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Charge pumping in mesoscopic systems coupled to a superconducting lead

Charge pumping in mesoscopic systems coupled to a superconducting lead. In collaboration with: E.J. Heller (Harvard) Yu.V. Nazarov (Delft). Workshop on “Mesoscopic Physics and Electron Interaction”, Trieste, 1 July 2002. Outline. • Pumping • Pumping of charge

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Charge pumping in mesoscopic systems coupled to a superconducting lead

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  1. Charge pumping in mesoscopic systems coupled to a superconducting lead In collaboration with: E.J. Heller (Harvard) Yu.V. Nazarov (Delft) Workshop on “Mesoscopic Physics and Electron Interaction”, Trieste, 1 July 2002

  2. Outline • • Pumping • • Pumping of charge • • Pumping of charge in presence of superconductivity • Application: Nearly-closed quantum dot • Conclusions

  3. U(x) = U sin(2x/a) 0 U(x+vt) = U sin(2x/a) cos(2t/T) + U cos(2x/a) sin(2t/T) 0 0 Adiabatic pumping of particles Idea behind pumping : to generate motion of particles by slow periodic modulations of their environment, e.g. their confining potential or a magnetic field. Thouless pump, 1983 : adiabatic transport of electrons in 1D periodic potential For moving potential, every minimum is shifted by a after each period T: Superposition of two standing waves with a phase difference can produce pumping

  4. Archimedean screw More than 2000 years old, used for pumping water ‘s Hertogenbosch, Netherlands

  5. 2DEG leads gates Pumping of charge through quantum dots Marcus group webpage Coulomb blockade turnstile • Electrons transported one by • one, pumped charge is quantized • “classical”pumping Kouwenhoven et al., PRL 67, 1626 (1992) Pothier et al., Europhys. Lett. 17, 249 (1992)

  6. Physical picture :a small change of system parameters X during a time t leads to a redistribution of charge Q within the system, due to changing electrostatic landscape. This produces electron flows I = Q /t i i i i Open quantum dots Spivak et al, PRL 51, 13226 (1995) The pumped charge depends on the interference of electron wavefunctions in the system.

  7. X (t) = X sin(t) X (t) = X sin(t + ) 1 1 2 2 Theory of quantum pumping [ Brouwer, PRB 58, R10135 (1998); Aleiner et al., PRL 81, 1286 (1998); Zhou, PRL 82, 608 (1999) ] Idea : view as transmission problem, and describe current in terms of the scattering matrix S of the system Conductance :Landauer formula Pumping : Brouwer, PRB 58, R10135 (1998)

  8. Quantum pumping experiment Switkes et al., Science 283, 1905 (1999) Experimental set-up, open quantum dot Redgates control the conductance of the point contacts Black gates are used for pumping Pumped current vs. phase difference 

  9. i Assume : 1. constant pair potential (r) =  e 2. ideal NS interface, i.e. no specular reflection for energies 0 <  <  0 0 Quantum pumping in the presence of superconductivity Presence of a superconductor introduces Andreev reflection :electron-to-hole reflection at the interface between a normal metal and a superconductor Phase coherent reflection: hole travels back along (nearly) the same path where the electron came from

  10. Pumped current into the normal lead : Blaauboer, PRB 65, 235318 (2002)

  11. T ,T « 1 and k T <  « : transport via resonanttransmission 1 2 B Applications : 1. Nearly-closed quantum dot Energy landscape Δ : level spacing  : level broadening Conductance: two normal leads Breit-Wigner formula one normal and one superconducting lead Beenakker, PRB 46, 12841 (1992)

  12. V : shape changing voltages , 1 2 Comparison I / I vs. at resonance for T = T N NS 1 2 G /G NS N G /G = 2 NS N I / I = 4 NS N Pumped current : Doubling of conductance due to presence of the holes Quadruplingof the pumped current due to presence of holes + absence of bias

  13. G /G < 2 NS N I /I = it depends NS N 4.23 for T = 1.26 T (maximum) 2 1 « 1 for T « T 2 1 Pumped current peak heights at higher temperatures, I / I  « k T «  N NS B I / I = 2.55 (maximum) N,peak NS,peak Comparison G / G vs. at resonance for T  T 2 1 NS N

  14. Conclusions • Presence of Andreev reflection enhances or reduces • the pumped current through quantum dots by a factor • varying from ~ 4.23 to « 1 • For dots with symmetric tunnel coupling to the leads • the enhancement is a factor of 4

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