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The persistent charge and spin currents in topological insulator Bi 2 Se 3 nanowires
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10.1063/1.3658853
/content/aip/journal/jap/110/9/10.1063/1.3658853
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/9/10.1063/1.3658853

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Sketch of a cylindrical Bi 2 X 3 nanowire. The blue sphere is the electron and the blue arrow indicates spin orientation of the electron. R is the radius of the nanowire.

Image of FIG. 2.
FIG. 2.

(Color online) The energy spectrum of a TI nanowire with R = 60 nm. The black dashed lines and the green solid lines denote the bulk and surface states, respectively.

Image of FIG. 3.
FIG. 3.

The DOS of the surface states of Bi 2 Se 3 TI nanowire with the radius R = 60 nm.

Image of FIG. 4.
FIG. 4.

(Color online) (a) The energy spectrum of the Bi 2 Se 3 TI nanowire as a function of the angular momentum quantum number m with R = 60 nm and kz  = 0. The spin-down and spin-up surface states are denoted by the red and blue squares, respectively. The black squares represent the bulk conduction and valence band states. (b) and (c) The density distributions of the bulk conduction and valence band states (marked by the black arrows in (a)). (d) and (e) are similar to (b) and (c), but for the surface states (marked by the red and blue arrows in (a)).

Image of FIG. 5.
FIG. 5.

(Color online) (a) The energy spectrum of a TI nanowire as a function of the angular momentum quantum number m with R = 60 nm and kz  = 0.1/nm. The surface states of conduction band and valence band are denoted by the red and blue squares, respectively. (b) and (c) The density distributions of the bulk conduction and valence band states (marked by the black arrows in (a)). (d) and (e) are similar to (b) and (c), but for the surface states (marked by the red and blue arrows in (a)).

Image of FIG. 6.
FIG. 6.

(Color online) The energies spacing between up and down branches of the surface states of TI wires at kz  = 0 as a function of the radius R. The solid lines are the numerical results calculated from the four band model. The red dashed lines are obtained from the analytical solution of surface Hamiltonian (6). ΔEj  = 2jA 0/R, where A 0 is the four band Hamiltonian parameter, j = ±1/2, ±3/2,. is total azimuthal angular quantum number.

Image of FIG. 7.
FIG. 7.

(Color online) The spatial distribution of spin orientation for different surface states with: (a) kz  = 0, j > 0; (b) kz  = 0, j < 0; (c) and small |j| number; (d) and small |j| number.

Image of FIG. 8.
FIG. 8.

(Color online) The spin orientation for different surface states at (a) kz  = 0; (b) kz  = 0.1/nm. The surface states of the up and down branches of surface state are shown in red and blue symbols, respectively.

Image of FIG. 9.
FIG. 9.

(Color online) The magneto energy spectra. (a) The energy of the surface states under different magnetic field of a TI wire with radius R = 60 nm and kz  = 0; (b) the same as (a), but with kz  = 0.1/nm. The red and black lines denote the up and down branches of the surface bands, respectively.

Image of FIG. 10.
FIG. 10.

(Color online) The Fermi energy (the upper panel) and the persistent CC (the lower panel) as a function of the magnetic flux, respectively. The electron density is n = 5 × 106/cm.

Image of FIG. 11.
FIG. 11.

(Color online) The maximum amplitude of persistent charge current (CCM ) and Fermi energy (EF  − E 0) as a function of the electron density. E 0 is a zero-point energy.

Image of FIG. 12.
FIG. 12.

The persistent SC as a function of the magnetic flux at electron density n = 5 × 106/cm.

Tables

Generic image for table
Table I.

The parameters used in our calculation. U, P, and V are short for the words: unit, parameters, and values, respectively.

Generic image for table
Table II.

The spin orientation calculated by the analytical surface Hamiltonian (6), where .

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/content/aip/journal/jap/110/9/10.1063/1.3658853
2011-11-08
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The persistent charge and spin currents in topological insulator Bi2Se3 nanowires
http://aip.metastore.ingenta.com/content/aip/journal/jap/110/9/10.1063/1.3658853
10.1063/1.3658853
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