Abstract
A model of a helical nanotube permitting analytical calculation of the spectrum and wave functions is proposed and studied. It is shown that the specific character of the symmetry of the Hamiltonian results in an electronic spectrum having no band structure despite the periodicity of the potential along the system axis. A two-dimensional ribbon rolled into a helix and a quasi-one-dimensional helix in a magnetic field are considered as limiting cases of the model. It is shown that the presence of additional local minima in the subbands of the electronic spectrum leads to a nonmonotonic dependence of the ballistic conductance of the system on the chemical potential.
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References
I. O. Kulik, Pis’ma Zh. Éksp. Teor. Fiz. 11(8), 407 (1970) [JETP Lett. 11 (8), 275 (1970)].
L. I. Magarill, D. A. Romanov, and A. V. Chaplik, Zh. Éksp. Teor. Fiz. 113(4), 1411 (1998) [JETP 86 (4), 771 (1998)].
V. A. Margulis and M. A. Pyataev, Phys. Rev. B: Condens. Matter 72, 075312 (2005).
D. N. Aristov, Phys. Rev. B: Condens. Matter 59, 6368 (1999).
J. Brüning, V. A. Geyler, V. A. Margulis, and M. A. Pyataev, J. Phys. A: Math. Gen. 35, 4239 (2002).
V. Ya. Prinz, Physica E (Amsterdam) 24, 54 (2004).
S. Roche, G. Dresselhaus, M. S. Dresselhaus, and R. Saito, Phys. Rev. B: Condens. Matter 62, 16092 (2000).
O. V. Kibis, Fiz. Tverd. Tela (St. Petersburg) 43(12), 2142 (2001) [Phys. Solid State 43 (12), 2237 (2001)].
V. M. Osadchiĭ and V. Ya. Prinz, Pis’ma Zh. Éksp. Teor. Fiz. 72(6), 451 (2000) [JETP Lett. 72 (6), 312 (2000)].
V. A. Geyler, O. G. Kostrov, and V. A. Margulis, Fiz. Tverd. Tela (St. Petersburg) 44(3), 449 (2002) [Phys. Solid State 44 (3), 467 (2002)].
A. A. Gorbatsevich, V. V. Kapaev, and Yu. V. Kopaev, Pis’ma Zh. Éksp. Teor. Fiz. 57(9), 565 (1993) [JETP Lett. 57 (9), 580 (1993)].
V. Ya. Demikhovskiĭ and A. A. Perov, Pis’ma Zh. Éksp. Teor. Fiz. 76(10), 723 (2002) [JETP Lett. 76 (10), 620 (2002)].
M. Okamoto, T. Uda, and K. Takayanagi, Phys. Rev. B: Condens. Matter 64, 033303 (2001).
M. V. Entin and L. I. Magarill, Phys. Rev. B: Condens. Matter 66, 205308 (2002).
V. Ya. Demikhovskiĭ and S. S. Savinskiĭ, Fiz. Tverd. Tela (Leningrad) 34(8), 2382 (1992) [Sov. Phys. Solid State 34 (8), 1278 (1992)].
L. I. Magarill and M. V. Éntin, Pis’ma Zh. Éksp. Teor. Fiz. 78(4), 249 (2003) [JETP Lett. 78 (4), 213 (2003)].
M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Phys. Rev. B: Condens. Matter 31, 6207 (1985).
V. F. Gantmakher, Fiz. Nizk. Temp. (Kharkov) 31(3), 436 (2005) [Low Temp. Phys. 31 (3), 331 (2005)].
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Original Russian Text © A.A. Grigor’kin, S.M. Dunaevskiĭ, 2007, published in Fizika Tverdogo Tela, 2007, Vol. 49, No. 3, pp. 557–561.