Applied Science and Convergence Technology 2023; 32(1): 19-22
Published online January 30, 2023
Copyright © The Korean Vacuum Society.
Hwanchul Jung and Yunchul Chung *
Department of Physics, Pusan National University, Busan 46241, Republic of Korea
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The conductance through a quantum point contact (QPC) when a quantum dot (QD) is coupled to the side of a QPC channel is studied. It is experimentally demonstrated that a 0.7 conductance plateau can be produced by tuning the Fano resonance between QD and the QPC channel. Numerical simulations show results similar to the experiment. A simple model that adds a Fano resonance peak to the QPC’s quantized conductance curve is introduced. According to the model, the plateau results when the increase in Fano peak conductance compensates for the decrease in QPC conductance when the QPC gate is pinched off. These results suggest that Fano resonance is a possible candidate for the origin of the 0.7 conductance anomaly observed in QPCs.
Keywords: Nanoscience, Technology
The so called 0.7 plateau, an unexpected conductance plateau observed around 0.7 ×
Device was fabricated on a GaAs/AlGaAs heterostructure 2-dimensional electron gas (2DEG) wafer with electron density of 3.1 × 1011 cm−2 and mobility of 2.9 × 106 cm2V−1s−1 at 4.2 K. The 2DEG was buried 63.5 nm below the surface of the wafer. The device was fabricated by optical and e-beam lithography processes on the GaAs/AlGaAs heterostructure [16,17]. All measurements were done at 80 mK in a dilution refrigerator. Conductance measurements were performed by applying 10µVrms sinusoidal voltage at a frequency of 487 Hz to the device and measuring the modulated current through the device. Figure 1(a) provides a scanning electron microscopy (SEM) picture of the device used in the experiment. Devices with two different QD diameters (300 and 600 nm) were used for the experiment. The QPC channel (green arrow) is defined between the 1D gate and two QD gates in the Fig. 1(a). The confinement state in the QD was controlled by the plunger gate. The right side of the QD (a small gap between two QD gates) was coupled to the QPC channel. The 1D gate controls the number of conducting modes in the QPC channel. The conductance through the device was measured between the source, S, and the drain, D, as shown in the figure. Figure 1(b) shows the measured Fano resonance through the device. The plunger gate voltage changed the energy states in the QD. The conductance through the QPC slowly decreased as the plunger gate voltage of the QD became more negative and finally pinched off at around −0.2 V. On top of slowly decreasing conductance curve, sharp asymmetric resonance peaks were observed, typical signatures of Fano resonance. Fano resonance can be regarded simply as interference between electrons flowing through the wire and electrons flowing through QD . Since the electronic phase changes by π before and after the QD’s resonance state, these phase changes caused constructive and destructive interference of electrons flowing through the device, resulting in Fano resonance. The observed peaks were fitted with the theoretical expression of the Fano resonance. The conductance
In Fig. 2, the conductance through the QPC as a function of 1D gate voltage was measured for various QD gate voltages. A 0.7 plateau was observed for the QPC coupled with a 300 nm diameter QD. The plunger gate voltage was set to −0.05 V to pinch off all conduction channels under the plunger gate. (Device was cooled down with +0.3 V voltage on all the gates). When the QD gate voltage was set to −0.69 V, sharp conductance dips (denoted by a red arrow) in the QPC plateau region were observed. A dip in the QPC conductance plateau is a typical sign of Fano resonance. However, as the QD gate voltage changed, these dips weakened and a conductance plateau began to appear around 0.7
The conductance through the device was calculated numerically using KWANT , a software package for quantum transport. The electrostatic potential profile of the device was calculated by analytically solving the Laplace equation . Figure 3(a) shows results calculated for a device coupled with a 300 nm diameter QD. These results are consistent with the experimental results shown in Fig. 2(a). It was found that the results can only be obtained when the gate voltages of the upper and lower QD gates are not the same. The lower QD gate voltage was shifted 30 mV negative from the upper QD gate voltage (i.e.,
Figure 3(b) shows results calculated for the device with 600 nm QD. Many small resonance peaks repeating one after another were observed, instead of a plateau. We believe that the frequent repetition of Fano peaks hindered the observation of the 0.7 plateau in our device. A detailed explanation is provided in the discussion. To obtain results similar to those of the experiment, the voltages of the upper and lower QD gates were assumed to be the same. The symmetrical gate voltages on the upper and lower QD gates made the resonance peaks stronger, making it difficult to create a broad resonance peak, which seems to be a necessary condition to form the 0.7 plateau.
In Fig. 4, we tried to reconstruct the 0.7 conductance plateau by adding omit the Fano resonance peak to an ideal quantized conductance curve of a QPC; calculations were performed using Eq. (1) and the KWANT simulator. Several Fano peaks with different asymmetry parameters (q) and ideal conductance quantization curve of a QPC are plotted in Fig. 4(a). The resonance width Γ was set to 3, a relatively wide peak width, representing a situation in which the QD is relatively open to the 1D wire. The asymmetry parameter
Althoughthe unusual plateau is named a ‘0.7 plateau’, it does not necessary mean that the conductance value is always 0.7. The name comes from the first report of an unexpected conductance plateau , observed around 0.7
A few resonant peaks followed the 0.7 plateau in the experiment, as shown in Fig. 2. This repetition is obvious, since Fano resonance occurs whenever a QD’s energy state aligns with the QPC’s Fermi energy. The peak repeats more frequently in the 600 nm QD device than in the 300 nm QD device because energy level spacing between confined energy states is smaller for the 600 nm QD, as shown in Fig. 2(c). To observe the 0.7 plateau, the spacing between the peaks must be wide enough so that the plateau region is not affected by the following peak. For the 600 nm QD device, no 0.7 plateau was observed in the experiments. We believe that the relatively small charging energy of the 600 nm QD made gaps between resonance peaks small, causing the resonance peaks to overlap and eventually hindering plateau development.
A real QPC device consists of only two split gates and does not have a QD coupled to a 1D channel, as our device does. However, the impurity potential (caused by modulation doping of the GaAs/AlGaAs heterostructure) inside the 1D channel can create a QD-like potential puddle, and thus lead to a resonance-like characteristic in the QPC conductance . The size of the localized state in the QPC cannot be bigger than the size of the QPC channel itself. Therefore, it is reasonable to assume that the diameter is less than 200 nm. Therefore, the energy level spacing is relatively larger than that in our device, resulting in less frequent resonance peaks. This partly explains why only a plateau or a peak  was observed in the real QPC device.
A ‘0.7-like’ conductance plateau was observed for a QPC device coupled with a QD on the side of the conduction channel. The origin of the 0.7 conductance plateau in our experiment can be explained by Fano resonance via the side-coupled QD. Numerical simulations show results similar to those of the experiment. The results were explained using a very simple model that adds the Fano resonance peak to the QPC’s quantized conductance curve. The conductance plateau resulted from the increase in Fano peak conductance compensating for the decrease in QPC conductance when the QPC gate was slowly pinched off. Although there are no side-coupled QDs in real QPC devices, an unexpected potential puddle caused by impurity potential inside the 1D channel can create a QD-like state. Therefore, we believe that Fano resonance via unexpected QD-like state in a QPC is a candidate for the origin of the 0.7 conductance anomaly.
This work was supported by a 2-year research grant from Pusan National University.
The authors declare no conflicts of interest.