Quantum Phase Slip Junctions

Transcription

1 Quantum Phase Slip Junctions Joël Peguiron Insitute of Physics, University of Basel Monday Morning Meeting, 24 April

2 Goal Monday Morning Meeting, 24 April

3 Evidence for Thermodynamic Fluctuations in a Superconductor R.D. Parks and R.P. Groff, PRL 18, 342 (1967) Probability of a fluctuation to a non-equilibrium state thickness t width w patch 0.2w*0.2w narrow superconducting strip f (f') current flow close to critical current J c current density around the "normal patch" above critical value time averaged resistance average over patch sizes and locations V T R N ' (non)-equilibrium free energy density volume temperature normal resistance of the region bounded by dashed lines Monday Morning Meeting, 24 April

4 Evidence for Thermodynamic Fluctuations in a Superconductor R.D. Parks and R.P. Groff, PRL 18, 342 (1967) Sn film length 1mm sample E w=10μm t=190nm J c =ΔT 3/2 Ginzburg-Landau without fluctuations sample C w=2.1μm t=58nm narrow R/R N =0.1 R/R N =0.01 from Ginzburg-Landau theory N(0) J(ΔT c )=0 density of states at the Fermi surface (crude) model deviation close to T c =T c -T Monday Morning Meeting, 24 April

5 Model Phys. Rev. 164, 498 (1967) Monday Morning Meeting, 24 April

6 Basic ideas 1) intrinsic resistance finite voltage steady increase of φ 1 -φ 2 no steady state! φ 1 φ 2 narrow superconducting channel 2) framework "A steady current is possible, however, if fluctuations in the interior of the superconductor reduce the phase difference at the same average rate as the voltage increases it." state of the system described by a parameter ψ(r) probability to find the system in a given state F { r } P exp k B T Concept of phase slip rate of transition from ψ to a neighboring minimum ψ' thermal activation over a barrier in function space barrier height ~ lowest saddle-point F Ginzburg-Landau free energy Monday Morning Meeting, 24 April

7 Free energy functional Ginzburg-Landau theory magnetic field negligible for the evaluation of the stationary solutions the barrier height validity: width w << penetration depth 1D: r x Monday Morning Meeting, 24 April

8 Local minima Uniform constant-current solutions k allowed wave-vector fixed by φ 1 -φ 2 up to 2π/L local minima of F Current carried maximal for k c =(α/3) 1/2 critical current Monday Morning Meeting, 24 April

9 Energy barrier F{ψ} δf 0 δf 1 k 2 L k in allowed finctional space transition rate: thermal activation δf 1 : evaluation from minimal solutions Ω attempt frequency δf 0 : estimation from the saddle-point solution of lower energy Monday Morning Meeting, 24 April

10 Results saddle-point solution energy difference between minima F 1 = h 2 e I mean barrier height work I V dt done in the phase slip process F 0 = H c 2 2 A condensation energy density A=tw cross-section of the channel ξ coherence length Monday Morning Meeting, 24 April

11 I-V characteristics phase-slip rate d 12 d t = [ exp F 0 F 1 /2 k B T exp F 0 F 1 /2 k B T ] phase slip amplitude 2π included rate k k-2π/l rate k k+2π/l V = ħ 2e d 12 d t V = ħ e exp F 0 k B T sinh h I 4 ek B T F 1 = h 2 e I attempt frequency = L F 0 k B T 1/ 2 1 s τ s characteristic relaxation time in time-dependent Ginzburg-Landau theory D.E. McCumber and B.I. Halperin, PRB 1, 1054 (1970) Monday Morning Meeting, 24 April

12 Experimental verification J.E. Lukens, R.J. Warburton, and W.W. Webb, PRL 25, 1180 (1970) R.S. Newbower, M.R. Beasley, and M. Tinkham, PRB 5, 864 (1972) M. Tinkham, Introduction to Superconductivity, 2nd ed. (1996) Monday Morning Meeting, 24 April

13 Quantum phase slip phase slip thermal activation over the barrier quantum phase slip tunneling signatures persistance/crossover at low temperatures coherent processes phase slip flux qubit Mooij & Harmans, New J. Phys. 7, 219 (2005) quantum phase slip junctions Mooij & Nazarov, Nat. Phys. 2, 169 (2006) Monday Morning Meeting, 24 April

14 Evidence for Macroscopic Quantum Tunneling in One-Dimensional Superconductors N. Giordano, PRL 61, 2137 (1988) total probability of escape ~ thermal activation + tunneling strong damping limit R MQT determined by a rate of the form α 0 β dimensionless damping factor assumed temperature-independent unknown constant (close to unity) artifact due to granularity? also seen in MoGe wires deposited on suspended carbon nanotubes Lau et al., PRL 87, (2001) Monday Morning Meeting, 24 April

15 Further developments Include electromagnetic interaction of phase slip events Model based on the effective action of a BCS superconductor metal to superconductor transition at μ=2 μ: dimensionless admittance (quantum phase transition at T=0) of the wire μ 50 r 0 /λ L r 0 : diameter of the wire A.D. Zaikin et al., PRL 78, 1552 (1997) Include electromagnetic environment former quantum phase transition becomes a crossover new quantum phase transition as a function of dissipation H.P. Büchler et al., PRL 92, (2004) Monday Morning Meeting, 24 April

16 Concept of quantum phase slip junction Energy levels of a superconducting loop Φ E n = L f n 2 f=φ/φ 0 n fluxoid number L inductance with a thin superconducting wire Φ phase slips induce a coupling E S H = [ 1 n L f n 2 n n E S 2 n 1 n n n 1 ] Equivalent circuit Phase slip flux qubit: dual of the Cooper pair box Monday Morning Meeting, 24 April

17 Phase slip junction E= E S 2 n n 1 n n n 1 = E S cos2 q Dual of the Josephson junction coupling E S phase slip rate Γ QPS E= E J 2 n n 1 n n n 1 = E J cos Applications "remake" all circuits containing Josephson junctions: SQUID,... current standard from current Shapiro steps Monday Morning Meeting, 24 April

18 Conclusion Monday Morning Meeting, 24 April