1. S. Y. Hsu ( 許世英 ) and K. M. Liu( 劉凱銘 ) May 29, 2007 NSC95-2112-M-009-040 and NSC94-2120-M-009-002 Department of Electrophysics, National Chiao Tung University Hsinchu, Taiwan

2. I e-e- A coherent electron system I PRB 27, 6083 (1983) Pumping in a Quantum Device left reservoir right reservoir V(t) DC current A phenomena when the dc current is generated in the system with the local perturbation only, without a global driving (bias). Quantum system Thouless pump : a traveling wave

3. Introduction  2DEG  Gate-confined nanostructures  Historical review on charge pumping Experimental results and discussion  Pumping and Rectification in our QD Summary

4. E1E1 energy EcEc EfEf 0.2eV Structure of GaAs/AlGaAs grown by MBE 10 nm, GaAs Cap 15 nm, δ- doping layer, Si, 2.6x10 18 cm -2 60 nm, spacer AlGaAs x=0.37 1500 nm, buffer layer GaAs 0.3mm GaAs substrate 8 nm, spacer AlGaAs 2DEG Two Dimensional Electron Gas Our wafers were grown by Dr.Umansky in Heiblum’s group at Wiezmann Institute in Israel. GaAs/AlGaAs 0.3K carrier density n s 2.4x10 11 cm -2 mobility  1.8x10 6 cm 2 /Vs Fermi wavelength λ F 51.4 nm mean free path e ~14  m 2DEG specification The 2DEG systems are generally formed by GaAs/AlGaAs heterostructure and contain a thin conducting layer in the interface.

5. Photo-lithographyE-beam lithography 0.5  m 190  m metal gates contact pads mesa

6. Gate confined nanostructures Applying negative voltages on the metal gates fabricated above a two dimensional electron gas(2DEG), a quasi-1D quantum conductor is formed. e-e- SourceDrain VgVg Three dimensional representation of V. For a parabolic confining potential Energy dispersion for 1D channel E n (for n=1,2,3) vs. longitudinal wavevector k x. Electrons in the source and drain fill the available states up to chemical potentials  s and  d, respectively. kxkx

7. 1D 2D T=0.3K Split gates confined QPC : d gap =0.3  m and channel =0.5  m Two terminal Landauer formula Each plateau corresponds to an additional mode as integer multiples of half the Fermi wavelength N : integer N

8. Quantum dots can be formed by placing two quantum point contacts in series in between source and drain and confining electrons in between to a small area characterized by F <L< . A coherent system

9. Quantized Pumping in narrow channel using SAWs I=nef, f=2.728GHz Pinched-off regime SAW generating transducer 2DEG Split gate A -Shilton et al., J. Phys. C. 8, L531(1996), PRB62, 1564 (2000). Surface Acoustic Waves  Electrons reside in potential valleys and are carried by the SAW.  Each plateau corresponds to a discrete number of electrons in an electron packet.

10. Adiabatic Charge Pumping in a QD For an open confined cavity with two parameters modifying wavefunction with a phase shift , use S-matrix and treat the ac field as a weak perturbation PRB 58, 10135 (1998). Brouwer (1998) V ac,1 sin(  t) V ac,2 sin(  t+  ) The charge  Q(m) entering or leaving the cavity through contact m(m=1,2) in an infinitesimal time: emissivity After Fourier Transform, integrating over one period and change of variables

11. Electron pumping in an open dot using two RF signals Switkes et al., Science 283, 1905 (1999) V ac sin(  t) V ac sin(  t+  ) V(  )  sin(  ) I bias =0 σ(A 0 )  f. s lope~3pA/MHz (20 electrons/cycle) For small driving amplitude, σ(A 0 )  V ac 2.

13. Rectification of displacement currents Brouwer, PRB63, 12130 (2001). Equivalent circuit for the experiment of Switkes et al.. The two ac gates coupled to the reservoir via stray capacitances C 1 and C 2. At low frequency, ac X 1 and X 2 generate displacement current through the dot. Average over one period,

14. qpc1 qpc2 V g1 V g2 The quantized conductance of each QPC is clearly present. Quantum dot is formed by placing two QPCs in series. We can adjust transmission mode number N=(n 1, n 2 ) for the “open” quantum dot. n 1 : mode number on the left QPC n 2 : mode number on the right QPC Experimental details

15. V ac sin(  t+  2 ) V ac sin(  t+  1 ) A 1m1m FG qpc2 qpc1  V ac sin(  t+  2 ) V sd sin(  t+  1 ) A 1m1m FG qpc2 qpc1  Measurements : Low frequency modulation technique (1) Pumping mode(2) Rectification mode A typical plot of I(  ).

16. reservoir I I’=? wider V ac1 sin(  t) V ac2 sin(  t+  ) V ac1 sin(  t) V ac2 sin(  t+  )

17. Experimental results DC current amplitude I p & I rect vs. ac driving frequency f for different couplings between dot and its reservoir. (n 1, n 2 ). DC current amplitude I p & I rect vs. ac driving amplitude V ac

18. Pumped current amplitude I p vs. ac driving amplitude V ac It’s in weak pumping regime. I p  V ac 2, in good agreement with the theoretical prediction. The relation extends well over a very wide current range, 3 orders in magnitude. Good resolution as small as few pA.

19. Rectification current amplitude I rect vs. V ac Consistent with the theoretical prediction.

20. I p is roughly linearly dependent with frequency. I p is smaller for larger N tot. V ac =15mV Pumped current amplitude I p vs. ac driving frequency f for different (n 1, n 2 )

21. I rect decreases with f for f  1MHz and slightly increases with f for f>1MHz. I rect increases with N (conductance), but saturates for N tot  4. Rectification current amplitude I rec vs. ac driving frequency f for different (n 1, n 2 )

22. Dependence of I p on the coupling bet. dot and its environments Comparing with (1,1) trace, multiply other traces with a factor (n 1 +n 2 )/2 I p is scaling with the ratio between mode numbers.

23. Why do n 1 and n 2 influence I p ? The escaping rate of electron in the dot n 1 and n 2 are transmission mode numbers of both “entrance” leads of the “open” dot, respectively.  For the larger mode number, electrons have stronger coupling strength between dot and reservoirs. With shorter dwell time, the coherent effect is reduced. Therefore, quantum pumping is suppressed w/. increasing N tot.  The escaping rate  esc increases with mode number linearly, and electrons are more likely to escape to the reservoirs.

24. The dc current characteristics of pumping and rectification effects are drastically different in our systems. Summary The pumping current decreases with increasing transmission mode numbers of the two QPCs due to the dephasing of the coherent electrons in the dot by rapid motions of entering and leaving the dot. The observed DC current in the pumping mode is mainly from the pumping effect. symmetric arrangement of pumping gates relative to both entrance leads of the dot

25. Acknowledgments: Dr. C.S. Chu (Theoretical support) Dr. V. Umansky (High mobility 2DEG support)