Terahertz Circular Dichroism in Commensurate Twisted Bilayer Graphene

TL;DR

This work addresses the challenge of achieving terahertz circular dichroism in non-magnetic materials by exploiting commensurate twisted bilayer graphene (C-TBG). Using tight-binding models to extract interlayer coherence scales $V_0$ and phase shifts $\varphi$, together with symmetry-based low-energy continuum descriptions, the authors show that strong interlayer hybridization in large-angle commensurate twists yields a robust THz ellipticity up to about $1.5$ mdeg, significantly larger than naive Dirac-model expectations. The dichroism is tunable by a perpendicular electric field $\\mathcal{E}$ and by doping, and is sensitive to lateral interlayer translation, making specific SE-even/SE-odd C-TBG structures (notably those with small unit cells) the most favorable. The results establish C-TBG as a magnetism-free platform for large terahertz circular dichroism with practical tunability, with implications for terahertz chiroptical devices and molecular sensing. The analysis also clarifies how finite-bilayer thickness corrections align with thin-layer predictions, reinforcing the experimental relevance of the reported effects.

Abstract

We report calculations of terahertz ellipticities in large-angle, 21.79$^\circ$ and 38.21$^\circ$, commensurate twisted bilayer graphene, and predict values as high as 1.5 millidegrees in the terahertz region for this non-magnetic material. This terahertz circular dichroism exhibits a magnitude comparable to that of chiral materials in the visible region. At low frequencies, the dichroic response is mediated by strong interlayer hybridization, which allows us to probe the symmetry and strength of these couplings. Crucially, lateral interlayer translation tunes this response, in contrast to small twist angle bilayer graphene's near invariance under under interlayer translation. We examine the magnitude and phase of the interlayer coupling for all structures containing fewer than 400 atoms per unit cell. Finally, we find that the dichroism can be manipulated by applying an electric field or with doping.

Figures (9)

• Figure 1: SE-odd and SE-even commensurate twisted bilayer graphene (C-TBG) differ by a small interlayer translation; visualized for the $\sqrt{7}\times\sqrt{7}$ structures. (a) The SE-odd structure exhibits points with at most $C_3$ symmetry. (b) The SE-even structure exhibits points with $C_6$ symmetry. (c) Momentum space contributions to $\text{Im}(\sigma^{xy})$ reveal the $l=2\hbar$ phase winding of the wavefunctions about the $K$ point in the SE-odd structure. (d) Interlayer shift makes the wavefunctions a superposition of angular momentum eigenstates and circular dichroism appears as visualized for the SE-even structure.
• Figure 2: Real space superlattice structures of the eight smallest SE-even C-TBG systems. The system with $N=4$ atoms is the AA stacked bilayer. The gray lines outline the unit cells and intersect at points of $C_6$ symmetry. The existence of these points is key to the sublattice symmetry; for a generic twist and shift of graphene bilayers there will be no points with $C_6$ symmetry.
• Figure 3: (a) Interlayer shift determines the low energy band structure, but the high energy band structure is invariant under shifts; visualized for the $N=28$ structure where $\vec{T}=(\bm{a}^M_1+\bm{a}^M_2)/7$. (b) While short range hoppings are sufficient to describe high energy degrees of freedom, for the $N=28$ structures sixth nearest neighbors ($4a_0$) is necessary to capture the low energy behavior. Longer range hoppings are needed to describe structures with larger unit cells.
• Figure 4: Representative low energy band structures of SE-even structures around the $K$ point. Energies are expressed in terms of the interlayer coherence $V_0$ so that the structures overlap and their universal Dirac behavior at large energies is manifest. The structures are not all the same since the twist angle and the phase $\varphi$ changes the band gap $2V_0\sin((\varphi-\theta)/2)$ and low energy dispersion. The $N=4$ structure (AA bilayer, $\theta=0$) is gapless while the largest gap for the structures with less than 400 atoms per unit cell is $1.617 V_0$ for the $N=364$ structure.
• Figure 5: Densities of states and band structures for SE-odd and SE-even structures with perpendicular electric field strengths from $0$ to $12V_0/ed\approx 0.1028$ V/nm. Top Row:(a) The SE-odd structure is gapless in the absence of an electric field, but develops a gap that rapidly saturates as $V_0\sqrt{x^2/(1+x^2)}$ where $x=4\mathcal{E}/V_0^2$ and to van Hove singularities develop at the band edges. (b) SE-odd structure in the absence of an electric field is gapless with a quadratic band touching similar to the Bernal bilayer. (c-e) In the presence of an electric field, SE-odd band structures are gapped and exhibit an avoided crossing above and below the Fermi energy corresponding to the field decoupling the layers at the $K$ point. Bottom Row:(f) The SE-even structures are always gapped with magnitude $2V_0\sin((\varphi-\theta)/2)$ for twist angle $\theta$. In the presence of an electric field, the Dirac points move away from the Fermi energy and the the band gap minima move away from the $K$ point linearly in field strength leading to an enhancement of the density of states at low energies and a delayed onset of universal Dirac cone behavior. (g-e) SE-even structures feature a constant gap and the Dirac cone separation scales linearly with the electric field.