Many-particle hybridization of optical transitions from zero-mode Landau levels in HgTe quantum wells

Abstract

We present far-infrared magnetospectroscopy measurements of a HgTe quantum well in the inverted band structure regime over the temperature range of 2 to 60 K. The particularly low electron concentration enables us to probe the temperature evolution of all four possible optical transitions originating from zero-mode Landau levels, which are split off from the edges of the electron-like and hole-like bands. By analyzing their resonance energies, we reveal an unambiguous breakdown of the single-particle picture indicating that the explanation of the anticrossing of zero-mode Landau levels in terms of bulk and interface inversion asymmetries is insufficient. Instead, the observed behavior of the optical transitions is well explained by their hybridization driven by electron-electron interaction. We emphasize that our proposed many-particle mechanism is intrinsic to HgTe quantum wells of any crystallographic orientation, including (110) and (111) wells, where bulk and interface inversion asymmetries do not induce the anticrossing of zero-mode Landau levels.

Figures (7)

• Figure 1: (a) Band structure in 8-nm-wide HgTe/Cd$_{0.7}$Hg$_{0.3}$Te QW at $T=2$ K grown on (001) CdTe buffer in the absence of the IIA effect. The blue and red curves represent band dispersion of electron-like (E$1$) and hole-like (H$1$ and H$2$) subbands, calculated within the 8-band k$\cdot$p Hamiltonian Q36. The solid and dashed curves correspond to the quasimomentum orientation along the crystallographic directions (001) and (110), respectively. (b) The energy of LLs in as a function of perpendicular magnetic field $B$. The numbers over the curves show the LL indices within the 8-band k$\cdot$p Hamiltonian Q36. The blue and red curves represent the zero-mode LLs from E$1$ and H$1$ subbands, respectively. The arrows represent the LL transitions observed in the vicinity of $B_c$Q49Q50Q51Q52Q53Q54Q57. The brown dotted curves represent the approximation of the linear dependence of the zero-mode LL energy on the magnetic field in the vicinity of $B_c$, used within the framework of Eq. (\ref{['eq:2']}).
• Figure 2: (a)-(d) Color maps of magnetoabsorption showing $\alpha$, $\alpha'$, $\beta$, $\beta'$ LL transitions as a function of magnetic field, measured at different temperatures $T$: (a) $2.0$ K, (b) $20$ K, (c) $40$ K, (d) $60$ K. The symbols represent position of the magnetoabsorption lines, whose energies are used in the evaluation of $\Delta{E}$. (e)-(h) Square of the energy difference for $|\hbar\omega_{\alpha'}-\hbar\omega_{\alpha}|$ and $|\hbar\omega_{\beta'}-\hbar\omega_{\beta}|$ at the same temperatures as in the respective top panels. The black and red solid curves are the fitting to Eq. (\ref{['eq:2']}) for the pairs ($\alpha$, $\alpha'$) and ($\beta$, $\beta'$), respectively. The results for other temperatures are provided in the Supplemental Material SM.
• Figure 3: Temperature evolution of $|M|$, $B_c$ and $\Delta$ extracted by fitting the difference in resonant energies for the pairs of ($\alpha$, $\alpha'$) LL transitions (black circles) and ($\beta$, $\beta'$) LL transitions (red triangles) by Eq. (\ref{['eq:2']}). The blue curves represent the calculations of $|M|$ and $B_c$ performed by using the 8-band k$\cdot$p Hamiltonian Q36.
• Figure 4: Function ${F}(\varphi,\theta)$ that defines the IIA-induced anticrossing gap between zero-mode LLs within the single-particle picture. The arrows indicate the $\theta$ angles corresponding to specific growth directions.
• Figure S1: The waterfall plot of magnetoabsorption spectra presented in Fig. 3 in the main text. The resonant energies for $\alpha$, $\beta$, $\alpha'$ and $\beta'$ transitions are marked by the symbols.