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Register a new userElectric Field Tunable Topological Phases in Graphene Nanoribbons
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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.
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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.
Topological insulators (TIs) are an emerging class of materials that host highly robust in-gap surface/interface states while maintaining an insulating bulk. While most notable scientific advancements in this field have been focused on TIs and related topological crystalline insulators in 2D and 3D, more recent theoretical work has predicted the existence of 1D symmetry-protected topological phases in graphene nanoribbons (GNRs). The topological phase of these laterally-confined, semiconducting strips of graphene is determined by their width, edge shape, and the terminating unit cell, and is characterized by a Z2 invariant (similar to 1D solitonic systems). Interfaces between topologically distinct GNRs characterized by different Z2 are predicted to support half-filled in-gap localized electronic states which can, in principle, be utilized as a tool for material engineering. Here we present the rational design and experimental realization of a topologically-engineered GNR superlattice that hosts a 1D array of such states, thus generating otherwise inaccessible electronic structure. This strategy also enables new end states to be engineered directly into the termini of the 1D GNR superlattice. Atomically-precise topological GNR superlattices were synthesized from molecular precursors on a Au(111) surface under ultra-high vacuum (UHV) conditions and characterized by low temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Our experimental results and first-principles calculations reveal that the frontier band structure of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This novel manifestation of 1D topological phases presents an entirely new route to band engineering in 1D materials based on precise control of their electronic topology, and is a promising platform for future studies of 1D quantum spin physics.
Magnetic carbon nanostructures are currently under scrutiny for a wide spectrum of applications. Here, we theoretically investigate armchair graphene nanoribbons patterned with asymmetric edge extensions consisting of laterally fused naphtho groups, as recently fabricated via on-surface synthesis. We show that an individual edge extension acts as a spin-$frac{1}{2}$ center and develops a sizable spin-polarization of the conductance around the band edges. The Heisenberg exchange coupling between a pair of edge extensions is dictated by the position of the second naphtho group in the carbon backbone, thus enabling ferromagnetic, antiferromagnetic, or non-magnetic states. The periodic arrangement of edge extensions yields full spin-polarization at the band extrema, and the accompanying ferromagnetic ground state can be driven into non-magnetic or antiferromagnetic phases through external stimuli. Overall, our work reveals precise tunability of the ${pi}$-magnetism in graphene nanoribbons induced by naphtho groups, thereby establishing these one-dimensional architectures as suitable platforms for logic spintronics.
Band gap control by an external field is useful in various optical, infrared and THz applications. However, widely tunable band gaps are still not practical due to variety of reasons. Using the orthogonal tight-binding method for $pi$-electrons, we have investigated the effect of the external electric field on a subclass of monolayer chevron-type graphene nanoribbons that can be referred to as jagged graphene nanoribbons. A classification of such ribbons was proposed and band gaps for applied fields up to the SiO$_2$ breakdown strength ($1$ V/nm) were calculated. According to the tight-binding model, band gap opening (or closing) takes place for some type of jagged graphene nanoribbons in the external electric field that lays in the plane of the structure and perpendicular to its longitudinal axis. Tunability of the band gap up to $0.6$ eV is attainable for narrow ribbons. In the case of jagged ribbons with armchair edges larger jags forming a chevron pattern of the ribbon enhance the controllability of the band gap. For jagged ribbons with zigzag and armchair edges regions of linear and quadratic dependence of the band gap on the external electric field can be found that are useful in devices with controllable modulation of the band gap.
Quantum-dot states in graphene nanoribbons (GNR) were calculated using density-functional theory, considering the effect of the electric field of gate electrodes. The field is parallel to the GNR plane and was generated by an inhomogeneous charge sheet placed atop the ribbon. Varying the electric field allowed to observe the development of the GNR states and the formation of localized, quantum-dot-like states in the band gap. The calculation has been performed for armchair GNRs and for armchair ribbons with a zigzag section. For the armchair GNR a static dielectric constant of {epsilon} approx. 4 could be determined.
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