Pair Tunneling Resonance in the Single-Electron Transport Regime

Abstract

We predict a new electron pair tunneling (PT) resonance in nonlinear transport through quantum dots with positive charging energies exceeding the broadening due to thermal and quantum fluctuations. The PT resonance shows up in the single-electron transport (SET) regime as a peak in the derivative of the nonlinear conductance, d 2 I=dV 2 , when the electrochemical potential of one electrode matches the average of two subsequent charge addition energies. For a single level quantum dot (Anderson model) we find the analytic peak shape and the dependence on temperature, magnetic field, and junction asymmetry and compare with the inelastic cotunneling peak which is of the same order of magnitude. In experimental transport spectroscopy the PT resonance may be mistaken for a weak SET resonance judging only by the voltage dependence of its position. Our results provide essential clues to avoid such erroneous interpretation. Introduction.-Electron tunneling spectroscopy has nowadays become a standard tool for investigating the in situ properties of single-electron transistors based on quantum dots in semiconductor heterostructures, nanowires, carbon nanotubes, and even single molecules. The basic spectroscopy rules derive from the simple energy resonance conditions for single-electron tunneling (SET) onto the dot. As a result, the bias positions of differential conductance (dI=dV) resonances depend linearly on the gate voltage due to capacitive effects [1]. In addition, inelastic cotunneling (COT) processes can often be distinguished as steps in dI=dV [2], allowing for spectroscopy of quantum dot excitations with increased energy resolution [3]. Here an electron is transferred from the high to the low biased electrode through the dot, using the excess biasenergy to excite the dot by an energy Á . Since these electron-hole charge transfer resonances involve only a virtual charging of the dot, they appear at a bias threshold V ¼ Á , independent of the gate voltage. These processes arise only in second order perturbation theory in the tunnel rate À.In this Letter we show that, in the same order of À, electron pair tunneling (PT) gives rise to distinct, measurable transport effects which, to our knowledge, have been overlooked so far. In a single coherent process, a pair of electrons is extracted from (added to) one electrode, resulting in a real (dis)charging of the dot by two electrons, involving a positive charging energy much larger than broadening due to thermal and quantum charge fluctuations. The corresponding PT resonance appears deep inside the SET region where a finite current is flowing and its position has the same gate-dependence as SET resonances. It might thus be mistaken for a weak SET resonance belonging to some excited state and one might thereby extract an erroneous level-structure from the spectroscopic

Charge fluctuations in nonlinear heat transport

“…We establish the complete classification of the nonlinear energy transport by noting the additional feature due to the tunneling of pairs [50] of either electrons or holes, which is again more prominent in the energy conductance [line (vii) in Fig. 2].…”

“…We go beyond standard approaches by including the competition of all tunneling rates O( ) and O( 2 ) (Fig. 1) into the stationary master equatioṅ [46] for more details of the calculations [45,50,51] of the transition rate matrix W and the current). We focus on the dominant energy dependence introduced by the interacting quantum dot, assuming a flat spectral density in the wide-band limit for the electrodes.…”

Quantum ballistic transport by interacting two-electron states in quasi-one-dimensional channels

“…We concentrate our efforts on calculating the lowest eigenstates for two interacting electrons since this sheds some light on the role played by electron-electron interaction in determining the nature for the switching of the ground state of a dilute electron system and consequently the lowest conductance plateaus. The complicated two-electron tunneling process 27,28 will not be considered here since it does not lead to conductance-plateau structures observed in our experiment. 25 We show below that there is a range of values of wire widths where the two-electron transport is mediated by anticrossing-level states based on Coulomb interaction, and therefore, it is not possible to describe the conductance in terms of a single-particle picture.…”

Tunneling of hybridized pairs of electrons through a one-dimensional channel

“…We explicitly determine the ground state of a dilute electron liquid and consequently the lowest conductance plateau. The complex two-electron tunneling [19,20] is not included in this review since it does not contribute to the formation of conductance-plateaus. Furthermore, we highlight below that there is a range of wire widths for which two-electron transport is mediated by anticrossing-level states based on the Coulomb interaction, and, therefore, it is not possible to describe the conductance by using a single-particle formalism.…”