Cyclotron spin-flip mode as the lowest-energy excitation of unpolarized integer quantum Hall states

The cyclotron spin-flip modes of spin unpolarized integer quantum Hall states $(\nu =2,4,6)$ have been studied with inelastic light scattering. The energy of these modes is significantly smaller compared to the bare cyclotron gap. Second-order exchange corrections are held responsible for a negative energy contribution and render these modes the lowest-energy excitations of unpolarized integer quantum Hall states.

Figure 1

$B$ dependence of ILS line energies. Triangles mark charge-density excitations, circles the CSFM. The dashed lines correspond to $\hslash {\omega }_{\mathrm{c}}$ and $2\hslash {\omega }_{\mathrm{c}}$. Top, left inset: ILS spectra at $B=0$ and $1\mathrm{T}$. Bottom, right inset: ILS spectrum at $2.4\mathrm{T}$.

Figure 2

Electron Zeeman energy $E_{\mathrm{Z}}$. The dashed line plots the expected Zeeman energy when taking $g_{\mathrm{Ga}\mathrm{As}}=-0.44$. The solid line is a linear fit to the data for $g_{\mathrm{QW}}=-0.4$. The inset depicts ILS spectra at a constant perpendicular field of $2\mathrm{T}$ but two different values of the total field. The right inset schematically illustrates the spin-triplet ($S=1$, $S_z=-1$, 0 and 1) cyclotron excitations for $\nu =2$.

Figure 3

The CSFM energy for the spin unpolarized $\nu =2$ quantum Hall state vs perpendicular field. The dashed line gives the cyclotron energy. The upper inset displays ILS spectra of the CSFM for two different in-plane momenta.

Figure 4

The CSFM exchange shift calculated from Eq. (3) with the modified Coulomb interaction $V\left(q\right)=q^{-1}{e}^{q^2{w}^2}\mathrm{erfc}\left(qw\right)$. Its absolute value at $w=0$ equals $(1-\ln 2)\backslash \mathrm{Ry}$.

Figure 5

ILS spectrum of the cyclotron spin-flip mode at the $\nu =4$ unpolarized quantum Hall state at the indicated values for $B_{\perp }$ and $B_{\mathrm{tot}}$.