najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2019-10-1-50-62najo-532Research ArticlePHYSICSФИЗИКАPersistent current in a chain of two Holstein–Hubbard rings in the presence of Rashba spin-orbit interactionChatterjeeA.

Hyderabad-500046

acsp@uohyd.ernet.inSmolkinaM. O.

Kronverkskiy, 49, St. Petersburg, 197101

vega14@mail.ruPopovI. Y.

Kronverkskiy, 49, St. Petersburg, 197101

popov1955@gmail.comUniversity of HyderabadIndiaITMO UniversityRussian Federation2019060820251015062Copyright © Chatterjee A., Smolkina M.O., Popov I.Y., 20252025Chatterjee A., Smolkina M.O., Popov I.Y.Chatterjee A., Smolkina M.O., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/532

The persistent current in a chain of two quantum rings threaded by an Aharonov–Bohm flux is studied in the presence of electron-phonon interactions and Rashba spin-orbit coupling. The chain is modeled by the Holstein–Hubbard–Rashba Hamiltonian, the phonon’s degrees of freedom were eliminated by the conventional Lang–Firsov transformation, the effective electronic Hamiltonian was diagonalized by using the Hartree–Fock approximation. The equations for ground state energy, persistent current and Drude weight were also obtained. The persistent current was calculated by differentiating the GS energy. The dependence of ground state energy, persistent current and Drude weight as a functions of flux for different values of Rashba spin-orbit interaction was numerically shown. The effects of Aharonov–Bohm flux, temperature, chemical potential spin-orbit interaction and electron-phonon interaction on the persistent current were also investigated.

spin-orbit interactionpersistent currentThis work was partially financially supported by the Government of the Russian Federation (grant 08-08), by grant 16-11-10330 of Russian Science Foundation. The authors thank Prof. R. Figari and Prof. W. Florek for interesting discussion.ReferencesButtiker M., Imry Y. and Landauer R. Josephson behavior in small normal one-dimensional rings. Phys. Lett. A, 1983, 96, P. 365–267.Buttiker M., Imry Y. and Landauer R. Josephson behavior in small normal one-dimensional rings. Phys. Lett. A, 1983, 96, P. 365–267.Cheung H.-F., Gefen Y., Riedel E.K. and Shih W.-H. Persistent current in small one-dimensional metal rings. Phys. Rev. B, 1988, 37, P. 6050–6062Cheung H.-F., Gefen Y., Riedel E.K. and Shih W.-H. Persistent current in small one-dimensional metal rings. Phys. Rev. B, 1988, 37, P. 6050–6062Takada Y. and Chatterjee A. Possibility of a metallic phase in the charge-density-wave-spin-density-wave crossover region in the onedimensional Hubbard-Holstein model at half filling. Phys. Rev. B., 2003, 67, P. 081102.Takada Y. and Chatterjee A. Possibility of a metallic phase in the charge-density-wave-spin-density-wave crossover region in the onedimensional Hubbard-Holstein model at half filling. Phys. Rev. B., 2003, 67, P. 081102.Sil S., Maiti S.K. and Chakrabarti A. Interplay of magnetic field and geometry in magneto-transport of mesoscopic loops with Rashba and Dresselhaus spin-orbit interactions. J. Appl. Phys., 2012, 112, P. 024321.Sil S., Maiti S.K. and Chakrabarti A. Interplay of magnetic field and geometry in magneto-transport of mesoscopic loops with Rashba and Dresselhaus spin-orbit interactions. J. Appl. Phys., 2012, 112, P. 024321.Manolescu A.,Daday C.,Gudmundsson V. Coulomb effects on the spin polarization of quantum ring. Nanosystems Phys. Chem. Math., 2011, 2(3), P. 29–36.Manolescu A.,Daday C.,Gudmundsson V. Coulomb effects on the spin polarization of quantum ring. Nanosystems Phys. Chem. Math., 2011, 2(3), P. 29–36.Monisha P.J., Sankar I.V., Sil S. and Chatterjee A. Persistent current in a correlated quantum ring with electron-phonon interaction in the presence of Rashba interaction and Aharonov–Bohm flux. Scientific Reports, 2016, 6, P. 20056.Monisha P.J., Sankar I.V., Sil S. and Chatterjee A. Persistent current in a correlated quantum ring with electron-phonon interaction in the presence of Rashba interaction and Aharonov–Bohm flux. Scientific Reports, 2016, 6, P. 20056.Voda A. Micro, Nanosystems and Systems on Chips: Modeling, Control, and Estimation. New York, John Wiley & Sons, 2013.Voda A. Micro, Nanosystems and Systems on Chips: Modeling, Control, and Estimation. New York, John Wiley & Sons, 2013.Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y. Wave dynamics on time-depending graph with Aharonov–Bohm ring. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9(4), P. 457–463.Eremin D.A., Grishanov E.N., Nikiforov D.S., Popov I.Y. Wave dynamics on time-depending graph with Aharonov–Bohm ring. Nanosystems: Physics, Chemistry, Mathematics, 2018, 9(4), P. 457–463.Lang I. and Firsov Y.A. Kinetic theory of semiconductors with low mobility. Sov. Phys. JETP, 1963, 16(5), P. 1301–1312.Lang I. and Firsov Y.A. Kinetic theory of semiconductors with low mobility. Sov. Phys. JETP, 1963, 16(5), P. 1301–1312.Cabib D. and Callen E. Charge order and antiferromagnetic order in the Hubbard model with nearest neighbor Coulomb interaction: Weak coupling. Phys. Rev. B, 1975, 12, P. 5249–5254.Cabib D. and Callen E. Charge order and antiferromagnetic order in the Hubbard model with nearest neighbor Coulomb interaction: Weak coupling. Phys. Rev. B, 1975, 12, P. 5249–5254.

The authors declare that there are no conflicts of interest present.