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Integer quantum Hall effect in a lattice model revisited: Kubo formalism
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10.1063/1.4748312
/content/aip/journal/jap/112/4/10.1063/1.4748312
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/4/10.1063/1.4748312
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of a square lattice subjected to a perpendicular magnetic field B .

Image of FIG. 2.
FIG. 2.

Energy levels for a square lattice () when is set at 0.1. The black lines represent the locations of the energy levels for the ordered (W = 0) case. On the other hand, the blue lines denote the positions of the energy levels for the disordered () case, where (a), (b), and (c) correspond to W = 1, 2, and 3, respectively.

Image of FIG. 3.
FIG. 3.

Transverse conductivity (red curve) as a function of Fermi energy for a square lattice () considering , W = 1, and . The Landau bands (light green) are superimposed on it.

Image of FIG. 4.
FIG. 4.

Longitudinal conductivity (red curve) as a function of Fermi energy for a square lattice () for the same parameter values given in Fig. 3. The Landau bands (light green) are superimposed on it.

Image of FIG. 5.
FIG. 5.

Probability amplitude (PA) at different lattice sites (N) of a square lattice () for the same parameter values as mentioned in Fig. 3. The top and bottom panels correspond to the results for the eigenstates selected from the left and right edges of the Landau band, respectively, while the middle one is for the eigenstates lie in the centre of the Landau band. The three different columns are associated with the three different Landau bands shown in Fig. 3. To understand the nature of energy eigenstates more clearly, in each figure, we present the results for two states those are chosen from the respective regions.

Image of FIG. 6.
FIG. 6.

Hall conductivity as a function of Fermi energy for a square lattice () with W = 1 and . The dark-violet, pink and blue lines correspond to Q = 5, 10, and 15, respectively.

Image of FIG. 7.
FIG. 7.

Hall conductivity as a function of Fermi energy for a square lattice () considering W = 1 and . The blue, pink, and dark-violet colors correspond to , 0.05, and 0.1, respectively.

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/content/aip/journal/jap/112/4/10.1063/1.4748312
2012-08-27
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Integer quantum Hall effect in a lattice model revisited: Kubo formalism
http://aip.metastore.ingenta.com/content/aip/journal/jap/112/4/10.1063/1.4748312
10.1063/1.4748312
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