Phase-sensitive measurements on superconducting quantum ...qs3.mit.edu/images/pdf/Van_Harlingen_Lecture_1.pdf · Cooper pair correlations enable a supercurrent in a tunnel junction

University of Illinois at Urbana-Champaign

2019 NSF/DOE/AFOSR Quantum Science Summer School (QS3) June 3-14, 2019 --- Penn State University

Dale J. Van Harlingen

LECTURE 1: Monday, June 3

Phase-sensitive measurements on superconducting quantum materials and hybrid superconductor devices

LECTURE 2: Tuesday, June 4

S-TI-S Josephson junction networks: a platform for exploring and exploiting topological states and Majorana fermions

Josephson physics and techniques useful for exploring superconductor materials and devices, focusing on probing unconventional superconductors and junctions

A specific device architecture that may support Majorana fermions and shows promise for manipulating them for quantum computation processes

Significant role of SUPERCONDUCTIVITY in Quantum Information Science

Quantum materials

Quantum sensing

Quantum computing and

Quantum simulation

Superconductors were the first and the most-studied many-body system and continue to be critical to materials research. Every time we think the field is fading out, new classes of superconductors emerge

e.g. HTSC, heavy fermion superconductors, pnictide superconductors, topological superconductors, twisted graphene superconductivity , …

Superconductors and devices are legendary for their sensitivity as detectors and probes of exotic phenomena. This in part because of their required low temperature operation that has driven cryogenic physics and technology, and in part because of their intrinsic quantum naturee.g. MRI, SQUIDs, quasiparticle mixers, axion detectors, …

Conventional superconductor-based qubits (transmons, etc.) are one of the leading technologies for quantum simulation and quantum computing, and topological qubits based on Majorana fermions are one of the most explored for next-generation candidates

Quantum communications Photons rule in this space, so one of the grand challenges in quantum information science is “transduction” --- the transfer of quantum state information from qubit platforms into telecommunication photons

Phase-sensitive measurements on superconducting quantum materials and hybrid superconductor devices

Agenda

1. Superconductivity --- very little, but enough

2. Phase-coherence

3. Josephson effect

4. Phase-dynamics ---- the RSJ-model

5. Multiply-connected geometries --- SQUIDs and arrays

6. Josephson interferometry

7. Applications to quantum materials

A. Measuring the order parameter of unconventional superconductors

B. Measuring the current-phase relation of Josephson junctions with unconventional barriers

Cryogenics – low temperature physics 1. Get rid of thermal motion2. Observe onset of new phenomena

Heike Kamerlingh Onnes Leiden, Netherlands

The Discovery of Superconductivity (1911)

First to liquify helium in 1908 Kamerlingh Onnes Lab, Leiden

Superconductivity R=0

Temperature (K)

Resistance ()

+ thousands of metallic compounds and alloys

More illuminating: what materials are NOT superconducting?

Magnetic materials (Mn, Fe, Co, Ni)

Extent of Superconductivity

Good metals (Cu, Ag, Au)

q

k1

k'1 k2

k'2

e e- -

Conventional (“classic”) superconductivity

BCS theory:Bardeen, Cooper, Schrieffer (1957)

MECHANISM = attractive phonon-mediatedelectron-electron interaction Cooper pairing

ky

kx

kz

(k) =

“s-wave”

EXCITATIONS = normal “quasiparticles” with an isotropic energy gap

GROUND STATE = superfluid pair condensate = ns e i macroscopic phase coherence

23.2K

Liquid He

John Bardeen

Leon Cooper

Bob Schrieffer

-3 -2 -1 0 1 2 30

1

2

3

e V /

G/G

(eV

>>

)

quasiparticle tunneling spectroscopy reveals the fully-formed energy gap

Tc increased slowly from 4K to 23K over 75 years from 1911 to 1986

phase

High Temperature Superconductivity (1986)Woodstock of Music (1969)

3 days / 33 acts / 500,000 hippies

Woodstock of Physics (1987)

8 hours / 50 talks / 2500 physicists

Georg BednorzAlex Müller

“Our lives will be changed” … this did not turn out at expected but is rather true for physicistschallenged our understanding of condensed matter physics

opened new opportunities for superconductor research

IBM Zurich Research Laboratory

Family tree of superconductors

pnictidesconventional

fullerenes

carbon

hydrogen sulphide

q

k1

k'1 k2

k'2

e e- -

Conventional (“classic”) superconductivity

BCS theory:Bardeen, Cooper, Schrieffer (1957)

MECHANISM = attractive phonon-mediatedelectron-electron interaction Cooper pairing

ky

kx

kz

(k) =

“s-wave”

EXCITATIONS = normal “quasiparticles” with an isotropic energy gap

GROUND STATE = superfluid pair condensate = ns e i macroscopic phase coherence

23.2K

Liquid He

John Bardeen

Leon Cooper

Bob Schrieffer

-3 -2 -1 0 1 2 30

1

2

3

e V /

G/G

(eV

>>

)

quasiparticle tunneling spectroscopy reveals the fully-formed energy gap

Tc increased slowly from 4K to 23K over 75 years from 1911 to 1986

phase

Phase constraint:

SC:

JJ:

2 2emn es

J + As

2 n

n h n

2e 0

J 0s

1 2

0

2 2 n

Phase Coherence in multiply-connected superconductorsrequirement of single-valuedness of the condenstate wavefunction

Ring with Josephson Junction (rf SQUID)

gauge-invariant phase magnetic flux

Superconducting Ring

flux quantization

1 2 1

1 20 02 1 2

2 2( - ) - A d A d A d

in center of SC

2 2emn es

J + As

150 2.07 x10 Wb

20 20 G m

1

21

2

2 2A d 2 e e n

2

1 20 1

2( - ) + A d 2 n

Josephson Effect

Josephson junction can be thought of as the “transistor” of superconducting electronics

IsS

S

IIc

Ib

50th Anniversary of the Josephson Effect

,

Josephson Effect

In general : “current-phase relation”

Cooper pair correlations enable a supercurrent in a tunnel junction that depends on the gauge-invariant phase difference across the junction:

I1 2

cI I sin

cI I cpr

2

1 20 1

2= ( - ) - A d

Ic is the maximum current before switching into a finite voltage state

d 2eV=dt

2e 2eV(t) Vdt t c c J

2eVI(t) I sin t I sin 2 f t

Phase dynamics --- phase winds according to the “Josephson relation”

(483.6 THz/V)J2eVf =

hJosephson frequency

483597.84841698 GHz/VJosephson standard volt defined by:

c c 0J

I Iwhere E2e 2

Josephson supercurrent

Josephson coupling energy

JU E cos

At constant V:

RSJ (Resistively-Shunted Junction) model

Josephson dynamics: “phase particle” moving in a tilted washboard potential

U

I

I=0

I=Ic

cV dVI I sin CR dt

2

c 2

d C dI I sin2eR dt 2e dt

dV =2e dt

2

c2

C d d ( I I cos ) 02e dt 2eR dt

I < Ic: static solution = constant V=0

I > Ic: dynamic solution evolves in time V > 0voltage oscillates at the Josephson frequency

“mass” “damping” “potential”

Model junction as a Josephson junction in parallel with a resistor and capacitance

S

S

I

1/42

c cp

cJ

2eI cos 2eI1 I= 1C C IL C

Josephson inductance

small oscillation frequency in washboard potential well

non-linear (depends on the current)0J

c

L ( ) =2 I cos( )

cI I sin

Phase dynamics in the superconducting state

cc

2eIdI dI cos cos Vdt dt

J

dIV Ldt

Important for superconducting qubits by creating anharmonic potential that allows lifting degeneracy of harmonic oscillator states

Equilibrium phase shifts

JU = 2E

Josephson plasma frequency

0c

IarcsinI

Barrier height drops

I

0

Bp U/k TT e

2

p p

U 0.877.2 1Rcp

Q e2

Critical current -- escape of phase particle from the potential well

Thermal activation over the barrier)

Macroscopic Quantum Tunneling (MQT) though the barrier

Thermal activation rate:

MQT rate:

Transition to the finite voltage state always occurs before Ic,the “thermodynamic critical current”, due to fluctuations:

(the numerical factors come from a WKB approximation for tunneling through the washboard potential barrier and damping corrections)

MQT dominates when

p B7.2k T

RSJ model ---current-biased

Shape of the I-V characteristic depends on the damping

I

V

2c

c0

2 I R C

“McCumber parameter”Low damping (large R): c > 1

I-V is hysteretic

I

V

High damping (small R): c < 1

I-V is single-valued

2 2cV R I I

IS tt

IS

IN

IS

For I>Ic, the junction switches abruptly to finite voltage and the supercurrent is sinusoidal and averages to zero

For I>Ic, the supercurrent is non-sinusoidal has a finite average and averages to zero

dc SQUID

A dc SQUID consists of two junctions embedded in a superconducting loop

c 00

I 2I cos

Ic2

1 20

2 0

2 2c c1 c2 c1 c2I (I I ) 4I I cos

0

c1 1 c2 2I I sin I sin

Symmetric SQUID Ic1 = Ic2 = I0Asymmetric SQUID Ic1 > Ic2

Ic1

Applied flux (0) Applied flux (0)-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.5

1.0

1.5

2.0

2.5

Crit

ical

cur

rent

(I0)

Crit

ical

cur

rent

(I0)

Modulation reduced

Ic1+Ic2

Ic1-Ic2Modulates to zero

(Ic1=1.5, Ic2=0.5)

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

2.5

dc SQUID w/ inductance

A finite inductance modifies the SQUID characteristic because the circulating currents generate a flux in the loop that adds to the applied flux

Inductive SQUID

0

0

2LI 0

loop 1 2L I I LJ

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

2.5

Applied flux (0)

Crit

ical

cur

rent

(I0)

J = I1-I2 = circulating current = applied flux

Modulation reduced

=1

This is an example of “self-field effects” in which the fields from the Josephson currents cannot be ignored

Dependence on

-5 -4 -3 -2 -1 0 1 2 3 4 50

1

2

3

4

0 1 2 3 40

1

2

3

4

Crit

ical

cur

rent

(I0)

Applied flux (0)

Volta

ge (I

0R)

Voltage (I0R)

I/I0 =

4

3.5

3

2.5

2

1.5

1.1

dc SQUID operation

A dc SQUID biased at constant current exhibits a voltage modulation wih applied magnetic flux (period in 0)

For highest field sensitivity, bias just above I0

n0

(n+½)0

Josephson Effect in extended junctions

“local current-phase relation”

The supercurrent depends on the local CPR and the local gauge-invariant phase difference across the junction:

Local relation --- tunneling is highly-directional so the supercurrent depends on the phase difference at each location across the junction

2

1 20 1

2(y) = ( ) - (y)) - A dy

J1 2 Critical current:

w = junction width t = barrier thickness

Phase coherent --- phases at each location are related interference

w/2

cw/2

I (y) = t J(y) dy

cJ( (y)) J (y) cpr( (y))

Small-junction limit --- ignore self-field effects (no screening of field by tunneling currents)

Josephson Interferometry: response to a magnetic field

Phase coherence magnetic field induces a phase variation:

Uniform magnetic field and small junction limit

linear phase variation

y(y)0

Bm

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

Ic/I

c0

Fraunhofer diffraction

pattern

xmagnetic thickness of barrier

Single-slit optical interference

b

barrierthickness

m = b +2

Uniform junction Fourier transform

Current-phase

relation

Order parameter symmetry

Critical current variation

Magnetic field

variations

Josephson Interferometry: what it can tell you

Gap anisotropyDomainsCharge traps

Flux focusingSelf-field from tunneling currentTrapped vorticesMagnetic particlesUnconventional

superconductivityNon-sinusoidal terms-junctionsExotic excitations e.g. Majorana fermions

Current-phase

relation



Magnetic field

variations





Josephson Interferometry: critical current variations

Uniform junction

Narrow junction dc SQUID

Wide junction dc SQUID

Asymmetric junctions (magnitude)

Three-junction SQUID

Josephson Interferometry: more critical current variations

Asymmetric junctions (magnitude and width)

Current-phase

relation



Magnetic field

variations





Theorists with new ideas Experimentalists with new materials

What unique phenomena can I probe with Josephson Interferometry

Is it superconducting?

YES NO

Is it unconventional or exotic? Can I make it into the barrier of a Josephson junction?

YES NO

Go away –I don’t care

Measure the pairing symmetry

Measure thecurrent‐phase relation

Go away –I don’t care

YES NO

When all you have is a hammer, everything looks like a nail

(For me, everything looks like a SQUID)

My Friends in Urbana

1. Ceramics --- oxide materials2. Tc --- higher than could be explained by conventional BCS3. Layered materials --- low dimensional effects and strong correlations4. Unusual properties --- thermodynamics, transport, electrodynamics, … 5. Unusual doping dependence --- complicated phase diagram6. Unusual vortex states and dynamics7. UNCONVENTIONAL SUPERCONDUCTIVITY

HTSC --- many exciting phenomena and mysteries

SCIENTISTS: new physics ENGINEERS: new applications of superconductivity

super-conductor

pseudo-gap

strange metal

normal metal

T

hole dopingelectron doping

Mott insulator

superconductor

Unconventional superconductivity

What does “unconventional” mean? Not BCS• Mechanism other than phonon-mediated pairing• Symmetry not s-wave … exhibits anisotropy in phase and/or magnitude

1st indication: UPt3 (heavy fermion) two peaks in specific heat

1st confirmation: YBa2Cu3O7-x (high-Tc superconductor) d-wave

Cuprate superconductors:

YBa2Cu3O7-x Tc = 92K

+_ _+

“d-wave”

0

0 90 180 270 3600 90 180 270 3600

0.5

1

px + i py

0

2

0 90 180 270 3600 90 180 270 3600

0.5

1

py.

0

2

0 90 180 270 3600 90 180 270 3600

0.5

1

px

RELATIVE PHASEMAGNITUDEPAIRING STATE

ODD PARITY STATES

Complex order parameter broken time-reversal symmetry

phase shift 0,

+-

+-

Determining the Pairing Symmetry --- A Roadmap for Experimentalists

Magnitude measurementsprobe quasiparticles ---but can be masked or mimicked by impurities

Phase measurementsgive a distinct signature ---less susceptible to microscopic details

Cuprate candidates

s vs. dx2-y

2

Evolution of the Corner SQUID Idea

DVH Group meetingJanuary 1992

B9 MRLDecember 1991

++

__

Unconventional SCsingle crystal

Conventional SCthin film loop

Josephson interferometry: measuring the phase anisotropy

dc SQUID(Superconducting QUantum Interference Device)

measures the phase shift inside the crystal between orthogonal directions

Wollman, Ginsberg, Leggett, Van Harlingen (1993)

Josephson tunnel junctions

tunneling selects direction in k-space

the corner SQUID

+_ _+

Josephson interferometry ---measuring the phase shift between different directions

SCcrystal

s-wave SC thin film

loopdc SQUID single junction

Josephson junctions

The corner SQUID experiment

-3 -2 -1 0 1 2 3

M a g n e tic f lu x ( 0)-3 -2 -1 0 1 2 3

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

M a g n e tic f lu x ( 0)

Crit

ical

cur

rent

s-wave d-wave+ +

-+

-

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0

1

2

3

4

5

6

7

8

edge SQUIDs

corner SQUIDs

Obs

erva

tions

Phase shift

D. A. Wollman, D. J. Van Harlingen, W. C. Lee, D. M. Ginsberg, and A. J. Leggett, Phys. Rev. Lett. 71, 2134 (1993)

100m

6 4 2 0 -2 -4 -6

Magnetic flux-6 -4 -2 0 2 4 6

0.0

0.2

0.4

0.6

0.8

1.0

Magnetic flux

Crit

ical

cur

rent

+

The corner junction experiment

s-wave-

++-

d-wave

-1000 -500 0 500 10000

20

40

60

Applied magnetic field (mG)

Crit

ical

cur

rent

( A

)

D. A. Wollman, D. J. Van Harlingen, J. Giapintzakis, and D. M. Ginsberg. Phys. Rev. Lett. 74, 797 (1995)

Tricrystal ring experiment Kirtley, Tsuei (IBM)

-SQUID Hilgenkamp, Mannhart (Augsburg)

Scanning SQUID Microscope

image

Further phase-sensitive measurements

60

75

Angles of the grain boundary junctions determines if there is a -phase shift in the SQUID modulation

Angles of the grain boundary junctions determines if there is a spontaneous circulating current

Manfred Sigrist and T. M. Rice, Rev. Mod. Phys. 67, 503 (1995)

Paramagnetic Meissner Effect

W. Braunisch, N. Knauf, G. Bauer, A. Kock, A. Becker, B. Freitag, A. Grütz, V. Kataev, S. Neuhausen, B. Roden, D. Khomskii, D. Colleen, J. Bock, and E. Preisler. Phys. Rev. B 48, 4030 - 4042 (1993)

Model: spontaneous supercurrents in multiply-connected d-wave grains

Experiment: enhanced magnetic flux in granular BSCCO composites

Grain boundary junctions

Geometry for testing symmetry: 45°-asymmetric junction facets sample different signs of the d-wave order parameter

“Multi-corner junction”

+

Maximum Ic not at B=O

Symmetric with respect to field polarity

S-wave would give Fraunhofer pattern

H. Hilgenkamp, J. Mannhart, and B. Mayer, Phys. Rev. B 53, 14586 (1996)

Cuprates--- all d-wave, all the time?+_ _+

The compilation of experiments --- spectroscopic, thermodynamic, transport, and phase-sensitive --- indicate that all of the cuprates have dx

2-y

2 symmetry

Tested by phase-sensitive Josephson inferometry

Many proposals for inducing alternative pairing symmetries but so far not seen --tested vs. material, temperature, carrier doping, magnetic impurities, …

formation of zero-energy bound quasiparticle states suppression of d-wave at interfaces and defects onset of SC phases with complex order parameters

at low temperature broken time-reversal symmetry

Example: Fragility of unconventional superconductors

s-wave superconductor: scattering does not affect superconductivity “Anderson theorem”+

unconventional superconductor: scattering changes magnitude and phase of the order parameter

dx2-y

2

dx2-y

2 +idxy

Onset of secondary order parameter:* increases B=0 critical current node lifted* breaks polarity symmetry broken TRS

Effect of onset of complex order parameter

45°-asymmetric grain boundary junction highly- sensitive to the addition of a complex component in the order parameter

-30 -20 -10 0 10 20 300

5

10

15

20

25

30

35

40

Crit

ical

Cur

rent

(A)

Applied Magnetic Field (G)

15.4K 9.0K 6.4K 1.5K

PREDICTION

EXPERIMENTNo evidence for a change in the order parameter symmetry over a wide temperature range and with doping of non-magnetic and magnetic impurities:

W. K. Neils and D. J. Van Harlingen, Phys. Rev. Lett. 88, 047001 (2002)

• d-wave superconductivity nucleates in spatially inhomogeneous “puddles” which couple together via the Josephson effect

• Produces a globally “s-wave”-like pairing symmetry despite local d-wave in grains (no preferred anisotropy)

• Overdoped LSCO crystals are a candidate for such a system

Where haven’t we looked? --- the strongly overdoped cuprates

David Hamilton(Illinois)

Masaki Fujita (Tohoku)

Steve Kivelson(Stanford)

Optimal-doping Overdoping

• LSCO (x=0.25, Tc=15K) crystal, grown by the Fujita group, is oriented via XRD, cut/polished, then mounted onto a sapphire substrate.

• Using dry-film photoresist masking, Josephson junctions are patterned onto a- and b- faces of the crystal

• Au (annealed) is used as the normal barrier. • Superconducting contacts are made with sputtered Nb.

Nb

Au

Exploring the region by Josephson interferometry

Josephson interferometry diffraction pattens --- edge or corner

• Also see broken field symmetry which could arise from complex order parameters or local magnetic field inhomogeneity

• Observe short-range field modulations features suggestive of grain boundary junctions --- indicates domains

Edge JJ Corner JJ

• We do not observe a s-wave state, but we cannot tell corner from edge diffraction patterns --- this may be regarded as definition of “s-wave –like”

Model system with d-wave domains and Wohlleben effects

Circulating currents from Wohlleben effect generates an inhomogeneous field that threads the junction

Field (flux quanta)

Model simulates both the rapid oscillations and the magnetic field asymmetry

Field (flux quanta)

Growing Family of Unconventional Superconductors

-(BEDT-TTF)2Cu[N(CN)2]Br

Organic superconductors

“anisotropic d-wave”

+_ _+

115 superconductors

CeCoIn5 Tc = 2.3K

+_ _+

“d-wave”

Heavy Fermion superconductors

UPt3 TcA = 0.50 TcB = 0.45KSr2RuO4 Tc = 1.5K

Ruthenate superconductors

px+ipy(kx

2-ky2) kz (kx+ iky)2 kz

Tc = 11.6K+_ _+

“d-wave”

Cuprate superconductors

YBa2Cu3O7-x Tc = 95K

The Quest for Complex Superconductors

Sr2RuO4 Tc = 1.5K

Ruthenate superconductors:

px+ipy

Josephson interferometry of complex order parameters

-3 -2 -1 0 1 2 30.0

0.2

0.4

0.6

0.8

1.00

/4

/2

3/4

Magnetic flux (/0)

Crit

ical

cur

rent

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.00

/2

3/4

/4

Magnetic flux (/0)

Crit

ical

cur

rent

Angle SQUID

Angle junction

= phase shift

Phase shifts from complex order parameters

-3 -2 -1 0 1 2 30.0

0.2

Magnetic flux (/0)

Cr

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.00

/2

3/4

/4

Magnetic flux (/0)

Crit

ical

cur

rent

Angle SQUID

Angle junction

= phase shift

Polarity asymmetry indicates broken time‐reversal symmetry

Current focus is on topological systems --- interplay of topology and superconductivityNew questions of pairing symmetry --- opportunities for Josephson interferometry

Superconductor/Topological Insulator bilayer Topological Superconductors e.g. CuxBi2Se3, NbxBi2Se3, …

Materials exhibit superconductivity, ferromagnetism, Andreev reflection, gate-dependent surface supercurrents, hints of p-wave superconductivity

S-TI bilayerS electrode

N barrier

Corner Junction experiment to test for proximity-induced p-wave symmetry

s + ps + (px+ipy)

(C. Kurter, A.Finck, E. Huemiller, and Y.-S.Hor)

Testing order parameter symmetry via corner SQUID/junction experiments

What’s next? the growing list of systems in which to determine the pairing symmetry

S/TI bilayersDoped-TIs --- topological superconductor candidatesFeTe1-xSex

PrOs4Sb12

YPtBiLAO/STO interface superconductorsTwisted bilayer graphene superconductorsCeCoIn5

CeCu2Si2UBe13

Sr2RuO4

???

Phase-sensitive measurements on superconducting quantum ...qs3.mit.edu/images/pdf/Van_Harlingen_Lecture_1.pdf · Cooper pair correlations enable a supercurrent in a tunnel junction

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