
dc v
olta
ge V
[μV
]
dc voltage V [μV]
frequency fd [GHz]
dc c
urre
nt I
[μA] rf am
p. A [a.u.]
a b c
d e f
dc v
olta
ge V
[μV
]
dc voltage V [μV]
frequency fd [GHz]
dc c
urre
nt I
[μA] rf am
p. A [a.u.]
dc v
olta
ge V
[μV
]
dc voltage V [μV]
frequency fd [GHz]
dc c
urre
nt I
[μA] rf am
p. A [a.u.]
fJ2fJ
fJ
fJ/2
2fJ
fJ/2
Trivial QW Topological QWn- and QSH regime p-regime
Erwann Bocquillon Paris - 25/05/2018
Acknowledgements
�11
Uni. Würzburg
▻ PhD student : J. Wiedenmann ▻ Staff : C. Brüne, H. Buhmann, L.W. Molenkamp ▻ Invited : T.M. Klapwijk ▻ Theory : F. Domínguez, E.M. Hankiewicz
RIKEN, Tōkyō
▻ R.S. Deacon, K. Ishibashi, S. Tarucha
Co-recipiendary : F.D. Parmentier (CEA Saclay)