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.
D. J. Thouless, Quantization of particle transport, Phys. Rev. B , 1983, 27(10): 6083 doi: 10.1103/PhysRevB.27.6083
2
M. Switkes, C. M. Marcus, K. Campman, and A. C. Gossard, An adiabatic quantum electron pump, Science , 1999, 283(5409): 1905 doi: 10.1126/science.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 doi: 10.1103/RevModPhys.82.1959
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 doi: 10.1007/BF01307664
5
P. W. Brouwer, Scattering approach to parametric pumping, Phys. Rev. B , 1998, 58(16): R10135 doi: 10.1103/PhysRevB.58.R10135
6
Q. Niu, Towards a quantum pump of electric charges, Phys. Rev. Lett. , 1990, 64(15): 1812 doi: 10.1103/PhysRevLett.64.1812
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 doi: 10.1103/PhysRevB.56.15180
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 doi: 10.1103/PhysRevB.80.165311
9
A. Agarwal and D. Sen, Equation of motion approach to non-adiabatic quantum charge pumping, J. Phys.: Condens. Matter , 2007, 19(4): 046205 doi: 10.1088/0953-8984/19/4/046205
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 doi: 10.1103/PhysRevB.78.085130
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 doi: 10.1088/0268-1242/25/2/024013
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 doi: 10.1103/PhysRevB.79.235442
13
R. Citro and F. Romeo, Pumping in a mesoscopic ring with Aharonov–Casher effect, Phys. Rev. B , 2006, 73(23): 233304 doi: 10.1103/PhysRevB.73.233304
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 doi: 10.1103/PhysRevLett.109.106402
15
Y. D. Wei, J. Wang, and H. Guo, Resonance-assisted parametric electron pump, Phys. Rev. B , 2000, 62(15): 9947 doi: 10.1103/PhysRevB.62.9947
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 doi: 10.1016/j.physleta.2013.01.041
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) doi: 10.1103/PhysRevB.66.201305
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 doi: 10.1103/PhysRevB.65.153311
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 doi: 10.1103/PhysRevLett.96.146802
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 doi: 10.1103/PhysRevLett.99.086601
21
R. Zhu and H. Chen, Quantum pumping with adiabatically modulated barriers in graphene, Appl. Phys. Lett. , 2009, 95(12): 122111 doi: 10.1063/1.3236785
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 doi: 10.1088/0953-8984/23/45/455302
23
E. Prada, P. San-Jose, and H. Schomerus, Quantum pumping in graphene, Phys. Rev. B , 2009, 80(24): 245414 doi: 10.1103/PhysRevB.80.245414
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 doi: 10.1103/PhysRevB.83.165451
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 doi: 10.1103/PhysRevB.84.073402
26
M. Moskalets and M. Büttiker, Dissipation and noise in adiabatic quantum pumps, Phys. Rev. B , 2002, 66(3): 035306 doi: 10.1103/PhysRevB.66.035306
27
M. Moskalets and M. Büttiker, Magnetic-field symmetry of pump currents of adiabatically driven mesoscopic structures, Phys. Rev. B , 2005, 72(3): 035324 doi: 10.1103/PhysRevB.72.035324
28
M. Moskalets and M. Büttiker, Time-resolved noise of adiabatic quantum pumps, Phys. Rev. B , 2007, 75(3): 035315 doi: 10.1103/PhysRevB.75.035315
29
M. Büttiker, A. Prêtre, and H. Thomas, Dynamic conductance and the scattering matrix of small conductors, Phys. Rev. Lett. , 1993, 70(26): 4114 doi: 10.1103/PhysRevLett.70.4114
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 doi: 10.1103/PhysRevB.62.R10618
31
W. W. Kim, Floquet formalism of quantum pumps, Int. J. Mod. Phys. B , 2004, 18(23): 3071 doi: 10.1142/S0217979204026317
32
R. Zhu, A scattering matrix approach to quantum pumping: Beyond the small-AC-driving-amplitude limit, Chinese Phys. B , 2010, 19(12): 127201 doi: 10.1088/1674-1056/19/12/127201
