Terahertz Landau level spectroscopy of Dirac fermions in millimeter-scale twisted bilayer graphene

TL;DR

The paper demonstrates millimeter-scale twisted bilayer graphene can be probed with free-space terahertz magneto-optics to measure inter-Landau-level gaps and extract the twist-angle–dependent Fermi velocity. By combining Hall-effect–based chemical potential estimates with terahertz cyclotron-resonance data, the authors determine the cyclotron mass and, from $\mu$ and $m^*$, the Fermi velocity across twist angles. The measurements show Dirac-like Landau level physics persists away from neutrality and yield Fermi velocities in agreement with prior STM and transport studies, validating a scalable THz approach for characterizing moiré materials. This approach broadens the toolbox for studying macroscopic quantum phenomena in two-dimensional materials and opens avenues for exploring collective excitations in TBG and related systems.

Abstract

Exotic electronic physics including correlated insulating states and fractional Chern insulators have been observed in twisted bilayer graphene in a magnetic field when the Fermi velocity vanishes, however a question remains as to the stability of these states which is controlled by the gap to the first excited state. Free-space terahertz magneto-optics can directly probe the gap to charge excitations which bounds the stability of electronic states, but this measurement has thus-far been inaccessible due to the micron size of twisted bilayer graphene samples, while the wavelength of terahertz light is up to a millimeter. Here we leverage advances in fabrication to create twisted bilayer graphene samples over 5 mm x 5 mm in size with a uniform twist angle and study the magnetic field dependence of the cyclotron resonance by a complex Faraday rotation experiment in p-doped large angle twisted bilayer graphene. These measurements directly probe charge excitations in inter-Landau level transitions and determine the Fermi velocity as a function of twist angle.

Figures (4)

• Figure 1: Electronic structure and doping of large angle twisted bilayer graphene. (a) Spectral function for a $9.43^\circ$ twist from a tight-binding model with phenomenological broadening $\eta=0.050$ eV, and (b) calculated density of states with chemical potential consistent with the $9^\circ$ experimental sample illustrated. (c) A linear fit to the asymmetric part of the measured Hall resistance in the $9^\circ$ sample gives the hole carrier density $n_h=3.966\times 10^{13}/\mathrm{cm}^2$. (d) Zooming in from the gross band structure to the fine structure of Landau levels the levels are separated by a cyclotron frequency $\hbar\omega_c$ in the terahertz range.
• Figure 2: Illustration of the incident terahertz beam (green) on the TBG sample and the resulting Faraday rotation. Labeled optical elements include beam splitter (BS), Auston switch (AS), off-axis parabolic mirror (OAP) terahertz polarizer (P), and delay stage (DS).
• Figure 3: Magneto-terahertz measurements of $7^\circ$, $9^\circ$, $10^\circ$ and $20^\circ$ twisted bilayer graphene. (a) Real and (b) imaginary parts of the Faraday rotation angle as dependent on magnetic field and light frequency; measured data is the solid lines and fits are the dashed lines. The samples are measured by terahertz pulses where the entire frequency range simultaneously probes the sample, however, the intensity of the pulse is much smaller at the extreme ends of the spectral range which results in noise at the upper end of the frequency range in the case $9^\circ$ sample. (c) Cyclotron frequency (gap between Landau levels) and (d) scattering rate extracted from fits to the experimental data; a fit to the formula $\omega_c=(e/m^*)\sqrt{B_i^2+B^2}$ gives the cyclotron mass $m^*$ and a length-scale $L_i=\sqrt{\hbar/eB_i}$ corresponding to disorder in the samples.
• Figure 4: Fermi velocities determined by magneto-optical spectroscopy (red), previous STM studies (gray), and quantum oscillations studies (yellow). Lower and upper dashed lines are the theoretical fit from Eq. \ref{['eq:vF-expected']} with $v_F^\mathrm{mono}=1.0$ and $1.2\times 10^6$ m/s respectively and $t_\perp = 0.1$ eV. Variation in monolayer Fermi velocity can originate from the level of doping elias2011dirachwang2012fermi.