We identify the relevant transport regime in terms of appropriate length scales. Therefore, the presented measurements are all close to the diffusive dirty metal regime, and carrier scattering at the sample boundaries alone cannot fully account for the value of the mean free path. This indicates that thermal averaging of interference contributions to the conductance is expected to be relevant. For figure b , the background resistance has been subtracted as described in the text. The raw data trace shows a strong modulation of the background resistance on a magnetic field scale of about mT.
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Note that this aspect is not present in AB rings realized e. It is connected to a special antiunitary symmetry of the Dirac Hamiltonian, which describes graphene well for low Fermi energies. In this work, we will show that the lifting of the valley degeneracy is also visible in the transport properties of graphene rings.
The paper is organized as follows: In the first part, we investigate the AB effect of graphene structures by numerically calculating the transmission of rings attached to infinitely extended leads.
We study both small rings in the one-mode regime and large rings with many modes propagating in both the leads and arms of the ring. In the latter we especially consider the high-field regime and the effects of disorder. In the second part of this work, we show that the breaking of valley-degeneracy by a magnetic field is also visible in the transport properties of graphene rings. We do this by numerically calculating the transmission of graphene rings that are weakly coupled to two leads.
This transmission shows peaks as a function of the Fermi energy EF which correspond to the energy levels of a closed ring; the lifting of their degeneracy can be observed as a splitting of the transmission peaks upon applying a magnetic field perpendicular to the ring. The second term accounts for a staggered on-site potential, i. Such a staggered potential corresponds to a mass term in the effective Dirac equation and will be used in the second part of this paper to suppress the inter-valley scattering that breaks the valley degeneracy [ 13 ].
The lattice points are determined by cutting a ring out of the graphene sheet [cf. In order to solve the transport problem to obtain the dimensionless conductance T within this tight-binding model, we use an adaptive recursive Green function method.
The parameters defining the shape are the inner and outer radius R1 and R2, respectively, and the width WL of the infinitely extended leads. The dashed line marks the points where the mass term used in Section 3 is zero. We begin by considering small graphene rings in the one-mode regime. One of the rings has zigzag type leads while the other has armchair type leads.
To expose a few more details of the frequency content of our data, we show the power spectra of the AB oscillations in figure 2 c and d. There we find pronounced peaks for the fundamental frequency and for several higher harmonics we show only the first five. Note that we plot the spectra on a logarithmic scale, since the fundamental frequency is strongly dominating over the higher ones. Because of the finite width of the rings, one has certain allowed deviations from these values.
For example, for the system of figure 2 a , the fundamental frequency is expected to lie between 0. We also performed calculations for various systems with different parameters and found the same behavior irrespective of the details like radii, width or lead type. Figure 2: Aharonov-Bohm oscillations [ a , b ] and corresponding power spectra [ c , d ] of small rings in the one-mode regime. Next, we turn to the case of larger graphene rings in the many-mode regime, i.
This is the regime applicable to the available experiments of Refs.
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Note that this aspect is not present in AB rings realized e. It is connected to a special antiunitary symmetry of the Dirac Hamiltonian, which describes graphene well for low Fermi energies. In this work, we will show that the lifting of the valley degeneracy is also visible in the transport properties of graphene rings. The paper is organized as follows: In the first part, we investigate the AB effect of graphene structures by numerically calculating the transmission of rings attached to infinitely extended leads.
Aharonov–Bohm interferences from local deformations in graphene
Metrics details Abstract One of the most interesting aspects of graphene is the close relation between its structural and electronic properties. The observation of ripples both in free-standing graphene and in samples on a substrate has given rise to active investigation of the membrane-like properties of graphene, and the origin of the ripples remains one of the most interesting open problems concerning this system. The interplay of structural and electronic properties is successfully described by the modelling of curvature and elastic deformations by fictitious gauge fields. These fields have become an experimental reality after the observation of the Landau levels that can form in graphene due to strain. Here we propose a device to detect microstresses in graphene based on a scanning-tunnelling-microscopy set-up able to measure Aharonov—Bohm interferences at the nanometre scale. The predicted interferences in the local density of states are created by the fictitious magnetic field associated with elastic deformations of the sample.
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