Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences

Phase diagram and crossover phases of topologically ordered graphene zigzag nanoribbons: role of localization effects

We computed the phase diagram of zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with non-universal topological entanglement entropy that exhibits significant variance. We explored the nature of non-local correlations in both the topologically ordered and crossover phases. In the presence of localization effects, strong on-site repulsion and/or doping weaken non-local correlations between the opposite zigzag edges of the topologically ordered phase. In one of the crossover phases, bothe-/2solitonic fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains solitonice-/2fractional charges but lacks charge transfer correlations. We also observed properties of non-topological, strongly disordered, and strongly repulsive phases. Each phase on the phase diagram exhibits a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.

Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines' chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.

New disordered anyon phase of doped graphene zigzag nanoribbon

We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigzag edges. We make the following new predictions, which can be experimentally tested: (1) In the low doping case and weak disorder regime, the soft gap in the tunneling density of states is replaced by a sharp peak at the midgap energy with two accompanying peaks. The [Formula: see text] fractional charges that reside on the boundary of the zigzag edges are responsible for these peaks. (2) We find that the midgap peak disappears as the doping concentration increases. The presence of [Formula: see text] fractional charges will be strongly supported by the detection of these peaks. Doped zigzag ribbons may also exhibit unusual transport, magnetic, and inter-edge tunneling properties.

Effects analogous to the Kekulé distortion induced by pseudospin polarization in graphene nanoribbons: confinement and coupling by breakdown of chiral correlation

We show here that potential barriers, applied to armchair nanoribbons, induce a hexagonal effective lattice, polarized in pseudospin on the sides of the barriers system, which has an effective unit cell greater than that of infinite graphene (pseudospin superstructure). This superstructure is better defined with the increase of the barrier potential, until a transport gap is generated. The superstructure, as well as the induced gap, are fingerprints of Kekulé distortion in graphene, so here we report an analogous effect in nanoribbons. These effects are associated with a breakdown of the chiral correlation. As a consequence, an effective zigzag edge is induced, which controls the electronic transport instead of the original armchair edge. With this, confinement effects (quasi-bound states) and couplings (splittings), both of chiral origin (decorrelation between chiral counterparts), are observed in the conductance as a function of the characteristics of the applied barriers and the number of barriers used. In general, the Dirac-like states in the nanoribbon can form quasi-bound states within potential barriers, which explains the Klein tunneling in armchair nanoribbons. On the other hand, for certain conditions of the barriers (widthLand potentialV) and the energy (E) of the quasi-particle, quasi-bound states between the barriers can be generated. These two types of confinement would be generating tunneling peaks, which are mixed in conductance. In this work we make a systematic study of conductance as a function ofE,LandVfor quantum dots systems in graphene nanoribbons, to determine fingerprints of chirality: line shapes and behaviors, associated with each of these two contributions. With these fingerprints of chirality we can detect tunneling through states within the barriers and differentiate these from tunneling through states formed between the barriers or quantum dot. With all this we propose a technique, from conductance, to determine the spatial region that the state occupies, associated with each tunneling peak.

Novel electrical properties and applications in kaleidoscopic graphene nanoribbons

As one of the representatives of nano-graphene materials, graphene nanoribbons (GNRs) have more novel electrical properties, highly adjustable electronic properties, and optoelectronic properties than graphene due to their diverse geometric structures and atomic precision configurations. The electrical properties and band gaps of GNRs depend on their width, length, boundary configuration and other elemental doping, etc. With the improvement of the preparation technology and level of GNRs with atomic precision, increasing number of GNRs with different configurations are being prepared. They all show novel electrical properties and high tunability, which provides a broad prospect for the application of GNRs in the field of microelectronics. Here, we summarize the latest GNR-based achievements in recent years and summarize the latest electrical properties and potential applications of GNRs.

Electronic cloaking effect of localized states induced in graphene nanoribbons

The cloaking effect of electronic states was only reported in bilayer graphene. Here in this work we show that this effect can also be induced in armchair graphene nanoribbons (AGNRs), by potential barriers that modulate the chirality property of the system (correlation between pseudospins). These barriers manipulate the chirality and generates pseudospin polarizations on the sides of the barrier, which leaves spatial regions in evidence, in which states behave differently. In AGNRs the extended states (ES), associated with the tunneling of Klein, use only some sites in the nanoribbon lattice (sublattice of ES). On the other hand, the barrier applied in the nanoribbon, induces states totally localized within the region of the barrier, these states use only the sites not used by the sublattice of ES. The localized states remain invisible for electronic transport for all the energies and characteristics of the barrier in the region of the first effective transport band, the same as the states are changing. This electronic cloaking effect can be suppressed by the application of a magnetic field, detecting in the conductance the previously invisible states in the form of Fano resonances. We discuss here the possibility of using this cloaking effect to generate mechanisms that can hide information or to activate hidden system effects.