Fano resonance in a cavity-reflector hybrid system

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Fano resonance in a cavity-reflector hybrid system

Chengyu Yan, Sanjeev Kumar, Michael Pepper, Patrick See, Ian Farrer, David Ritchie, Jonathan Griffiths, and Geraint Jones

Phys. Rev. B 95, 041407(R) – Published 26 January 2017

Abstract

We present the results of transport measurements in a hybrid system consisting of an arch-shaped quantum point contact (QPC) and a reflector; together, they form an electronic cavity in between them. On tuning the arch-QPC and the reflector, an asymmetric resonance peak in resistance is observed at the one-dimension to two-dimension transition. Moreover, a dip in resistance near the pinch-off of the QPC is found to be strongly dependent on the reflector voltage. These two structures fit very well with the Fano line shape. The Fano resonance was found to get weakened on applying a transverse magnetic field, and smeared out at 100 mT. In addition, the Fano-like shape exhibited a strong temperature dependence and gradually smeared out when the temperature was increased from 1.5 to 20 K. The results might be useful in realizing devices for quantum information processing.

Received 10 October 2016
Revised 1 December 2016

DOI:https://doi.org/10.1103/PhysRevB.95.041407

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Ballistic transport Quantum interference effects

Two-dimensional electron gas

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chengyu Yan^1,2,*, Sanjeev Kumar^1,2, Michael Pepper^1,2, Patrick See³, Ian Farrer^4,†, David Ritchie⁴, Jonathan Griffiths⁴, and Geraint Jones⁴

¹London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
²Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
³National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, United Kingdom
⁴Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom

^*uceeya3@ucl.ac.uk
^†Present address: Department of Electronic and Electrical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, United Kingdom.

Article Text

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Issue

Vol. 95, Iss. 4 — 15 January 2017

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Images

Figure 1
Schematic of the device and the experiment setup. (a) The yellow blocks are metallic gates and red squares are Ohmics; excitation current is fed to Ohmic 1 while 2 is grounded; Ohmics 3 and 4 are voltage probes. The opening angle of the arch is $45^{\circ}$ and the radius (also the distance between the arch gate and reflector) is 1.5 $μ m$ , both the length and width of the QPC embedded in the arch is 200 nm, the length of the inclined surface of the reflector is 3. $0 μ m$ , and the width is 300 nm. (b) Differential conductance measurement of the QPC (main plot) and the reflector (inset). To be noted that in this plot when the QPC was measured, the reflector was grounded, and vice versa. The voltage applied to the QPC (reflector) was $V_{a}$ $(V_{r})$ . Three regimes are identified from the reflector voltage characteristic and labeled as regime 1 (a-b), regime 2 (b-c), and regime 3 (c-d).
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Figure 2
$R$ as a function of arch-QPC voltage for various $V_{r}$ . (a) Result in regime 1: A strong asymmetric resonance structure highlighted by a dotted rectangle occurs around $- 0.2$ V. (b) Result in regime 2: The resonance structure slowly evolves into a broad shoulder structure (marked by the solid line), meanwhile, a dip gradually forms at the pinch-off regime of the arch-QPC (marked by the dashed line). (c) Result in regime 3: Intensity of both the shoulder structure and the dip decreases with less negative reflector voltage. Data have been offset vertically by $10 Ω$ in each plot for clarity.
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Figure 3
Theoretical fitting of (a) the resonance and (b) the dip structures. It is remarkable that both the resonance structure $(V_{r} = - 0.30$ V) and the dip $(V_{r} = - 0.25$ V) follow a well-defined Fano line shape. The horizontal black dotted line is a guide to the eye, reflecting that the saturated values on the left end of the experimental data (the 1D regime of QPC) and that on the right (the 2D regime) do not align. This may be due to a dramatic variation in DOS at the 1D-2D transition. The inset in (a) and (b) shows the Fano factor $q$ as a function of $V_{r}$ in the range where the structures are observable.
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Figure 4
$R$ as a function of reflector voltage for various $V_{a}$ . (a) The arch-gate voltage was fixed at $- 0.23$ V $(□)$ , $- 0.19$ V $(⋄)$ , and 0 V $(△)$ , respectively, while sweeping the reflector voltage; data have been offset vertically by $50 Ω$ for clarity. (b) Theoretical fitting of $Δ R (V_{r}, V_{a}) = R (V_{r}, V_{a}) - R (V_{r}, 0)$ , where $V_{a} = - 0.23$ V, and using Eq. (1), where $q = 1.47$ , it is clear that the data follow a Fano line shape.
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Figure 5
Effect of perpendicular magnetic field. In (a) and (b) the transverse magnetic field is incremented from 0 (bottom trace) to $\pm 150$ mT (top trace), respectively, and it is seen that both the peak (marked by the solid line) and the dip (highlighted by the dashed line) rapidly weaken against the field, almost smearing out at $\pm 100$ mT. Data have been offset vertically by $20 Ω$ for clarity.
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Figure 6
Temperature dependence of $R$ . (a) $R$ in regime $1 (V_{r} = - 0.3$ V) as a function of temperature from 1.5 K (top trace) to 20 K (bottom trace): It may be seen that the intensity of both the peak and the dip structures decreases with increasing temperature. Data have been offset vertically by $20 Ω$ for clarity. (b) The temperature dependence of $R$ for $V_{a} = - 0.50$ $(□)$ , $- 0.23$ $(⋄)$ , $- 0.19$ $(▽)$ , and 0 V $(◯)$ ; solid lines are a guide to the eye. (c) Mott fitting for the temperature dependence of the peak structure, $Δ R (V_{a}, T) = R (V_{a}, T) - R (0, T)$ , where $V_{a} = - 0.23$ V, $R_{1} = - 0.2656$ $k Ω, R_{2} = 0.4238$ $k Ω, T_{0} = 1.2$ K.
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