Possible evidence for Harper broadening in the yellow exciton series of Cu2O at ultrahigh magnetic fields

TL;DR

The paper investigates hydrogen-like excitons in the Cu2O yellow series under ultrahigh magnetic fields to test the limits of the effective mass approximation and to search for Harper broadening. By performing magneto-absorption spectroscopy across non-destructive pulsed magnets, single-turn coils, and electromagnetic flux compression up to 520 T, the authors identify the spin Zeeman split $2p_0$ and $3p_0$ states and extract a reduced exciton mass $\mu^* = 0.415 \pm 0.01\,m_e$, incorporating spin Zeeman effects into the hydrogenic model. A notable finding is the abrupt increase in the FWHM of the $2p_0^{S_z=+1}$ transition above 300 T, consistent with Harper broadening as the magnetic length $\ell_B$ approaches the lattice constant, indicating a breakdown of the effective mass description in the ultrahigh-field regime. The results imply that ultrahigh magnetic fields can qualitatively alter excitonic and lattice-scale physics, with potential connections to Hofstadter-like fractal spectra in real materials.

Abstract

Hydrogen-like systems in ultra-high magnetic fields are of significant interest in interdisciplinary research. Previous studies have focused on the exciton wavefunction shrinkage under magnetic fields down to artificial crystal lattices (e.g., quantum wells, superlattices), where the effective mass approximation remains valid. However, further compression toward the natural crystal lattice scale remains experimentally challenging. In this study, we report magneto-absorption measurements on the yellow-exciton series in Cu2O using pulsed magnetic fields of up to 500 T. The strong low energy absorption features are assigned to the spin Zeeman split 2p0 and 3p0 exciton states. The high field data provides a value for the reduced effective mass of the exciton u* = 0.415 \pm 0.01me. Intriguingly, the broadening of the 2p0 ground state transition exhibits a sudden increase for ultrahigh magnetic fields above 300 T, providing possible evidence for Harper broadening - an indication of the breakdown of the effective mass approximation when the magnetic length becomes comparable to the lattice constant of the crystal.

Figures (4)

• Figure 1: (a) Exciton absorption spectra of Cu$_2$O for both $\sigma^+$ (blue lines) and $\sigma^-$ (green lines) measured in NDPM with fields up to 60 T. (b) Exciton absorption spectra of Cu$_2$O measured in EMFC with field up to 500 T. Both experiments were performed on the same sample in the Faraady geometry. The spectra are shifted vertically for clarity.
• Figure 2: Energies for 2p$_{0}^{S_z=\pm1}$ and 3p$_{0}^{S_z=\pm1}$ excitonic absorption as a function of applied magnetic field at 45 K. The green and blue symbols indicate the absorption energy determined from $\sigma^+$ and $\sigma^-$ polarizations. Data points below 32 T, taken from ref artyukhin2018magneto, are shown as light blue and green closed circles. The orange and violet curves are fits to the excitonic absorption energy using the hydrogen model in a magnetic field. The energy evolution of 2p$_0^{S_z=+1}$ deviates from the hydrogen model at fields above 300 T
• Figure 3: (a) Fit to the absorption spectrum of Cu$_2$O measured at $B=120$ T and $T=45$ K using multiple Gaussian functions. The red line is the measured absorption spectra, and the blue line is the superimposed fitting line. The orange line indicates the subtracted background used when making the Gaussian fits. (b) The multiple Gaussian function used to fit the experimental data.
• Figure 4: (a) FWHM of 2p$_0^{S_z=+1}$ excitonic absorption as a function of magnetic field normalized by the zero-field FWHM ($\simeq 2.9$ meV). (b) Normalised FWHM of 2p$_0^{S_z=+1}$ excitonic absorption as a function of magnetic length $\ell_B = \sqrt{\hbar/eB}$.