Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in ...dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as Z2 topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.
We theoretically demonstrate that the second-order topological insulator with robust corner states can be realized in two-dimensional Z_{2} topological insulators by applying an in-plane Zeeman ...field. The Zeeman field breaks the time-reversal symmetry and thus destroys the Z_{2} topological phase. Nevertheless, it respects some crystalline symmetries and thus can protect the higher-order topological phase. By taking the Kane-Mele model as a concrete example, we find that spin-helical edge states along zigzag boundaries are gapped out by the Zeeman field whereas the in-gap corner state at the intersection between two zigzag edges arises, which is independent of the field orientation. We further show that the corner states are robust against the out-of-plane Zeeman field, staggered sublattice potentials, Rashba spin-orbit coupling, and the buckling of honeycomb lattices, making them experimentally feasible. Similar behaviors can also be found in the well-known Bernevig-Hughes-Zhang model.
The existence of inequivalent valleys K and K' in the momentum space of 2D hexagonal lattices provides a new electronic degree of freedom, the manipulation of which can potentially lead to new types ...of electronics, analogous to the role played by electron spin. In materials with broken inversion symmetry, such as an electrically gated bilayer graphene (BLG), the momentum-space Berry curvature Ω carries opposite sign in the K and K' valleys. A sign reversal of Ω along an internal boundary of the sheet gives rise to counterpropagating 1D conducting modes encoded with opposite-valley indices. These metallic states are topologically protected against backscattering in the absence of valley-mixing scattering, and thus can carry current ballistically. In BLG, the reversal of Ω can occur at the domain wall of AB- and BA-stacked domains, or at the line junction of two oppositely gated regions. The latter approach can provide a scalable platform to implement valleytronic operations, such as valves and waveguides, but it is technically challenging to realize. Here, we fabricate a dual-split-gate structure in BLG and present evidence of the predicted metallic states in electrical transport. The metallic states possess a mean free path (MFP) of up to a few hundred nanometres in the absence of a magnetic field. The application of a perpendicular magnetic field suppresses the backscattering significantly and enables a junction 400 nm in length to exhibit conductance close to the ballistic limit of 4e
/h at 8 T. Our experiment paves the way to the realization of gate-controlled ballistic valley transport and the development of valleytronic applications in atomically thin materials.
We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We ...illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.
Bilayer graphene with an interlayer potential difference has an energy gap and, when the potential difference varies spatially, topologically protected one-dimensional states localized along the ...difference’s zero lines. When disorder is absent, electronic travel directions along zero-line trajectories are fixed by valley Hall properties. Using the Landauer–Büttiker formula and the nonequilibrium Green’s function technique, we demonstrate numerically that collisions between electrons traveling in opposite directions, due to either disorder or changes in path direction, are strongly suppressed. We find that extremely long mean free paths of the order of hundreds of micrometers can be expected in relatively clean samples. This finding suggests the possibility of designing low power nanoscale electronic devices in which transport paths are controlled by gates which alter the interlayer potential landscape.
Experimental electrical double-layer capacitances of porous carbon electrodes fall below ideal values, thus limiting the practical energy densities of carbon-based electrical double-layer capacitors. ...Here we investigate the origin of this behaviour by measuring the electrical double-layer capacitance in one to five-layer graphene. We find that the capacitances are suppressed near neutrality, and are anomalously enhanced for thicknesses below a few layers. We attribute the first effect to quantum capacitance effects near the point of zero charge, and the second to correlations between electrons in the graphene sheet and ions in the electrolyte. The large capacitance values imply gravimetric energy storage densities in the single-layer graphene limit that are comparable to those of batteries. We anticipate that these results shed light on developing new theoretical models in understanding the electrical double-layer capacitance of carbon electrodes, and on opening up new strategies for improving the energy density of carbon-based capacitors.
We study the possibility of realizing topological phases in graphene with randomly distributed adsorbates. When graphene is subjected to periodically distributed adatoms, the enhanced spin-orbit ...couplings can result in various topological phases. However, at certain adatom coverages, the intervalley scattering renders the system a trivial insulator. By employing a finite-size scaling approach and Landauer-Büttiker formula, we show that the randomization of adatom distribution greatly weakens the intervalley scattering, but plays a negligible role in spin-orbit couplings. Consequently, such a randomization turns graphene from a trivial insulator into a topological state.
We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved ...time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√U(2)+t(⊥)(2), where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.
Low‐energy density has long been the major limitation to the application of supercapacitors. Introducing topological defects and dopants in carbon‐based electrodes in a supercapacitor improves the ...performance by maximizing the gravimetric capacitance per mass of the electrode. However, the main mechanisms governing this capacitance improvement are still unclear. We fabricated planar electrodes from CVD‐derived single‐layer graphene with deliberately introduced topological defects and nitrogen dopants in controlled concentrations and of known configurations, to estimate the influence of these defects on the electrical double‐layer (EDL) capacitance. Our experimental study and theoretical calculations show that the increase in EDL capacitance due to either the topological defects or the nitrogen dopants has the same origin, yet these two factors improve the EDL capacitance in different ways. Our work provides a better understanding of the correlation between the atomic‐scale structure and the EDL capacitance and presents a new strategy for the development of experimental and theoretical models for understanding the EDL capacitance of carbon electrodes.
Dopants, defects, and double layers: Electrochemical measurements and ab initio calculations on single‐layer CVD‐grown graphene show that topological defects improve the density of states and N‐dopants can tune the Fermi level of graphene, both of which influence the quantum capacitance connected in series with the Helmholtz capacitance and therefore modify the electrical double‐layer (EDL) capacitance.
Graphene is a promising material for designing next-generation electronic and valleytronic devices, which often demand the opening of a bandgap in the otherwise gapless pristine graphene. To date, ...several conceptually different mechanisms have been extensively exploited to induce bandgaps in graphene, including spin–orbit coupling and inversion symmetry breaking for monolayer graphene, and quantum confinement for graphene nanoribbons (GNRs). Here, we present a multiscale study of the competing gap opening mechanisms in a graphene overlayer and GNRs proximity-coupled to topological insulators (TIs). We obtain sizable graphene bandgaps even without inversion symmetry breaking and identify the Kekulé lattice distortions caused by the TI substrates to be the dominant gap opening mechanism. Furthermore, Kekulé distorted armchair GNRs display intriguing nonmonotonous gap dependence on the nanoribbon width, resulting from the coexistence of quantum confinement, edge passivation, and Kekulé distortions. The present study offers viable new approaches for tunable bandgap engineering in graphene and GNRs.
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