Aharonov-Bohm effect and broken valley degeneracy in graphene rings

By P. Recher, B. Trauzettel, A. Rycerz, Y. Blanter, C. Beenakker, A. Morpurgo. 2007

191 citations recorded by the source corpus.

We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modeled by a space-dependent mass term in the Dirac equation. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. We compare our analytical model to another type of ring with strong intervalley scattering. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/35284fa45656a335c6e2b10738147e0c6f91d479

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In Atomic and Molecular Physics, and Optics

1. Franco Nori
2. Y. Bliokh
3. V. Freilikher
4. G. Giavaras
5. A. Rozhkov
6. Sahel Ashhab
7. K. Bliokh
8. I. Georgescu

In Materials Chemistry

1. G. Giavaras
2. Franco Nori
3. Y. Bliokh
4. V. Freilikher
5. A. Rozhkov

Citations in the corpus

• Electronic properties of mesoscopic graphene structures: Charge confinement and control of spin and charge transport (2011, background): “Theoretical investigations of graphene rings showed that the valley-induced orbital degeneracy is lifted, as a result of the ring confinement and the applied magnetic field [165].”
• Colloquium: The transport properties of graphene: An introduction (2010, unknown): “The Dirac Hamiltonian (3) in polar coordinates r and ϕ reads (Hentschel and Guinea, 2007; Peres et al., 2009a; 13 Recher et al., 2007) HK = −ivF~ ( 0 L− L+ 0 ) , (14) with L± = e±iϕ(∂/∂r±ir−1∂/∂ϕ).”