Aharonov-Bohm effect and broken valley degeneracy in graphene rings

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.

[1]  A. V. Fedorov,et al.  Substrate-induced bandgap opening in epitaxial graphene. , 2007, Nature materials.

[2]  Jeroen van den Brink,et al.  Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations , 2007 .

[3]  Andre K. Geim,et al.  The rise of graphene. , 2007, Nature materials.

[4]  C. Beenakker,et al.  Detection of valley polarization in graphene by a superconducting contact. , 2006, Physical review letters.

[5]  G. Burkard,et al.  Spin qubits in graphene quantum dots , 2006, cond-mat/0611252.

[6]  C. Beenakker,et al.  Valley filter and valley valve in graphene , 2006, cond-mat/0608533.

[7]  R. Friend,et al.  Anomalous energy transfer dynamics due to torsional relaxation in a conjugated polymer. , 2006, Physical review letters.

[8]  D. V. Khveshchenko,et al.  Electron localization properties in graphene. , 2006, Physical review letters.

[9]  B L Altshuler,et al.  Weak-localization magnetoresistance and valley symmetry in graphene. , 2006, Physical review letters.

[10]  M I Katsnelson,et al.  Strong suppression of weak localization in graphene. , 2006, Physical review letters.

[11]  L. Brey,et al.  Electronic states of graphene nanoribbons studied with the Dirac equation , 2006, cond-mat/0603107.

[12]  R. Gilmore.  Elementary Quantum Mechanics in One Dimension , 2004 .

[13]  L. Vandersypen,et al.  Single-shot read-out of an individual electron spin in a quantum dot , 2004, Nature.

[14]  Klaus Richter,et al.  Spin interference effects in ring conductors subject to Rashba coupling , 2003, cond-mat/0309228.

[15]  L. Vandersypen,et al.  Zeeman energy and spin relaxation in a one-electron quantum dot. , 2003, Physical review letters.

[16]  Tsuneya Ando,et al.  Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice. , 2002, Physical review letters.

[17]  A. Morpurgo,et al.  One-dimensional ring in the presence of Rashba spin-orbit interaction: Derivation of the correct Hamiltonian , 2002 .

[18]  Lydia L. Sohn,et al.  Introduction to Mesoscopic Electron Transport , 1997 .

[19]  M. Berry,et al.  Neutrino billiards: time-reversal symmetry-breaking without magnetic fields , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.