Magnetically tuned topological phase in graphene nanoribbon heterojunctions

Abstract

The interplay between topology and magnetism often triggers the exotic quantum phases. Here, we report an accessible scheme to engineer the robust $\mathbb{Z}_{2}$ topology by intrinsic magnetism, originating from the zigzag segment connecting two armchair segments with different width, in one-dimensional graphene nanoribbon heterojunctions. Our first-principle and model simulations reveal that the emergent spin polarization substantially modifies the dimerization between junction states, forming the special SSH mechanism depending on the magnetic configurations. Interestingly, the topological phase in magnetic state is only determined by the width of the narrow armchair segment, in sharp contrast with that in the normal state. In addition, the emergent magnetism increases the bulk energy band gap by an order of magnitude than that in the nonmagnetic state. We also discuss the $\mathbb{Z}$ topology of the junction states and the termination-dependent of topological end states. Our results bring new way to tune the topology in graphene nanoribbon heterostructure, providing a new platform for future one-dimensional topological devices and molecular-scale spintronics.

Figures (5)

• Figure 1: (a) Typical unit cell of the $L_{1}$-$L_{2}$-$N_{1}$-$N_{2}$-GNRH. Here, $3$-$3$-$9$-$17$-GNRH is schematically shown. Black circles and white circles represent carbon atom and passivated hydrogen atoms, respectively. (b) Potential magnetic configurations. Red and blue circles stand for spin up and spin down, respectively. The size of colored circles denote the relative magnitude of spin polarization.
• Figure 2: Energy spectrum of $8$-$8$-$9$-$17$-GNRH. Left, and right panels are for NM, and AFMB configurations, respectively. Top panels are for the LDOS and energy spectrum maps, the horizontal axis is the real-axis coordinate along $x$, the longitudinal axis is energy and the brightness stands for the relative strength of DOS. There are two nearly degenerate states near the Fermi energy. Two lower panels are the real space LDOS distribution of the two junction states.
• Figure 3: Topological phase diagrams of GNRH. (a) and (b) for the NM configuration, (c) for AFMB configuration, and (d) for AFMC configuration. (a) Topological phase diagram with respect to $L_1$ and $L_2$ for fixed $N_{1}=9, N_{2}=17$. (b), (c) and (d) Topological phase diagram with respect to $N_1$ and $N_2 - N_1$ with fixed $L_{1}=2, L_{2}=3$. The gray, and blank area, denote the topologically non-trivial ($\mathbb{Z}_{2}=1$), and trivial phase ($\mathbb{Z}_{2}=0$), respectively. The blue colored scale indicates the magnitude of bandgap. The topological phase diagram for magnetic configurations is insensitive to $L_{1/2}$ in (c) and (d). The AFMA configuration is always a normal insulator.
• Figure 4: (a) From left to right, the band structures evolution with fixed $L_{1}=2$ and $L_{2}=3$ under the mean field approximation. The parity of the bands at high symmetry points is marked with "$+$" (even) and "$-$" (odd). The red dash line shows the SSH fitting results. The fitted parameters are shown inset. (b) The positions of the WCs and the schematic hopping process between WCs for the four possible configurations. Red, and blue arrows represent the intra- ($t_{1}$) and inter-dimer ($t_{2}$) hopping, respectively. For magnetic configurations, only the spin-up hopping channel is shown.
• Figure 5: Topological end states. (a)DOS of $2$-$3$-$11$-$19$-GNRH obtained by the $\pi$-orbital Hubbard model simulations. The grey shaded area represents the DOS contribution of end cell. A finite $2$-$3$-$11$-$19$-GNRH with ten unitcells is adopted. Here, $\mathbb{Z}_{2}=1$ for AFMB, AFMC, and NM configurations, while AFMA is not a $\mathbb{Z}_{2}$ topological insulator. The broaden factor is set to 5 meV. (b) Same as (a), but for $2$-$3$-$5$-$13$-GNRH. (c)DOS of $2$-$3$-$11$-$19$-GNRH with ten unitcells, the corresponding unitcell is changed and shown inset. (d)Same as (c), but for $2$-$3$-$5$-$13$-GNRH. (e) The real space LDOS of the zero mode end states of $2$-$3$-$11$-$19$-GNRH in AFMB phase. (f) Same as (e), but for $2$-$3$-$11$-$19$-GNRH in AFMC phase.