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Register a new userTopological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z2 Invariants, and Junction States
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Graphene nanoribbons (GNRs) have recently been shown by Cao, Zhao, and Louie [Cao, T.; Zhao, F.; Louie, S. G. Phys. Rev. Lett. 2017, 119, 076401] to possess distinct topological phases in general, characterized by a Z2 invariant. Cove-edged and chevron GNRs moreover are chemically and structurally diverse, quasi-one-dimensional (1D) nanostructures whose structure and electronic properties can be rationally controlled by bottom-up synthesis from precursor molecules. We derive the value of the topological invariant of the different types of cove-edged and chevron GNRs, and we investigate the electronic properties of various junctions formed by these GNRs, as well as such GNRs with the more common armchair or zigzag GNRs. We study the topological junction states at the interface of two topologically distinct segments. For an isolated GNR having two ends of different terminations, topological end states are shown to develop only at the topologically nontrivial end. Our work extends the explicit categorization of topological invariants of GNRs beyond the previously demonstrated armchair GNRs and provides new design rules for novel GNR junctions as well as future GNR-based nanoelectronic devices.
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Knowledge of the topology of the electronic ground state of materials has led to deep insights to novel phenomena such as the integer quantum Hall effect and fermion-number fractionalization, as well as other properties of matter. Joining two insulators of different topological classes produces fascinating boundary states in the band gap. Another exciting recent development is the bottom-up synthesis (from molecular precursors) of graphene nanoribbons (GNRs) with atomic precision control of their edge and width. Here we connect these two fields, and show for the first time that semiconducting GNRs of different width, edge, and end termination belong to different topological classes. The topology of GNRs is protected by spatial symmetries and dictated by the terminating unit cell. We have derived explicit formula for their topological invariants, and show that localized junction states developed between two GNRs of distinct topology may be tuned by lateral junction geometry. The topology of a GNR can be further modified by dopants, such as a periodic array of boron atoms. In a superlattice consisted of segments of doped and pristine GNRs, the junction states are stable spin centers, forming a Heisenberg antiferromagnetic spin 1/2 chain with tunable exchange interaction. The discoveries here are not only of scientific interest for studies of quasi one-dimensional systems, but also open a new path for design principles of future GNR-based devices through their topological characters.
We investigate quantum transport properties of triangular graphene flakes with zigzag edges by using first principles calculations. Triangular graphene flakes have large magnetic moments which vary with the number of hydrogen atoms terminating its edge atoms and scale with its size. Electronic transmission and current-voltage characteristics of these flakes, when contacted with metallic electrodes, reveal spin valve and remarkable rectification features. The transition from ferromagnetic to antiferromagnetic state under bias voltage can, however, terminate the spin polarizing effects for specific flakes. Geometry and size dependent transport properties of graphene flakes may be crucial for spintronic nanodevice applications.
Graphene nanoribbons (GNRs) possess distinct symmetry-protected topological phases. We show, through first-principles calculations, that by applying an experimentally accessible transverse electric field (TEF), certain boron and nitrogen periodically co-doped GNRs have tunable topological phases. The tunability arises from a field-induced band inversion due to an opposite response of the conduction- and valance-band states to the electric field. With a spatially-varying applied field, segments of GNRs of distinct topological phases are created, resulting in a field-programmable array of topological junction states, each may be occupied with charge or spin. Our findings not only show that electric field may be used as an easy tuning knob for topological phases in quasi-one-dimensional systems, but also provide new design principles for future GNR-based quantum electronic devices through their topological characters.
A recent experimental study showed that an induced folded flap of graphene can spontaneously drive itself its tearing and peeling off a substrate, thus producing long, micrometer sized, regular trapezoidal-shaped folded graphene nanoribbons. As long as the size of the graphene flaps is above a threshold value, the tug of war between the forces of adhesion of graphene-graphene and graphene-substrate, flexural strain of folded region and carbon-carbon (C-C) covalent bonds favor the self-tearing and self-peeling off process. As the detailed information regarding the atomic scale mechanism involved in the process remains not fully understood, we carried out atomistic reactive molecular dynamics simulations to address some features of the process. We show that large thermal fluctuations can prevent the process by increasing the probability of chemical reactions between carbon dangling bonds of adjacent graphene layers. The effects of the strength of attraction between graphene and the substrate on the ribbon growth velocities at the early stages of the phenomenon were also investigated. Structures with initial armchair crack-edges were observed to form more uniform cuts than those having initial zigzag ones. Our results are of importance to help set up new experiments on this phenomenon, especially with samples with nanoscale sized cuts.
In topological systems, a modulation in the gap onset near interfaces can lead to the appearance of massive edge states, as were first described by Volkov and Pankratov. In this work, we study graphene nanoribbons in the presence of intrinsic spin-orbit coupling smoothly modulated near the system edges. We show that this space modulation leads to the appearance of Volkov-Pankratov states, in addition to the topologically protected ones. We obtain this result by means of two complementary methods, one based on the effective low-energy Dirac equation description and the other on a fully numerical tight-binding approach, finding excellent agreement between the two. We then show how transport measurements might reveal the presence of Volkov-Pankratov states, and discuss possible graphene-like structures in which such states might be observed.
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