Superconducting Pair Transport in S Graphene S G CNRS-EWHA Winter School 2012 Feb. 9, 2012; Ewha Womans Univ. Hu-Jong Lee Physics, POSTECH Quantum Transport and Superconductivity Laboratory Center for Topological Matter
Outline Pair transport in S – mono-layer graphene – S junctions 1. – 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 Patterning Zero dimension One dimension Functionality
Graphene graphene lattice SP 2 covalent hybrid orbital of a carbon atom π ‘A’ sublattice σ ‘B’ sublattice a 1 a ° 2 2.46 A π -orbital σ -bond Two equivalent sublattices Two atoms per unit cell (real space)
Band Structure and Low -Energy Dispersion K M r = υ h E k F Γ E F K’ • Dirac cone • Linear dispersion at zero energy - Massless relativistic Dirac fermions υ - But moving with Fermi velocity F - Carrier type and density are easily controlled by gating
Chirality or Pseudospin in Graphene Lattice E E electron-like k y K ’ K k x k x hole-like pseudospin or chirality Chirality – momentum-locked phase value of a carrier in graphene when the carrier moves along a Dirac cone (or the sublattice index)
Graphene Preparation – Mechanical Exfoliation exfoliated graphene on Si sub natural graphite 2 3 1 10 μ m thin graphite on tape transferring graphene onto Si substrate
Graphene Preparation – Mechanical Exfoliation 10 μ m 10 μ m 10 μ m 10 μ m
Pair transport in S – mono-layer graphene – S junctions 1. – 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 Effect V Josephson relations; S I S L R ψ ψ I L R High-freq. Josephson oscillation; ; Josephson coupling strength I c Δ ; SC strength in electrodes
Graphene-based Josephson Junction SC Paring Condition; - opposite momentum (k, -k) in two different valleys - opposite spins ( ) K K’ S S G Heersche et al., Nature 446 56 (2007) - Finite supercurrent for d < ξ - Supercurrent is carried either by electron-like carriers in the conduction band or by hole-like carriers in the valence band
Supercurrent in Graphene – Josephson Effect SC Paring Condition; - opposite momentum (k, -k) in two different valleys - opposite spins ( ) Heersche et al., Nature 446 56 (2007) S V bg = -50 V CNP S G +1 V Al-G-Al -7.5 V Heersche et al., Nature 446 56 (2007) - Josephson coupling is modulated by backgating - Al electrodes; low T c (=1.2 K) small gap Δ (=0.17 meV) - Josephson device applications ; higher-gap electrodes are required
Sam ple PbI n-G-PbI n Junction T = 6 mK T c = 7 K H = 4.2 kG μ = 1400 cm 2 /Vs @ V bg =-50 V monolayer graphene Finite resistance at V CNP Pb 0.93 In 0.07 –G–Pb 0.93 In 0.07 junction - PbIn/Au (200/10 nm) - spacing btw electrodes = 300 nm
Hysteresis in I V Characteristics - IV curve is hysteretic – underdamped tunneling JJ - Finite carrier diffusion time effective capacitance Carrier diffusion time; 2 L τ = = R C D N eff D Effective junction capacitance; 2 L = = C 10 - 80 fF eff R D N 3 PbIn–G–PbIn 2 V bg = -60 V Junction 1 V CNP =- 4 V I ( μ A) 0 -1 -2 -3 -200 -100 0 100 200 V ( μ V)
V BG Dependence of I c - Asymmetry by the hysteresis - Supercurrent is gate-voltage dependent - Large enhancement of I c Heersche et al., Nature 446 56 (2007) Gate-voltage dependence of I c PbIn–G–PbIn Al-G-Al Junction V CNP =- 4 V J c (0) ~ 9.4 × 10 -3 A/cm ; record high
T Dependence of I c - Asymmetry by the hysteresis - Supercurrent is gate-voltage dependent Gate-voltage dependence of I c T dependence of I c PbIn–G–PbIn Junction V CNP =- 4 V
I c vs V BG Gate-voltage-dependent supercurrent 15 10 G (mS) 5 3 V bg = -60V I ( μ A) 0 0 -3 -200 0 200 V ( μ V) Proximity junction with diffusive N layer - Variation of I c should follow G n - I c does not vanish even at the CNP Ambegaokar-Baratoff relation - R does not diverge at the CNP
Magnetic-Field Modulation of I c ( Fraunhofer Pattern) S S S S S S - Fraunhofer pattern - I c is modulated by a magnetic field - Distribution of screening current varies with magnetic field
Microw ave Response of JJ – Shapiro Steps Shapiro steps - Cooper pairs tunneling in resonance with microwaves D. Jeong et al ., Phys. Rev. B 83, 094503 (2011) 2 3 V bg 2 1 1 n =0 n =0 -1 -1 -2 -2 -3 Vertical current steps;
Microw ave Response of JJ – Shapiro Steps Shapiro steps - Cooper pairs tunneling in resonance with microwaves 3 ∆ V bg = 60 V 4 3 dV/dI (a.u.) 3 2 2 2 I ( μ A) 1 1 1 -1 0 n =0 n =0 -1 -1 -2 -2 -2 -3 -3 slope ~ 2.07 μ V/GHz -4 h =2.12 μ V/GHz 2 e -3 P 1/2 (a.u.) 2 e Δ ∝ I J ( ) n n hf Vertical current steps;
Multiple Andreev Reflection n = 3 n = +1, +2, +3….. Conductance peak at Δ =1.1 meV; close to the value of 1.35 meV of bulk Pb
Pair transport in S – mono-layer graphene – S junctions 1. – 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 Junction - W ashboard Potential current-biased RCSJ model washboard potential IV characteristics Current (I) : Phase particle Voltage (V)
Josephson Junction - W ashboard Potential current-biased RCSJ model - Switching probability; SC state is switched to resistive state in a stochastic way P Γ Current (I) TA Potential Barrier Γ MQT Voltage (V)
Therm al Activation vs MQT Switching Rate; ; thermal activation ; MQT (independent of T ) P Distribution Width of P(I) ; plasma frequency ~ several tens GHz Temperature, T
A Few of Previous Studies Phase particle in single JJs Voss et al., PRL, 1981 Devoret et at, PRL, 1985 MQT of a single vortex Wallraff et al., Nature, 2003 Lee et al., PRB, 2010 Phase particle in stacked JJs Inomata et al., PRL, 2005 Jin et al., PRL, 2006 Ueda et al., APL, 2007 Bae et al., PRB, 2009 This work; in gate-controlled graphene-based JJs Jeong et al., PRB, 2011 Lee et al., PRL, 2011
Sw itching Current Distribution P ( I c ) ; Phase Diffusion (PD) ; Thermal Activation (TA) ; MQT MQT PD TA 2.40 K 2 V bg = -60 V 2.20 K 6.2 P 0.26 K 3 Counts/10 0.16 K 2.00 K 6.0 I ( μ A) 0.09 K 0.51 K 0.68 K 1 0.85 K 0.05 K 1.00 K 1.20 K 1.50 K 1.80 K 5.8 I 5.6 0 100 200 0 V ( μ V) 1 2 3 4 5 6 I ( μ A ) 100 switching events
Sw itching Current Distribution Aw ay from DP ; Phase Diffusion (PD) ; Thermal Activation (TA) ; MQT MQT PD TA 2.40 K 2 V bg = -60 V 2.20 K 0.26 K 3 Counts/10 0.16 K σ ∝ 2.00 K 2/3 T 0.09 K 0.51 K 0.68 K 1 0.85 K 0.05 K 1.00 K 1.20 K 1.80 K 1.50 K 0 1 2 3 4 5 6 MQT TA PD I ( μ A )
MQT PD TA } − ∫ I } } = Γ − c 1 P I ( ) ( ) I I [1 P I dI ( ') '] c c 0 MQT PD TA Fulton and Dunkleberger, 5 10 PRB 9, 4760 (1974) 4 10 -1 ) Γ (s 3 10 2 10 1 2 3 4 5 6 I ( μ A)
Sw itching Current Distribution near DP PD } 1.5 V bg = 0 V 0.028 TA } MQT 3 1.0 } Counts/10 0.02 MQT TA PD SD/I c0 0.5 V bg = 0 V 0.0 0.1 1 0.3 0.6 0.9 1.2 I ( μ A) T (K)
P ( I c ) Near and Aw ay from DP V bg = -60 V V bg = -60 V 1.5 V bg = 0 V 0.028 3 1.0 Counts/10 0.02 SD/I c0 0.5 0.0 0.1 1 0.3 0.6 0.9 1.2 T (K) I ( μ A)
− ∫ I = Γ − c 1 P I ( ) ( ) I I [1 P I dI ( ') '] MQT PD TA } } } c c 0 PD } 1.5 V bg = 0 V TA } MQT 3 1.0 } Counts/10 0.5 0.0 0.3 0.6 0.9 1.2 I ( μ A)
V bg Dependence of Different Escaping Regim es Gil-Ho Lee, D. Jeong, J.-H. Choi, Y.-J. Doh, and H.-J. Lee, PRL 107 , 146605 (2011) MQT TA PD V bg = 0 V T = 6 mK 0.02 H = 4.2 kG SD/I c0 -10 V -15 V T* TA 0.01 -20 V V bg = -60 V T* MQT 0.05 0.1 0.5 1 5 T (K) - Different regimes are identified in a single SGS junction by varying the carrier density in graphene using V bg
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