Superconducting Pair Transport in S Graphene S G CNRS-EWHA - - PowerPoint PPT Presentation

Physics, POSTECH

Quantum Transport and Superconductivity Laboratory Center for Topological Matter

Hu-Jong Lee

G S S

CNRS-EWHA Winter School 2012

• Feb. 9, 2012; Ewha Womans Univ.

Superconducting Pair Transport in Graphene

Outline

1. Pair transport in S–mono-layer graphene–S junctions

– Basic concept – graphene and Josephson coupling – Pair transport in graphene

• 2. Switching current distribution in mono-layer GJJs

– Basic concept – switching current distribution – Gate tuning of different switching regimes – MQT, TA, PD – Observation of quantized levels in washboard potential

• 3. Top-gated bilayer GJJs

– E-field-induced band gap opening – S-I transition in top-gated bilayer GJJs

• 4. Josephson coupling across a graphene p-n potential barrier

– Klein tunneling of Cooper pairs

Carbon Allotropes : in Diverse Dim ensions

Two dimension Three dimension One dimension Zero dimension Patterning Functionality

1

a

2

a

Graphene

2.46 A

°

‘A’ sublattice ‘B’ sublattice

graphene lattice

(real space) Two equivalent sublattices Two atoms per unit cell π-orbital σ-bond SP2 covalent hybrid

• rbital of a carbon atom

π σ

• Dirac cone
• Linear dispersion at zero energy

Band Structure and Low -Energy Dispersion

• Massless relativistic Dirac fermions
• But moving with Fermi velocity
• Carrier type and density are easily controlled by gating

F

υ

F

E k υ = r h

K M Γ K’

EF

Chirality or Pseudospin in Graphene Lattice

pseudospin or chirality

K K’

kx ky kx E E

Chirality – momentum-locked phase value of a carrier in graphene when the carrier moves along a Dirac cone (or the sublattice index) electron-like hole-like

natural graphite

Graphene Preparation – Mechanical Exfoliation

exfoliated graphene on Si sub

1 3

10 μm

2

thin graphite on tape transferring graphene onto Si substrate

Graphene Preparation – Mechanical Exfoliation

10 μm 10 μm 10 μm 10 μm

1. Pair transport in S–mono-layer graphene–S junctions

– Basic concept – graphene and Josephson coupling – Pair transport in graphene

• 2. Switching current distribution in mono-layer GJJs

– Basic concept – switching current distribution – Gate tuning of different switching regimes – MQT, TA, PD – Observation of quantized levels in washboard potential

• 3. Top-gated bilayer GJJs

– E-field-induced band gap opening – S-I transition in top-gated bilayer GJJs

• 4. Josephson coupling across a graphene p-n potential barrier

– Klein tunneling of Cooper pairs

Josephson relations;

; Josephson coupling strength ; SC strength in electrodes

High-freq. Josephson oscillation;

V

L

S

R

S

L

ψ

R

ψ

I

I

Josephson Effect

Δ

c

I

• Finite supercurrent for d < ξ
• Supercurrent is carried either by electron-like carriers in the conduction band
• r by hole-like carriers in the valence band

S S G

Graphene-based Josephson Junction

Heersche et al., Nature 446 56 (2007)

SC Paring Condition;

• opposite momentum (k, -k) in two different valleys
• opposite spins ( )

K K’

• Josephson coupling is modulated by backgating
• Al electrodes; low Tc (=1.2 K)

small gap Δ (=0.17 meV)

• Josephson device applications ; higher-gap electrodes are required

S S G

Supercurrent in Graphene – Josephson Effect

Heersche et al., Nature 446 56 (2007)

SC Paring Condition;

• opposite momentum (k, -k) in two different valleys
• opposite spins ( )

Heersche et al., Nature 446 56 (2007) Al-G-Al CNP

+1 V

• 7.5 V

Vbg= -50 V

Pb0.93In0.07–G–Pb0.93In0.07 junction

• PbIn/Au (200/10 nm)
• spacing btw electrodes = 300 nm

monolayer graphene μ = 1400 cm2/Vs @ Vbg=-50 V Tc = 7 K

Sam ple PbI n-G-PbI n Junction

T = 6 mK H = 4.2 kG Finite resistance at VCNP

• 3
• 2
• 1

1 2 3

• 200
• 100

100 200

I (μA) V (μV) V

bg= -60 V

PbIn–G–PbIn Junction

Hysteresis in I V Characteristics

• IV curve is hysteretic – underdamped tunneling JJ
• Finite carrier diffusion time effective capacitance

VCNP=- 4 V

Carrier diffusion time;

2 D N eff

L R C D τ = =

2 eff N

L C R D = =

Effective junction capacitance;

10 - 80 fF

• Supercurrent is gate-voltage dependent
• Asymmetry by the hysteresis

PbIn–G–PbIn Junction Jc(0) ~ 9.4×10-3 A/cm ; record high

VBG Dependence of I c

Heersche et al., Nature 446 56 (2007) Al-G-Al Gate-voltage dependence of Ic

• Large enhancement of Ic

VCNP=- 4 V

• Supercurrent is gate-voltage dependent
• Asymmetry by the hysteresis

PbIn–G–PbIn Junction

T Dependence of I c

Gate-voltage dependence of Ic

VCNP=- 4 V

T dependence of Ic

Gate-voltage-dependent supercurrent

I c vs VBG

Proximity junction with diffusive N layer

• Variation of Ic should follow Gn
• Ic does not vanish even at the CNP
• R does not diverge at the CNP

I (μA) V (μV)

• 200

200

• 3

3 V

bg= -60V

10 5 15

G (mS) Ambegaokar-Baratoff relation

S S S S S S

Magnetic-Field Modulation of I c ( Fraunhofer Pattern)

• Fraunhofer pattern - Ic is modulated by a magnetic field
• Distribution of screening current varies with magnetic field

Shapiro steps - Cooper pairs tunneling in resonance with microwaves

Microw ave Response of JJ – Shapiro Steps

Vbg

Vertical current steps;

1 2 3

• 1
• 2
• 3

n=0 1 2

• 1
• 2

n=0

• D. Jeong et al., Phys. Rev. B 83, 094503 (2011)

Shapiro steps - Cooper pairs tunneling in resonance with microwaves

Microw ave Response of JJ – Shapiro Steps

2 ( )

n n

e I J hf Δ ∝ 2 h e

slope ~ 2.07 μV/GHz =2.12 μV/GHz

dV/dI (a.u.) P1/2 (a.u.) I (μA)

∆Vbg = 60 V

3

• 3

1 1 2 2 3 4

• 4
• 3
• 2
• 2
• 1
• 1

n=0

n=0 1 2 3

• 1
• 2
• 3

Vertical current steps;

Conductance peak at

Multiple Andreev Reflection

Δ=1.1 meV; close to the value of 1.35 meV of bulk Pb n = 3 n= +1, +2, +3…..

1. Pair transport in S–mono-layer graphene–S junctions

– Basic concept – graphene and Josephson coupling – Pair transport in graphene

• 2. Switching current distribution in mono-layer GJJs

– Basic concept – switching current distribution – Gate tuning of different switching regimes – MQT, TA, PD – Observation of quantized levels in washboard potential

• 3. Top-gated bilayer GJJs

– E-field-induced band gap opening – S-I transition in top-gated bilayer GJJs

• 4. Josephson coupling across a graphene p-n potential barrier

– Klein tunneling of Cooper pairs

: Phase particle

Josephson Junction - W ashboard Potential

current-biased RCSJ model washboard potential

Voltage (V) Current (I)

IV characteristics

Voltage (V) Current (I)

Potential Barrier

TA

Γ

MQT

Γ

Josephson Junction - W ashboard Potential

• Switching probability; SC state is switched

to resistive state in a stochastic way

P current-biased RCSJ model

Temperature, T Distribution Width of P(I)

; thermal activation ; MQT (independent of T)

Therm al Activation vs MQT

Switching Rate;

~ several tens GHz

; plasma frequency

P

Phase particle in single JJs Phase particle in stacked JJs Wallraff et al., Nature, 2003 Lee et al., PRB, 2010 Voss et al., PRL, 1981 Devoret et at, PRL, 1985 Inomata et al., PRL, 2005 Jin et al., PRL, 2006 Ueda et al., APL, 2007 Bae et al., PRB, 2009 MQT of a single vortex

A Few of Previous Studies

Jeong et al., PRB, 2011 Lee et al., PRL, 2011 This work; in gate-controlled graphene-based JJs

Sw itching Current Distribution P( I c)

I P

1 2 3 4 5 6 1 2

0.09 K 0.16 K 2.20 K 2.40 K 2.00 K 1.80 K 1.50 K 0.68 K 0.85 K 1.20 K 1.00 K 0.26 K

Counts/10

3

I ( μ A )

0.05 K 0.51 K

Vbg = -60 V

; Phase Diffusion (PD) ; Thermal Activation (TA) ; MQT

100 200 5.6 5.8 6.0 6.2

I (μA) V (μV) 100 switching events PD TA MQT

Sw itching Current Distribution Aw ay from DP

MQT TA PD

2/3

T σ ∝

1 2 3 4 5 6 1 2

0.09 K 0.16 K 2.20 K 2.40 K 2.00 K 1.80 K 1.50 K 0.68 K 0.85 K 1.20 K 1.00 K 0.26 K

Counts/10

3

I ( μ A )

0.05 K 0.51 K

Vbg = -60 V

; Phase Diffusion (PD) ; Thermal Activation (TA) ; MQT

PD TA MQT

Fulton and Dunkleberger, PRB 9, 4760 (1974)

1

( ) ( ) [1 ( ') ']

c

I c c

P I I I P I dI

−

= Γ −∫

1 2 3 4 5 6 10

2

10

3

10

4

10

5

Γ (s

• 1)

I (μA)

}

} }

PD TA MQT PD TA MQT

0.3 0.6 0.9 1.2 0.0 0.5 1.0 1.5

Counts/10

3

I (μA)

Vbg = 0 V

} }

PD TA MQT

}

0.1 1 0.02

SD/Ic0 T (K)

0.028

Vbg = 0 V MQT TA PD

Sw itching Current Distribution near DP

Vbg = -60 V

0.1 1 0.02

SD/Ic0 T (K)

0.028

Vbg = -60 V

P( I c) Near and Aw ay from DP

0.3 0.6 0.9 1.2 0.0 0.5 1.0 1.5

Counts/10

3

I (μA)

Vbg = 0 V

}

}

}

PD TA MQT

1

( ) ( ) [1 ( ') ']

c

I c c

P I I I P I dI

−

= Γ −∫

0.3 0.6 0.9 1.2 0.0 0.5 1.0 1.5

Counts/10

3

I (μA)

Vbg = 0 V

} }

PD TA MQT

}

0.05 0.1 0.5 1 5 0.01 0.02

SD/Ic0 T (K)

Vbg Dependence of Different Escaping Regim es

• Different regimes are identified in a single SGS junction by varying the carrier

density in graphene using Vbg

Gil-Ho Lee, D. Jeong, J.-H. Choi, Y.-J. Doh, and H.-J. Lee, PRL 107, 146605 (2011)

PD TA MQT T = 6 mK H = 4.2 kG

• 20 V
• 15 V
• 10 V

Vbg = 0 V Vbg = -60 V

T*MQT T*TA

PD TA MQT 0.05 0.1 0.5 1 5 0.01 0.02

SD/Ic0 T (K)

T*MQT T*TA

Vbg = -60 V

• 20 V
• 15 V
• 10 V

Vbg = 0 V

Vbg Dependence of Different Escaping Regim es

• Different regimes are identified in a single SGS junction by varying the carrier

density in graphene using Vbg

Gil-Ho Lee, D. Jeong, J.-H. Choi, Y.-J. Doh, and H.-J. Lee, PRL 107, 146605 (2011)

PD TA MQT

Vbg-T phase diagram of GJJ

PD TA MQT

Vbg-T phase diagram of GJJ

}

Energy Level Quantization Probed by MW Excitation

}

}

in the MQT regime

Gil-Ho Lee et al., PRL 107, 146605 (2011)

n = 4 n = 10 5 6 7 8 9

Ir

Possible Realization of Defect-free Qubits

Two-level systems (TLS) in amorphous materials

L R

unwanted resonator

ωr

R.W. Simmonds …., PRL 93, 077003 (2004)

TLS gives unwanted resonance with qubit and additional decoherence.

Single crystalline graphene is free from TLS.

• Different escaping regime, MQT, TA, PD, of phase particles

are accessed by simply varying backgate voltage in a single GJJ.

• Transition between different energy levels by multiphoton

absorption

• Promissing for new quantum information device application

using graphene –based JJ

Sum m ary

1. Pair transport in S–mono-layer graphene–S junctions

– Basic concept – graphene and Josephson coupling – Pair transport in graphene

• 2. Switching current distribution in mono-layer GJJs

– Basic concept – switching current distribution – Gate tuning of different switching regimes – MQT, TA, PD – Observation of quantized levels in washboard potential

• 3. Top-gated bilayer GJJs

– E-field-induced band gap opening – S-I transition in top-gated bilayer GJJs

• 4. Josephson coupling across a graphene p-n potential barrier

– Klein tunneling of Cooper pairs

Lecture will be given for this subject but the note will not provided because the content is currently in preparation for publication.

1. Pair transport in S–mono-layer graphene–S junctions

– Basic concept – graphene and Josephson coupling – Pair transport in graphene

• 2. Switching current distribution in mono-layer GJJs

– Basic concept – switching current distribution – Gate tuning of different switching regimes – MQT, TA, PD – Observation of quantized levels in washboard potential

• 3. Top-gated bilayer GJJs

– E-field-induced band gap opening – S-I transition in top-gated bilayer GJJs

• 4. Josephson coupling across a graphene p-n potential barrier

– Klein tunneling of Cooper pairs

Lecture will be given for this subject but the note will not provided because the content is currently in preparation for publication.

• Prof. Y.-J. Doh

Korea Univ.

• Dr. J.-O Lee

KRICT

• D. Jeong

G.-H. Lee

Acknow ledgm ent

This work was supported by National Research Foundation through SRC – Center for Topological Matter

• Dr. J.-H. Choi

PbIn junction S-I transition Bipolar junction Switching current distribution

• M. Kim

Andreev Spectroscopy

n=1 n=2 n=3 n=4 n=5 Conductance peak at