Search for topological superconductivity in HgTe Josephson ...

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

http://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

http://www.lpa.ens.fr

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 »


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 »


Topology & band structure

�3

▻ Brillouin zone ⇔ torus

BZ

kx

ky

⇔



�3


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



�3


⇒ 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


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)


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)


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

=



�5



k ?"k ",�k #



=

=

†

� =1

2(c+ c†)



�5



k ?"k ",�k #



=

N

ST

=

†

� =1

2(c+ c†)



�5



k ?"k ",�k #



=

N

ST


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)



�6




� �ei�




�6




� �ei�


(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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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


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


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.


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


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)

Search for topological superconductivity in HgTe Josephson ...

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