Geometric interference in a high-mobility graphene annulus p-n junction device

Son T. Le, Albert F. Rigosi, Joseph A. Hagmann, Christopher Gutiérrez, Ji Ung Lee, and Curt A. Richter

Phys. Rev. B 105, 045407 – Published 10 January 2022

Abstract

The emergence of interference is observed in the resistance of a graphene annulus p-n junction device as a result of applying two separate gate voltages. The observed resistance patterns are carefully inspected, and it is determined that the position of the peaks resulting from those patterns is independent of temperature and magnetic field. Furthermore, these patterns are not attributable to Aharonov-Bohm oscillations, Fabry-Pérot interference at the junction, or moiré potentials. The device data are compared with those of another device fabricated with a traditional Hall bar geometry, as well as with quantum transport simulation data. Since the two devices are of different topological classes, the subtle differences observed in the corresponding measured data indicate that the most likely source of the observed geometric interference patterns is quantum scarring.

Received 3 September 2021
Revised 22 November 2021
Accepted 22 December 2021

DOI:https://doi.org/10.1103/PhysRevB.105.045407

Physics Subject Headings (PhySH)

Transport phenomena

Graphene

Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Son T. Le^1,2,3, Albert F. Rigosi ¹, Joseph A. Hagmann¹, Christopher Gutiérrez^1,4,5, Ji Ung Lee², and Curt A. Richter^1,*

¹Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
²College of Nanoscale Science and Engineering, State University of New York Polytechnic Institute, Albany, New York 12203, USA
³Theiss Research, Inc., La Jolla, California 92037, USA
⁴Maryland NanoCenter, University of Maryland, College Park, Maryland 20742, USA
⁵Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California 90095, USA

^*curt.richter@nist.gov

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Vol. 105, Iss. 4 — 15 January 2022

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Images

Figure 1
Edge-state test structure. (a) An AFM image of the device is shown, with labels indicating the number of the electrical contact. Two buried gates, $G_{1}$ and $G_{2}$ , are represented by blue and red shading, respectively. The green and purple dashed lines mark cross-sectional images overlaid with illustrative elements in (b) and (c).
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Figure 2
Resistance of test structure. (a) The resistance profile along $V_{G 1} = V_{G 2}$ [as defined in Fig. 1] is shown (with the Dirac point occurring at approximately −2.6 V). The patterns in resistance are indicated by black arrows. (b) Two types of fits are performed for data analysis. The purple curve represents the Dirac peak fitting for mobilities and carrier density extraction (labeled “Fit”), whereas the blue curve is a smoothed background used to enhance the nature of the patterns. (c) The smoothed curves are subtracted from both gate voltages to enhance the $Δ R$ map. The types of unipolar (n/n, p/p) or bipolar (p/n, n/p) regions are shown in each corner of the map.
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Figure 3
(a) A 2D projection of the $Δ R$ map of Fig. 2 is shown to clarify which profiles are extracted for the discussion of the data analysis. (b) The first profile is taken along the unipolar diagonal of the map, with the profile exhibiting a strong oscillatory behavior near the Dirac point. (c) Similar behaviors are seen for the second profile taken along $V_{G 2} = - 4 V$ .
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Figure 4
The $Δ R$ maps are shown with varying parameters to show temperature and magnetic field dependence. The analysis done here is meant to determine if Aharonov-Bohm (A-B) oscillations have any significant contribution to observations in the resistance maps. The maps are taken at zero-field and (a) 4.1 K, (b) 310 mK, and (c) 5 K, with (d) being taken at 5 K and 0.1 T. Note that the case of 1.8 K is shown in Fig. 3. All gate voltage graphs have axes that are vertically reflected to match simulation axes. (e) A-B oscillations were extracted from the data between 0 and 0.1 T, with a magnified region shown just below the graph in light blue to determine the periodicity of those oscillations. (f) The Fourier transform of the amplitude of these oscillations is plotted to determine the distribution seen in the data. This distribution was fitted with one peak representing h/e.
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Figure 5
(a) The software package Kwant was used to simulate $Δ R$ maps in devices similar to the one fabricated in Fig. 1. The first simulation was for a graphene circle of similar outer radius to the device. (b) The simulated $Δ R$ map for (a) is shown here, bearing little resemblance to the observed behavior. (c) A total resistance profile is measured on a standard Hall bar device, which shares a topological resemblance to the simulated system in (a). No significant patterns are observed in this case, indicating that the missing central region is crucial to the simulation rather than the circular shape. An example curve along the unipolar diagonal in dotted white. (d) The example curve (red in the upper right inset) has its background subtracted in the same manner as Fig. 2 and is plotted (black curve) alongside the curve from Fig. 3 (transparent blue curve) to highlight the lack of periodicity. (e) The corresponding model is shown for a graphene device in the shape of an annulus. (f) The simulated $Δ R$ map for the annulus bears a closer resemblance to the data, namely in its display of electronic interference near the Dirac point. All gate voltage graphs have axes that are vertically reflected to match simulation axes.
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Figure 6
(a) The local density of states (LDOS) is calculated for the geometry of the actual device (unipolar case). (b) The LDOS is calculated for the case in which the right half of the device is at the Dirac point and (c) when that same region is tuned such that the device becomes bipolar. The left axis of the color scale applies to (a) and (c), whereas the right axis (orange) applies to (b) only. (d) A $Δ R$ profile is used here to demonstrate the inherent asymmetry in amplitude between the unipolar and bipolar configurations. Further, the profile's periodicity is extracted to compare with other observations in the literature. All polarities in these calculations were set to $\pm 10^{12} {cm}^{- 2}$ .
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