Mesoscopic Mechanism of Adiabatic Charge Transport

Abstract

We consider adiabatic charge transport through mesoscopic metallic samples caused by a periodically changing external potential. We find that both the amplitude and the sign of the charge transferred through a sample per period are random sample specific quantities. The characteristic magnitude of the charge is determined by the quantum interference. [S0031-9007(98) PACS numbers: 72.15.Rn Let us apply an external potential f͑r, t͒, which is changing slowly and periodically in time to a metallic sample. This potential causes finite net charge Q transported across the sample per period. This phenomenon, known as adiabatic charge transport [1], has been investigated in several papers [1][2][3][4] for a closed system characterized by its ground state wave function corresponding to the instantaneous value of the external potential f͑r, t͒. However, in real experimental situations exact eigenfunctions of electrons are ill defined: The electron energy levels are broadened due to inelastic processes at T fi 0, and, in the case of an open system, are further broadened due to finite dwell time.Here we present a theory of adiabatic charge transport in "open mesoscopic systems." We demonstrate that at low T both the magnitude and the sign of Q are sample specific quantities. The typical value of Q in disordered (chaotic) systems turns out to be determined by quantum interference effects. We evaluate this value and find that it is much larger than the one in ballistic systems. This enhancement manifests of the well-known fact that at low temperatures, all electronic characteristics of mesoscopic samples are extremely sensitive to changes in the scattering potential [5][6][7][8].Let us start with a qualitative picture of the mesoscopic adiabatic charge transport. The wave functions of electrons in disordered systems exhibit sample specific spatial fluctuations. Therefore, the spatial electron density profile is changing slowly in time, together with the external potential f͑r, t͒. According to the continuity relation, variation of the charge density in time requires currents in the system. The question arises: What is the condition for a total charge transfer during one period to be nonzero? Let the pumping potential f͑r, t͒ be characterized by a finite set of functions g͑t͒ ͕g a ͑t͖͒, a 1, . . . , m, which are periodic with the same period t 0 :f͑r, t͒ f͑ ͑ ͑r, g͑t͒͒ ͒ ͒ X a f a ͑r͒g a ͑t͒ .The time evolution of the functions g͑t͒ represents a motion of a point in m dimensional space M . Because of the periodicity of f͑r, t͒, the trajectory C of this point is closed. The above-mentioned currents lead to Q fi 0, provided C encloses a finite area in M. This requires that m $ 2.To calculate Q we will use the Keldysh technique for the Green function matrix equation [9] ͑i≠ t 2 H 0 2 f͑r, t͒͒Ĝ͑r, rwhereĜ is a 2 3 2 matrix, G 11 0, G 12 G A , G 21 G R , and G 22 G K , with G R,A,K being the retarded, advanced, and Keldysh Green functions, respectively. H 0 is the Hamiltonian for electrons which includes impurity scattering po...

Parametric pumping at finite frequency

“…(3,4) in connection to the experimental data of Ref. 2, let's first examine the low frequency limit of these results and show that the conventional parametric pumping theory is recovered 3,4 .…”

“…Even in the weaker pumping regime, small deviations from V dot (0) = 0 could already be seen 2 . The traditional and successful parametric pumping theory 3,4 , valid in the adiabatic regime and up to first order in frequency, requires two pumping parameters which traverse in a closed path in parameter space in each cyclic period and the pumping signal is proportional to the enclosed area by the path. Accordingly, if the two pumping parameters are in phase so that the enclosed area is zero, the pumping signal V dot (0) should vanish.…”

“…Parametric electron pump [1][2][3][4][5][6][7] is an interesting device which delivers a finite DC current to the outside world at zero bias potential, by cyclic variations of two device control parameters. Recently, an adiabatic quantum electron pump was reported in an open quantum dot where the pumping signal was produced in response to the cyclic deformation of the confining potential 2 .…”

Photovoltaic Current Response of Mesoscopic Conductors to Quantized Cavity Modes

“…When the parity violation is due to random interference, the sign of this current will fluctuate from sample to sample and its rootmean-square (RMS) size in this case depends on the power in the EM field [5,6,8,9,10,11]. Hence after this PV current is calibrated it can be used for detection of the power in the incident EM field.The previous theoretical description [5,6,9,10,11,12] of the PV current has employed a classical treatment of the EM fields, since this description was sufficient for the systems studied experimentally [7,8,13,14,15]. In this case the RMS PV current is a monotonically increasing function of the EM field power.…”

“…This effect arises in mesoscopic conductors because the phase-coherent transmission through the device almost always violates parity symmetry and the nonequilibrium distribution created by the EM field sets up a steady-state current dictated by this parity violation. When the parity violation is due to random interference, the sign of this current will fluctuate from sample to sample and its rootmean-square (RMS) size in this case depends on the power in the EM field [5,6,8,9,10,11]. Hence after this PV current is calibrated it can be used for detection of the power in the incident EM field.…”