Persistent currents in a multicomponent Tomonaga-Luttinger liquid: Application to a mesoscopic semiconductor ring with spin-orbit interaction

We study persistent currents in semiconductor ballistic rings with spin-orbit Rashba interaction. We use as a working model the multicomponent Tomonaga-Luttinger liquid which arises due to the nonparabolic dispersion relations of electrons in the rings with rather strong spin-orbit coupling. This approach predicts some characteristic features of persistent currents, which may be observed in experimental studies of semiconductor ballistic rings.

Figure 1

The lowest radial band in the two-band approximation $({\alpha }_0=3.0)$. Solid thick line: hard-wall potential. Dashed thick line: singular oscillator potential.

Figure 2

The lowest radial band in the hard-wall potential $({\alpha }_0=3.0)$. Solid thick line: two-band approximation. Solid thin line: one-band approximation.

Figure 3

The lowest radial band in the singular oscillator potential $({\alpha }_0=3.0)$. Dashed thick line: two-band approximation. Dashed thin line: one-band approximation.

Figure 4

The lowest radial band in the hard-wall potential $({\alpha }_0=6.0)$. Solid thick line: two-band approximation. Solid thin line: one-band approximation.

Figure 5

Persistent currents $I∕I_0$ vs flux $\Phi ∕{\Phi }_0$ at $u=0.4$ and different values of $\eta$ (fixed $\mu$, $N_e=4N_0+2$).

Figure 6

Persistent currents $I∕I_0$ vs flux $\Phi ∕{\Phi }_0$ at $u=0.0$ and different values of $\eta$ (fixed $\mu$, $N_e=4N_0+2$).

Figure 7

Persistent currents $I∕I_0$ vs flux $\Phi ∕{\Phi }_0$ at $\eta =0.3$ and different values of $u$ (fixed $\mu$, $N_e=4N_0+2$).

Figure 8

Persistent currents $I∕I_0$ vs flux $\Phi ∕{\Phi }_0$ at $u=0.4$ and different values of $\eta$ (fixed $\mu$, odd $N_e$).