Electronic and optical properties in helical trilayer graphene under compression

We built three periodic structures of high-angle helical trilayer graphene (hTLG-1, hTLG-2, and hTLG-3) with a relative interlayer rotation angle (<i>θ</i> = 21.78°) and different initial vertical stacking (locally a <i>C</i>₆ or <i>C</i>₃ symmetry) between consecutive bilayers. Two-dimensional (2D) real-space moiré patterns and the corresponding calculated diffraction patterns showed symmetry differences between the periodic structures. Once the atomic models were characterized in both real and reciprocal spaces, the electronic and linear optical properties of these hTLG systems were studied using density functional theory (DFT) calculations and interlayer compression (<i>δ</i>) as an additional degree of freedom. The electronic band structures and total density of states (DOS), the real part of in-plane 2D linear optical conductivity (Re[<i>σ</i>_2D]), and optical absorption (<i>α</i>) properties were studied. The electronic properties revealed an electron-hole asymmetry around the Fermi energy at different <i>δ</i> values, although strong hole localization at high compression (<i>δ</i> ≤ -19%) was obtained. Indeed, we found high Re[<i>σ</i>_2D] values: Re[<i>σ</i>_2D(<i>ħω</i> = 90 meV)] ∼ 9.5<i>σ</i>₀, Re[<i>σ</i>_2D(<i>ħω</i> = 65 meV)] = 18<i>σ</i>₀, and Re[<i>σ</i>_2D(<i>ħω</i> = 170 meV)] = 10<i>σ</i>₀ for the hTLG-1, hTLG-2 and hTLG-3, respectively, when <i>δ</i> = -21.6%. <i>σ</i>₀ = <i>e</i>²π/2<i>h</i>, is the optical conductivity of monolayer graphene. In addition, an <i>α</i> enhancement in the visible spectrum was obtained. These results demonstrate the relevance of the initial vertical stacking and interlayer compression on the electronics and optics of hTLG superlattices.