Single electron charging effects in semiconductor quantum dots

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas (2 DEG) of a GaAs/AlGaAs heterostructure. The gate structure allows an independent control of the conductances of the two tunnel barriers separating the quantum dot from the two 2 DEG leads, and enables us to vary the number of electrons that are localized in the dot. We have measured Coulomb oscillations in the conductance and the Coulomb staircase in current-voltage characteristics and studied their dependence on the conductances of the tunnel barriers. We show experimentally that at zero magnetic field charging effects start to affect the transport properties when both barrier conductances are smaller than the first quantized conductance value of a point contact at 2e ²/h. The experiments are described by a simple model in terms of electrochemical potentials, which includes both the discreteness of the electron charge and the quantum energy states due to confinement.     

Coulomb blockade electrometer with a high-T c island

We report on a successful attempt to fabricate a Coulomb blockade electrometer consisting of an ultrasmall YBa₂Cu₃O_7−δ (YBCO) island coupled to two gold electrodes through a high-resistance native surface tunnel barrier. A third electrode placed near the island was used as an electrostatic gate. Spectra typical for tunneling into the YBCO superconductor were reproducibly measured. At temperatures below 0.5 K the low-bias conductance was suppressed by the Coulomb blockade. The blockade could be periodically varied by the gate potential. An external magnetic field of up to 5 T strongly influenced the transport via the island but without any change in the period of the Coulomb oscillations. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 112–117 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Out-of-equilibrium admittance of single electron box under strong Coulomb blockade

We study admittance and energy dissipation in an out-of-equilibrium single electron box. The system consists of a small metallic island coupled to a massive reservoir via single tunneling junction. The potential of electrons in the island is controlled by an additional gate electrode. The energy dissipation is caused by an AC gate voltage. The case of a strong Coulomb blockade is considered. We focus on the regime when electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. We obtain the admittance under the specified conditions. It turns out that the energy dissipation rate can be expressed via charge relaxation resistance and renormalized gate capacitance even out of equilibrium. We suggest the admittance as a tool for a measurement of the bosonic distribution corresponding collective excitations in the system.     

Conductance peak splitting in charge polarized coupled quantum dots

We report a measurement of linear conductance through a series double dot as a function of the total double dot charge and the charge difference for interdot tunnel conductances between zero and one mode. The dots are defined by ten independently tunable electrostatic gates on the surface of a GaAs/AlGaAs heterostructure to allow separate adjustment of dot charge and interdot conductance. For weak interdot tunneling the measured double dot conductance agrees with a transport model in which each dot is individually governed by Coulomb blockade theory. As interdot tunnel conductance increases toward one mode, the measured conductance peak positions and shapes indicate both a relaxation of the charge quantization condition for individual dots and quantum mechanical charge sharing between dots. The results are in quantitative agreement with many body charge fluctuation theory.     

Conductance oscillations and transport spectroscopy of a quantum dot

Results are reported for low temperature measurements of the conductance through small regions of a two-dimensional electron gas (2 DEG). An unconventional GaAs heterostructure is used to form a 2 DEG whose density can be tuned by the gate voltage applied to its conductive substrate. Electron beam lithography is used to pattern a narrow channel in the 2 DEG interrupted by two constrictions, defining a small 2 DEG island between them. The conductance is found to oscillate periodically with the gate voltage, namely with electron density. Calculations of the capacitance between the substrate and the island show that the period of oscillation corresponds to adding one electron to the island. The oscillatory behavior results primarily from the discreteness of charge and the Coulomb interaction between electrons. However, the observed temperature dependence of these oscillations requires a more sophisticated treatment which includes the quantized electron energy levels as well. The magnetic field dependence of the oscillations allows us to extract the discrete energy spectrum of the quantum dot in the quantum-Hall regime.     

Coulomb blockade in an open quantum dot

We report the observation of Coulomb blockade in a quantum dot contacted by two quantum point contacts each with a single fully transmitting mode, a system thought to be well described without invoking Coulomb interactions. Below 50 mK we observe a periodic oscillation in the conductance of the dot with gate voltage, corresponding to a residual quantization of charge. From the temperature and magnetic field dependence, we infer the oscillations are mesoscopic Coulomb blockade, a type of Coulomb blockade caused by electron interference in an otherwise open system.     

Interference and interactions in mesoscopic rings

We consider a mesoscopic ring connected to external reservoirs by tunnel junctions. The ring is capacitively coupled to an external gate electrode and may be pierced by a magnetic field. Due to strong electron–electron interactions within the ring the conductance shows Coulomb blockade oscillations as a function of the gate voltage, while Aharonov–Bohm interference effects lead to a dependence on the magnetic flux. The Hamiltonian of the ring is given by a Luttinger model that allows for an exact treatment of both interaction and interference effects. We conclude that the positions of conductance maxima as a function the external parameters can be used to determine the interaction parameter , and the shapes of conductance peaks are strongly affected by electron correlations within the ring.     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

Single electron charging in parallel coupled quantum dots

We report low-temperature conductance measurements in the Coulomb blockade regime on two nominally identical tunnel-coupled quantum dots in parallel defined electrostatically in the two-dimensional electron gas of a GaAs/AlGaAs heterostructure. At low interdot tunnel coupling we find that the conductance measured through one dot is sensitive to the charge state of the neighboring dot. At larger interdot coupling the conductance data reflect the role of quantum charge fluctuations between the dots. As the interdot conductance approaches 2e²/h, the coupled dots behave as a single large dot.     

Single Cooper pair pump

We have operated a Cooper pair pump, a linear array of superconducting tunnel junctions in which single Cooper pairs are moved under the influence of ac signals applied to two gate electrodes. The pump is based on the Coulomb blockade of charge tunneling. Because of the small junction capacitance precisely one Cooper pair is transferred per ac cycle. The current-voltage characteristics of this device show current plateaus close to 2ef, wheref is the frequency of the ac voltages. Deviations are explained in terms of Zener tunneling, Cooper pair co-tunneling, and sporadic quasiparticle tunneling.     

SINGLE-ELECTRON TRANSISTORS FOR FUTURE APPLICATIONS

Single electron transistors with wire channels are fabricated by a nanoelectrode-pair technique. Their characteristics strongly depend on the channel widths and the voltages on the in-plane gates. A few dips in the Coulomb blockade oscillations were observed at the less positive gate voltages for a device with a 70nm-wide wire due to Coulomb blockade between the coupled dots. By applying negative voltages to the in-plane gates, the oscillations became periodic, which indicated the formation of a single dot in the conducting channel. These gates facilitate fabricating single-electron transistors with single dot structures, which have potential applications on its integration.     

Precise implementation of cluster transfer matrix method in the single electron box

The partition function of the single electron box (SEB), a small metallic island connected by a tunnel junction to the source lead and by a gate capacitor to the gate, can be expressed in path-integral form, which contains the effective action of the collective variable, phase, after integrating out the background electron degrees of freedom. The cluster transfer matrix method (CTM) is applied to the SEB. By using an improved numerical algorithm and more intensive calculations with larger cluster size, we obtained a highly accurate result for the effective charging energy of SEB up to a large barrier conductance. With a clear converging tendency and the fact that we do not use any approximation in calculation of the partition function, our CTM calculation is systematic and exact. The result is in excellent agreement with the real time renormalization group method of König and Schoeller.     

Single electron tunneling at large conductance: The semiclassical approach

We study the linear conductance of single electron devices showing Coulomb blockade phenomena. Our approach is based on a formally exact path integral representation describing electron tunneling nonperturbatively. The electromagnetic environment of the device is treated in terms of the Caldeira-Leggett model. We obtain the linear conductance from the Kubo formula leading to a formally exact expression which is evaluated in the semiclassical limit. Specifically we consider three models. First, the influence of an electromagnetic environment of arbitrary impedance on a single tunnel junction is studied focusing on the limits of large tunneling conductance and high to moderately low temperatures. The predictions are compared with recent experimental data. Second, the conductance of an array of N tunnel junctions is determined in dependence on the length N of the array and the environmental impedance. Finally, we consider a single electron transistor and compare our results for large tunneling conductance with experimental findings. Received 2 February 2000     

Low energy dynamics of two-dimensional lateral tunnel junctions

We report on the low temperature tunneling characteristics of two-dimensional lateral tunnel junctions (2DLTJs) consisting of two coplanar two-dimensional electron systems separated by an in-plane tunnel barrier. The tunneling conductance of the 2DLTJ exhibits a characteristic dip at small voltages—consistent with the phenomenon of zero-bias anomaly in low-dimensional tunnel junctions—and a broad conductance peak at the Coulombic energy scale. The conductance peak remains robust under magnetic fields well into the quantum Hall regime. We identify the broad conductance maxima as the signature of the pseudogap in the tunneling density of states below the characteristic Coulomb interaction energy of the 2DLTJ.     

Enhanced conductance blockade due to Pauli exclusion in tunnel junctions with half-metallic electrodes

A defect-state mediated conductance blockade effect has been studied in magnetic tunnel junctions consisting of La_0.7Sr_0.3MnO₃ (LSMO) electrodes and a SrTiO₃ (STO) barrier. The blockade threshold is an order of magnitude greater than the Coulomb charging energy estimated from the conductance oscillations at low temperature. The blockade voltage decreases with the increase of the temperature or the magnetic field, whereas the Coulomb charging energy washes out at higher temperature but it does not show strong dependence on magnetic field. An explanation is offered in terms of the spin blockade effect due to the combination of the discrete Coulomb charging on the defect state in STO and the half-metallicity of the LSMO electrodes. The result sheds new light on the half-metallic nature of LSMO.     

Adiabatic charge pumping in carbon nanotube quantum dots

We investigate charge pumping in carbon nanotube quantum dots driven by the electric field of a surface acoustic wave. We find that, at small driving amplitudes, the pumped current reverses polarity as the conductance is tuned through a Coulomb blockade peak using a gate electrode. We study the behavior as a function of wave amplitude, frequency, and direction and develop a model in which our results can be understood as resulting from adiabatic charge redistribution between the leads and quantum dots on the nanotube.     

Variation of co-tunneling and Kondo effects by control of the strength of coupling between a vertical dot and a two-dimensional electron gas

We have fabricated a vertical quantum dot with lateral coupling, modulated by a split gate voltage, to a two-dimensional electron. We thereby control not only electron configurations but also the strength of coupling between the dot and the lateral lead, by applying gate voltages. We have measured the conductance enhancement when the applied bias exceeds the single-electron excitation energy, in the Coulomb blockade regime. This conductance enhancement disappears as the split gate voltage decreases (reducing the coupling). This indicates that this enhancement is caused by inelastic co-tunneling. Furthermore, we observed a conductance enhancement at zero source–drain bias with stronger coupling. An anomaly is observed that we attribute to Kondo resonance between the dot and the leads.     

Topological quantization of current in quantum tunnel contacts

It is shown that an account of the Berry phase (a topological ϑ-term), together with a dissipative term in the effective action S[ϕ] of the tunnel contacts, induces a strong quantization of the tunnel current at low temperatures. This phenomenon, as the Coulomb blockade, reflects a discrete charge structure of the quantum shot noise and can ensure a quantization of the tunnel current without a capacitive charging energy E _C when the latter is strongly suppressed by quantum fluctuations. Since the value of the ϑ parameter is determined by the gate voltage, this effect allows us to control the current through the contact. A possible physical application of this effect is proposed. The text was submitted by the author in English.     

Spacing and width of Coulomb blockade peaks in a silicon quantum dot

We present an experimental study of the fluctuations of Coulomb blockade peak positions of a quantum dot. The dot is defined by patterning the two-dimensional electron gas of a silicon MOSFET structure using stacked gates. The ratio of charging energy to single-particle energy is considerably larger than in comparable GaAs/AlGaAs quantum dots. The statistical distribution of the conductance peak spacings in the Coulomb blockade regime was found to be unimodal and does not follow the Wigner surmise. The fluctuations of the spacings are much larger than the typical single-particle level spacing and thus clearly contradict the expectation of random matrix theory. Measurements of the natural line width of a set of several adjacent conductance peaks suggest that all of the peaks in the set are dominated by electrons being transported through a single-broad energy level.     

单电子三势垒隧穿结I-V特性研究

在正统理论的基础上，提出了单电子三势垒隧穿结模型的主方程，并用线性方程组解法求出了其稳态解.通过数值模拟，得到了该系统的I-V特性曲线.发现其有别于双势垒隧穿结的情况，在传统库仑台阶的平台处曲线存在波纹状结构，分析得出这是由于第二个库仑岛上的电子数变化对I-V曲线的影响.此外，研究了各物理参数对I-V曲线的影响，发现三结系统可以降低对温度的要求，并应用Fermi能级处的能级间隔估算出出现库仑台阶现象的最高温度Tmax，为相关单电子器件的参数选择提供了理论依据. 关键词： 正统理论 库仑台阶 主方程 隧穿概率