Dirac semimetal phases in chiral carbon nanoscrolls

Abstract

Chirality induced by rolling a two-dimensional material into a spiral geometry reshapes its electronic band structure. In this work, we theoretically investigate the topological properties of carbon nanoscrolls under an axial magnetic field, focusing on structures in which chirality is encoded through shifted edge alignments. In contrast to unshifted structures, where mirror symmetry pins the Dirac cones to half a flux quantum, chiral carbon nanoscrolls lack this symmetry, and Dirac cones emerge at magnetic flux values away from half a flux quantum. We demonstrate that these Dirac cones are topologically protected by combined inversion-time reversal symmetry and remain robust even when sublattice symmetry is broken. Furthermore, we show that the number of Dirac cones and their real-space probability distributions depend on the number of turns and the magnetic field strength. Our study elucidates the role of chirality in the band topology of nanoscroll geometries.

Figures (13)

• Figure 1: Sketch of two one-round nanoscrolls. The black lines indicate intralayer, nearest-neighbor hopping $r_0$, whereas the red lines indicate the interlayer hopping $r_1$. The purple rectangle highlights the difference in boundary alignment: no shift in panel (a), with a shift in panel (b). In each panel, the red sites correspond to one unit cell, which is repeated infinitely many times along the axial direction in order to produce an infinitely long nanoscroll.
• Figure 2: Example of unit cells for one-round and two-round nanoscrolls with chiral vectors $\vec{C}=(-3,6)$, $\vec{C}=(0,6)$, and $\vec{C}=(-1,6)$. Green and purple dots denote lattice sites belonging to different layers. The red line indicates which sites are aligned on top of each other in a scroll configuration. The numbers in the two-round nanoscroll with $\vec{C}=(-3,6)$ correspond to the site labels in Fig. \ref{['fig:scroll_axial_view']}. Each unit cell is repeated infinitely along the axial $\hat{x}$ direction, forming a nanoscroll with translational symmetry along its axis.
• Figure 3: The schematic diagram illustrates the construction of the model and the corresponding Hamiltonian. The red and black lines represent the hopping in the structure, while the blue dashed line represents a continuous path extending from the interior of the scroll to infinity. The red hopping terms that cross this line acquire the magnetic flux $\phi$.
• Figure 4: (a) The band structures of the one-round carbon nanoscroll with chiral vector $\vec{C}=(-2, 12)$ under various magnetic fluxes $\phi$. The subfigures, presented from left to right, correspond to $\phi=\pi$, $-0.3188$, and $0.3188$, respectively. Unlike unshifted structures, the Dirac cones no longer appear at $\phi = \pi$. (b) The band gap of the system at the Fermi level $E=0$ is plotted as a function of the momentum $k$ and the magnetic flux $\phi$. The yellow circles highlight the two Dirac cones, located approximately at $(k, \phi) \approx (-2.2765, 0.3188)$ and $(2.2765, -0.3188)$.
• Figure 5: For one-round carbon nanoscrolls with $m=12$, the Dirac cones are observed at both positive (left) and negative (right) momenta. The magnetic flux, $\phi$, at which these Dirac cones appear is observed to exhibit a linear dependence on the chiral index $n$.