Figure 9: (Color online) (a,b) Oscillator strength and (c,d) the corresponding transition energies ΔE for the 1 → 2 (blue curves) and 1 → 3 (red curves) transitions between the intragap energy states of the kink-antink profile as function of (a,c) and (b,d) the external magnetic field B0 (the energy levels are labeled by (1), (2), (3) in Fig. 5(a)). Dashed curves and solid curves in panels (a,c) display the results respectively for a zero and non-zero magnetic field. The insets in panels (a),(b) show the wavespinors of the levels (1) and (3) corresponding to the points with zero oscillator strength.

Mentions: Figure 9 displays the oscillator strength and the corresponding transition energy for the mid-gap levels of the kink-antikink potentials as function of (a,c) and (b,d) external magnetic field B0 (the energy branches are labeled by (1), (2), (3) in Figure 5(a)). The wavefunction for the energies corresponding to the kink states (1), (3) are localized around x' = d whereas the antikink energy levels confine the carriers around x = - d and consequently the oscillator strength by the transition between the kink and the antikink states (e.g. 1 → 2) is zero in the absence or either presence of magnetic field (blue solid curves in panels (a,b)). The inset of panel (a) indicates that the wavespinors satisfy the and relations at and B0 = 0 which leads to a zero oscillator strength for the 1 → 3 transition. In contrast to the single kink profile the shift in the intragap energies of the kink-antikink potential leads to a non-zero value for the oscillator strength at (red solid curve in (a)). The oscillator strength as function of the external magnetic field is shown in panel (b) for . The inset in panel (b) shows the wavefunction of the states (1) and (3) at B0 ≈ 1.6 T where, the same relations as for the single kink potential between the wavespinors ( and ) leads to a zero value for the oscillator strength.