We investigate phase-coherent transport and show Aharonov-Bohm (AB) oscillations in quasiballistic graphene rings with hard confinement. Aharonov-Bohm oscillations are observed in a graphene quantum ring with a topgate covering one arm of the ring. As graphene is a gapless semiconductor, this. Graphene rings in magnetic fields: Aharonov–Bohm effect and valley splitting. J Wurm1,2, M Wimmer1, H U Baranger2 and K Richter1. Published 3 February.

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Curves are plotted with offsets for clarity.

[] Aharonov-Bohm oscillations and magnetic focusing in ballistic graphene rings

The amplitude of the Aharonov—Bohm oscillations is modulated as a function of magnetic field on the same scale as the background resistance, indicating that a finite number of paths traphene a range of different areas contribute to the oscillations.

We discuss the latter effect in more detail below, since the relative change in the Fermi wavelength is expected to be more pronounced in graphene compared to conventional metals.

B 80 Crossref. Series I Physics Physique Fizika.

In athe raw data are shown, while for bthe background has been removed. The Deutsche Physikalische Gesellschaft DPG with a tradition extending back to is the largest physical society in the world with more than 61, members.

For more information see text. Since then, amazing progress in the grzphene of increasingly more complex nanostructures has been made. Horizontal lines indicate frequencies for inner, mean, and outer radii as illustrated in the ahaeonov.

B 77 Crossref. Moreover we show signatures of magnetic focusing effects at small magnetic fields confirming ballistic transport. Frequency range of individual AB oscillation modes marked by arrows. However, due to limited sample stability, the visibility of the oscillations at a given back gate voltage depends on the back gate voltage history.


These oscillations are well explained by taking disorder into account allowing for a coexistence of hard- and soft-wall confinement. To find out more, see our Privacy and Cookies policy. Inset shows larger measurement range.

However, trying to relate the visibilities observed in the two experiments quantitatively assuming that all experimental parameters except the ring radius are the bogm would lead to a phase-coherence length l smaller than the ring circumference L and only slightly larger than the ring radius r 0.

The Aharonov–Bohm effect in a side-gated graphene ring – IOPscience

This correlation voltage is on the same scale as the phase jumps of the Aharonov—Bohm oscillations. Closer inspection shows that the antisymmetric part in the magnetic field of each trace not shown is more than a factor of 10 smaller than the symmetric part. The observed data can be interpreted within existing models for ‘dirty metals’.

Therefore measurements presented here were taken over only small ranges of back gate voltage after having allowed the sample to stabilize in this range. The geometrical aspect ratio is roughly one-third of this aspect ratio estimated from the sample resistance at the charge neutrality point. Note that in order for interference to happen at all, part of the wave function has to leak to the reflecting edge channel as otherwise unitarity ensures perfect transmission.

Finally, we report on the observation of the AB conductance oscillations in the quantum Hall regime at reasonable high magnetic fields, where we find regions with enhanced AB oscillation visibility with values up to 0. We investigate the magnetoresistance of a side-gated ring structure etched out of single-layer graphene. We identify the relevant transport regime in terms of appropriate length scales.

The measured resistance R meas consists of the following parts: It therefore remains unclear to us how the concept of the Thouless energy as an energy scale for wave function correlations can be transferred to the graphene system. The width of this peak is significantly smaller than the range of frequencies expected from the range of possible enclosed areas in our geometry indicated as a gray-shaded region in figure 2 c.


A magnetic field is applied perpendicular to the sample plane.

B 75 Crossref. Minima and maxima of the conductance are approximately horizontal and vertical on this plot. We have observed Aharonov—Bohm oscillations in four-terminal measurements on a side-gated graphene ring structure.

In order to determine this lever arm ratio, we have performed measurements of conductance fluctuations in the plane of the back gate voltage V BG and the side gate voltage V SG not shown. We remark here that this assumption, and the reasoning based on it as given in the main text, corresponds to the usual argument made for dirty metals. In athe raw data are shown. B 79 Crossref. A close up of the 4. For clarity the trace is duplicated with an offset see red arrow.

A Crossref. Vertical dashed lines again represent cyclotron radii as depicted in panel d. Buy this article in print.

The observed data can be interpreted within existing models for dirty metals. Cao J et al Phys.

The Aharonov–Bohm effect in a side-gated graphene ring

In panel c the traces are plotted with an offset for clarity. We observe that the trajectory of the electron starting in the left lead performs a skipping orbit which after four reflections at the boundary enters the right lead.

B 76 Crossref.