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Transport Properties of Clean Quantum Point Contacts Home Search Collections Journals About Contact us My IOPscience Transport properties of clean quantum point contacts This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 New J. Phys. 13 113006 (http://iopscience.iop.org/1367-2630/13/11/113006) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 188.155.208.225 The article was downloaded on 05/11/2011 at 07:08 Please note that terms and conditions apply. New Journal of Physics The open–access journal for physics Transport properties of clean quantum point contacts CRossler¨ 1, S Baer, E de Wiljes, P-L Ardelt, T Ihn, K Ensslin, C Reichl and W Wegscheider Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland E-mail: [email protected] New Journal of Physics 13 (2011) 113006 (16pp) Received 6 June 2011 Published 3 November 2011 Online at http://www.njp.org/ doi:10.1088/1367-2630/13/11/113006 Abstract. Quantum point contacts are fundamental building blocks for mesoscopic transport experiments and play an important role in recent interference and fractional quantum Hall experiments. However, it is unclear how electron–electron interactions and the random disorder potential influence the confinement potential and give rise to phenomena such as the mysterious 0.7 anomaly. Novel growth techniques of AlX Ga1 X As heterostructures for high- mobility two-dimensional electron gases enable− us to investigate quantum point contacts with a strongly suppressed disorder potential. These clean quantum point contacts indeed show transport features that are obscured by disorder in standard samples. From these transport data, we are able to extract those parameters of the confinement potential that describe its shape in the longitudinal and transverse directions. Knowing the shape (and hence the slope) of the confinement potential might be crucial for predicting which interaction-induced states can best form in quantum point contacts. 1 Author to whom any correspondence should be addressed. New Journal of Physics 13 (2011) 113006 1367-2630/11/113006+16$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 Contents 1. Introduction 2 2. Experimental details 2 2.1. Lateral shifting of the quantum point contact (QPC) ............... 4 2.2. The 0.7 anomaly in the perpendicular magnetic field ............... 5 2.3. Finite bias spectroscopy .............................. 8 2.4. Extracting the QPCs’ shape parameters ..................... 11 2.5. Spin-resolved transport at low temperatures ................... 13 3. Conclusion 15 Acknowledgment 15 References 15 1. Introduction Quantum devices on semiconductor nanostructures rely on quantum point contacts (QPCs) as the basic building blocks. Quantized conductance was observed early on [1, 2] and has been used as a signature of the quality of a quantum point contact QPC. With ever improving sample quality and the methodology for the detection of non-Abelian anyons in the ν 5/2 fractional quantum Hall state, several experiments [3–5] have recently used the properties= of QPCs fabricated on ultra-high-mobility two-dimensional electron gases (2DEGs). In view of proposals to investigate fractional quantum Hall states in confined geometries and interferometer-like setups, a detailed understanding and the control of QPCs are essential. Here we present experimental data that go beyond previously published data by demonstrating experiments that profit from the extraordinary cleanliness of the high-mobility 2DEG. In contrast to standard 2DEGs, we do not observe defect-induced resonances when the QPCs are shifted laterally. Higher-order half-plateaus are observed in the finite-bias differential conductance (at a magnetic field B 0 T), as well as spin-split half-plateaus at B 2 T. Finally, the 0.7 anomaly is investigated⊥ = as a function of temperature and in perpendicular⊥ = magnetic field. 2. Experimental details The samples are fabricated on a high-mobility wafer with a 2DEG residing z 160 nm beneath the surface. The high mobility is achieved by placing Si dopants in a narrow= GaAs layer sandwiched by AlAs layers [6–8]. The population of the X band in AlAs results in hardly mobile electrons, which screen the static disorder potential but do not cause a measurable parallel conductance. Optical lithography is employed to define Hall bars via mesa etch and deposition 15 2 of Au/Ge Ohmic contacts. Processed Hall bars have an electron density of nS 3.5 10 m− 2 1 = × and Drude mobilities in the range of µ 1000–2000 m (Vs)− . The characterization as well as subsequent experiments are carried out= at a temperature of T 1.3 K if not stated otherwise. Schottky electrodes are defined via electron beam lithography and= the subsequent deposition of Ti/Au. AFM micrographs of two QPCs are shown in the insets of figures 1(a) and (b). The gates appear bright with the gap between them being w 200 nm (a) and w 500 nm (b). Applying a voltage of V . 1.1 V to the gates depletes the= underlying 2DEG and= creates a constriction G − between source and drain. The source–drain current ISD and the voltage drop across the QPC New Journal of Physics 13 (2011) 113006 (http://www.njp.org/) 3 a) 15 G1 ISD 10 /h) 2 (2e 200 nm G2 QPC1 G 5 T = 1.3 K VSD = 0 mV 0 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 VG1&G2 (V) b) 25 G1 20 /h) 15 2 (2e 10 500 nm G2 QPC2 G T = 1.3 K 5 VSD = 0 mV 0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 VG1&G2 (V) Figure 1. (a) Inset: atomic force micrograph of the sample surface. The two Schottky gates appear bright; the GaAs surface appears dark. The distance between the gates is w 200 nm. When the gates are negatively biased, free electrons reside only in the= electron gas underneath the dark areas. Main graph: differential conductance of QPC1, measured as a function of the voltage applied to gates G1 and G2. Quantized conductance in multiples of G 2 e2/h indicates the formation of discrete subbands between the tips of the gates.= (b) Differential conductance of QPC2, which is w 500 nm wide and l 1 µm long. = ≈ VD are measured in four-terminal configuration while applying a small lock in amplitude of V 100 µV at a frequency of f 33 Hz to the source and drain. A dc source–drain voltage ac = ac = VSD can be added to Vac with both voltages being applied symmetrically with respect to the common reference potential of the source, drain and gates. Most transport properties of the employed high-mobility heterostructures are hysteretic as a function of gate bias [9]. Therefore all traces are recorded in the same sweep direction by sweeping towards more negative values of gate voltage. Figure 1(a) shows the differential conductance G dISD/dVD (VSD 0 mV) of QPC1, plotted as a function of the voltage applied to gates G1= and G2. From the= Fermi wavelength of the 2DEG λ √2π/n 42 nm and the distance of the gates, it would be expected that F = S = n w/(kF/2) 9–10 modes can be observed due to confinement transverse to the electron flow≈ [2]. Indeed,= the number of quantized plateaus in figure 1(a) agrees with this estimation, indicating that the largest electronic width of the QPC matches the lithographic gap of the New Journal of Physics 13 (2011) 113006 (http://www.njp.org/) 4 -1 QPC1 T = 1.3 K -2 3 2 1 (V) G2 0.7 × 2e2/h V 0 nG2 -3 nG1 |dG/dVG1&G2| (a.u.) -4 0 1 -4 -3 -2 -1 VG1 (V) Figure 2. Transconductance GTC dG/dVG1&G2 of QPC1, plotted in false colors as a function of the voltages applied= to gates G1 and G2. Integer conductance 2 values of G 0, 1, 2, 3,... 2 e /h result in GTC 0 (black), steps in-between integer conductance= values× appear bright. A faint= red stripe with G 0.7 2 e2/h indicates the presence of a 0.7 anomaly in the QPC. The strong increase≈ × of the conductance at the right and top border (white) marks the gate pinch- off, where the 2DEG underneath gates G1 (right) and G2 (top) starts to be depleted. If both gates are biased identically, 12–13 plateaus are observed between QPC pinch-off and gate pinch-off. When the ratio of gate-voltages is varied by following the lowest transconductance-stripe, the number of plateaus in dependence of either VG1 or VG2 can be varied, indicating that the QPC is shifted laterally between the gates. Scattering centers in-between the gates would appear as straight lines with the slope corresponding to their capacitance to gates G1 and G2. No such defects are visible in this scan. Schottky split-gates. Due to the larger gate-spacing of QPC2, correspondingly more modes are observed in figure 1(b) and a significantly larger gate bias has to be applied in order to pinch off. We observe irreversible charging of the sample typically at VG 5 V, which limits the QPCs’ range of operation. ∼ − 2.1. Lateral shifting of the quantum point contact (QPC) QPC1 can be further characterized by varying the voltages applied to each of the gates, which is not possible for QPC2 due to its extreme pinch-off voltage. Figure 2 shows the transconductance GTC dG/dVG1&G2 of QPC1 in grayscale, plotted as a function of VG1 and VG2. Black areas correspond= to pinch-off (bottom left) and successive conductance plateaus (marked by 1, 2, 3).
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