Frequency dependence of the admittance of a quantum point contact

Abstract

Using a Boltzmann-like kinetic equation derived in the semiclassical approximation for the partial Wigner distribution function, we determine the ac admittance of a two-dimensional quantum point contact ͑QPC͒ for applied ac fields in the frequency range Ϸ0 -50 GHz. We solve self-consistently an integral equation for the spatial distribution of the potential inside the QPC, taking into account the turning points of the semiclassical trajectories. The admittance of the QPC is a strong function of the gate voltage. This gate voltage can be used to ''tune'' the number of open channels ͑N͒ for electron transport. We show that, for most values of gate voltage, the imaginary part of the total admittance is positive for NϾ1, so that the QPC has an inductive character, because of the predominant role of the open channels. In contrast, for Nϭ0 or 1, for most values of the gate voltage, the imaginary part of the admittance is negative, corresponding to capacitive behavior. For gate voltages near values at which channels open or close, very strong nonlinear effects arise, and the admittance oscillates rapidly ͑with its imaginary part sometimes changing sign͒ both as the function of gate voltage ͑at fixed frequency͒ and as a function of frequency ͑at fixed gate voltage͒. Experimental observation of these oscillations would provide an important test of our semiclassical approach to the ac response of a QPC. We explore the low-frequency regime and investigate the extent to which one can understand the admittance in terms of a static conductance and a ''quantum capacitance'' and a ''quantum inductance.'' We show that it is possible to choose the gate voltage so that there is a large, low-frequency regime in which the admittance is well approximated by a linear function of frequency. In this regime, the admittance can be treated by ''equivalent circuit'' concepts. We study how this approach breaks down at higher frequencies, where strongly nonlinear behavior of the admittance arises. We estimate the value of frequency, c , at which the crossover from the low-frequency linear regime to the high-frequency nonlinear behavior occurs. For chosen parameters of a QPC, c Ϸ10 GHz. ͓S0163-1829͑98͒02339-X͔ PHYSICAL REVIEW B 15 OCTOBER 1998-I VOLUME 58, NUMBER 15 PRB 58 0163-1829/98/58͑15͒/9894͑13͒/$15.00 9894

Numerical toolkit for electronic quantum transport at finite frequency

“…However, as all the calculations were performed on perfectly transmitting channels there is no "Landauer dipole" in the problem. Calculations done assuming perfect screening (enforcing current and gauge conservation 44,89 suggest that the above physical signatures remain observable in presence of screening, and in particular should allow for the measurement of the time of flight.…”

ac response of quantum point contacts with a split-gate configuration

“…3,4 Although there has been substantial progress for direct current transport in QPCs over the last two decades, little attention has been paid to the alternating current transport in QPCs. [5][6][7][8][9] However, ac transport in QPCs is critical for designing and manipulating ultrafast operations in future QPC-based devices. 10 Recently, Hohls et al measured the admittance of QPCs at frequencies up to 300 MHz.…”

Charge Relaxation Resistances and Charge Fluctuations in Mesoscopic Conductors

“…Deviations from the equilibrium charge distribution can occur in various ways [3,2]. If the capacitances to the gate are large the charge distribution takes the form of a dipole [3,9] across the QPC. If the geometrical capacitance for this dipole is large the QPC can be charged vis-a-vis the gate [2].…”

“…A more realistic treatment of the charge distribution of a quantum point contact includes a dipole across the quantum point contact itself [3,9] and in the presence of the gates includes a quadrupolar charge distribution [2].…”

“…We cite here only a review [2], a few original works [3,4] and some of the recent works [5][6][7][8][9][10][11][12][13] to indicate the breadth of interest in this field.…”