Anharmonic effect of adiabatic quantum pumping

Abstract

Based on the scattering matrix approach, we systematically investigate the anharmonic effect of the pumped current in double-barrier structures with adiabatic time-modulation of two sinusoidal AC driven potential heights. The pumped current as a function of the phase difference between the two driven potentials looks like to be sinusoidal, but actually it contains sine functions of double and more phase difference. It is found that this kind of anharmonic effect of the pumped current is determined combinedly by the Berry curvature and parameter variation loop trajectory. Therefore small ratio of the driving amplitude and the static amplitude is not necessary for harmonic pattern in the pumped current to dominate for smooth Berry curvature on the surface within the parametervariation loop.

Graphical abstract

Keywords

quantum pumping / anharmonic effect / Berry curvature / instant scattering matrix expansion

References

[1] D. J. Thouless, Quantization of particle transport, Phys. Rev. B, 1983, 27(10): 6083

[2] M. Switkes, C. M. Marcus, K. Campman, and A. C. Gossard, An adiabatic quantum electron pump, Science, 1999, 283(5409): 1905

[3] D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys., 2010, 82(3): 1959

[4] M. Büttiker, H. Thomas, and A. Prêtre, Current partition in multiprobe conductors in the presence of slowly oscillating external potentials, Z. Phys. B, 1994, 94(1-2): 133

[5] P. W. Brouwer, Scattering approach to parametric pumping, Phys. Rev. B, 1998, 58(16): R10135

[6] Q. Niu, Towards a quantum pump of electric charges, Phys. Rev. Lett., 1990, 64(15): 1812

[7] V. I. Talyanskii, J. M. Shilton, M. Pepper, C. G. Smith, C. J. B. Ford, E. H. Linfield, D. A. Ritchie, and G. A. C. Jones, Single-electron transport in a one-dimensional channel by high-frequency surface acoustic waves, Phys. Rev. B, 1997, 56(23): 15180

[8] F. Romeo and R. Citro, Adiabatic pumping in a double quantum dot structure with strong spin-orbit interaction, Phys. Rev. B, 2009, 80(16): 165311

[9] A. Agarwal and D. Sen, Equation of motion approach to non-adiabatic quantum charge pumping, J. Phys.: Condens. Matter, 2007, 19(4): 046205

[10] P. Devillard, V. Gasparian, and T. Martin, Charge pumping and noise in a one-dimensional wire with weak electron– electron interactions, Phys. Rev. B, 2008, 78(8): 085130

[11] S. Roddaro, E. Strambini, L. Romeo, V. Piazza, K. Nilsson, L. Samuelson, and F. Beltram, Charge pumping in InAs nanowires by surface acoustic waves, Semicond. Sci. Technol., 2010, 25(2): 024013

[12] X. L. Qi and S. C. Zhang, Field-induced gap and quantized charge pumping in a nanoscale helical wire, Phys. Rev. B, 2009, 79(23): 235442

[13] R. Citro and F. Romeo, Pumping in a mesoscopic ring with Aharonov–Casher effect, Phys. Rev. B, 2006, 73(23): 233304

[14] Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Topological states and adiabatic pumping in quasicrystals, Phys. Rev. Lett., 2012, 109(10): 106402

[15] Y. D. Wei, J. Wang, and H. Guo, Resonance-assisted parametric electron pump, Phys. Rev. B, 2000, 62(15): 9947

[16] Y. C. Xiao, W. Y. Deng, W. J. Deng, R. Zhu, and R. Q. Wang, Quantum pump in a system with both Rashba and Dresselhaus spin–orbit couplings, Phys. Lett. A, 2013, 377(10-11): 817

[17] B. G. Wang and J. Wang, Optimal quantum pump in the presence of a superconducting lead, Phys. Rev. B, 2002, 66(20): 201305(R)

[18] J. Wang and B. G. Wang, Quantization of adiabatic pumped charge in the presence of superconducting lead, Phys. Rev.B, 2002, 65(15): 153311

[19] N. B. Kopnin, A. S. Melnikov, and V. M. Vinokur, Resonance energy and charge pumping through quantum SINIS contacts, Phys. Rev. Lett., 2006, 96(14): 146802

[20] S. Russo, J. Tobiska, T. M. Klapwijk, and A. F. Morpurgo, Adiabatic quantum pumping at the josephson frequency, Phys. Rev. Lett., 2007, 99(8): 086601

[21] R. Zhu and H. Chen, Quantum pumping with adiabatically modulated barriers in graphene, Appl. Phys. Lett., 2009, 95(12): 122111

[22] R. Zhu and M. L. Lai, Pumped shot noise in adiabatically modulated graphene-based double-barrier structures, J. Phys.: Condens. Matter, 2011, 23(45): 455302

[23] E. Prada, P. San-Jose, and H. Schomerus, Quantum pumping in graphene, Phys. Rev. B, 2009, 80(24): 245414

[24] A. Kundu, S. Rao, and A. Saha, Quantum charge pumping through a superconducting double barrier structure in graphene, Phys. Rev. B, 2011, 83(16): 165451

[25] M. Alos-Palop and M. Blaauboer, Adiabatic quantum pumping in normal-metal–insulator–superconductor junctions in a monolayer of graphene, Phys. Rev. B, 2011, 84(7): 073402

[26] M. Moskalets and M. Büttiker, Dissipation and noise in adiabatic quantum pumps, Phys. Rev. B, 2002, 66(3): 035306

[27] M. Moskalets and M. Büttiker, Magnetic-field symmetry of pump currents of adiabatically driven mesoscopic structures, Phys. Rev. B, 2005, 72(3): 035324

[28] M. Moskalets and M. Büttiker, Time-resolved noise of adiabatic quantum pumps, Phys. Rev. B, 2007, 75(3): 035315

[29] M. Büttiker, A. Prêtre, and H. Thomas, Dynamic conductance and the scattering matrix of small conductors, Phys. Rev. Lett., 1993, 70(26): 4114

[30] J. E. Avron, A. Elgart, G. M. Graf, and L. Sadun, Geometry, statistics, and asymptotics of quantum pumps, Phys. Rev. B, 2000, 62(16): R10618

[31] W. W. Kim, Floquet formalism of quantum pumps, Int. J. Mod. Phys. B, 2004, 18(23): 3071

[32] R. Zhu, A scattering matrix approach to quantum pumping: Beyond the small-AC-driving-amplitude limit, Chinese Phys. B, 2010, 19(12): 127201

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg