Number Of Dirac Points Research Articles

Tight-binding studies of uniaxial strain in T-graphene nanoribbons

The role of uniaxial strain in armchair, T-graphene nanoribbons (ATGNRs) with symmetric and asymmetric structures is investigated using a nearest-neighbour, tight-binding (TB) model. ATGNRs with structural symmetry and two a sub-lattice structure exhibit Dirac points at zero strain. Application of uniaxial strain to these systems induces multiple Dirac points under compression (up to −20% strain), with the number of these points commensurate with the number of tetra-carbon base-units along the width of the unit cell, accounting also for the mirror symmetry of the structure. Under tensile, uniaxial strain (up to 20% extension), the induced asymmetry in the carbon tetrabond results in the number of Dirac points being reduced, although a minimum number are preserved due to the fundamental mirror-symmetry of the symmetric ATGNR. Asymmetric ATGNRs, which are semiconductors, are shown to have tunable band-gaps that decrease as a function of increasing ribbon width and uniaxial strain. Uniaxial strain induces a single Dirac point at the band edge of these systems under high compression (16%), with the closing of the band gap linked to symmetry-induced perturbations in the structure that override the symmetry-breaking, gap-opening mechanisms. In summary, the TB model shows ATGNRs to have suitable device features for flexible electronics applications, such as band-gap tuning, and for the strain engineering of relativistic properties.

Design of 2D massless Dirac fermion systems and quantum spin Hall insulators based on sp\u2013sp2 carbon sheets

Grapheneis a massless Dirac fermion system, featuring Dirac points in momentum space. It was also first identified as a quantum spin Hall (QSH) insulator when considering spin–orbit coupling (SOC), which opens a band gap at the Dirac points. This discovery has initiated new research efforts to study the QSH effect, towards its application for quantum computing and spintronics. Although the QSH effect has been observed in HgTe quantum wells, the SOC strength of graphene is too small (~1 µeV) to induce the topological insulator phase in an experimentally achievable temperature regime. Here, we perform a systematic atomistic simulation to design two-dimensional sp–sp2 hybrid carbon sheets to discover new Dirac systems, hosting the QSH phase. 21 out of 31 newly discovered carbon sheets are identified as Dirac fermion systems without SOC, distinct from graphene in the number, shape, and position of the Dirac cones occurring in the Brillouin zone. Moreover, we find 19 out of the 21 new Dirac fermion systems become QSH insulators with a sizable SOC gap enhanced up to an order of meV, thus allowing for the QSH effect at experimentally accessible temperatures. In addition, based on the 26 Dirac fermion systems, we make a connection between the number of Dirac points without SOC and the resultant QSH phase in the presence of SOC. Our findings present new prospects for the design of topological materials with desired properties.

Double trigonal warping and the anomalous quantum Hall step in bilayer graphene with Rashba spin–orbit coupling

We demonstrate that the trigonal warping observed in bilayer graphene is doubled in the presence of Rashba spin–orbit (RSO) coupling, i.e. the Dirac points along the three-fold symmetry axis are doubled. There are now seven Dirac points. Furthermore, the RSO interaction breaks the electron–hole symmetry of the magnetic band structure. The most intriguing feature is that the step of the quantum Hall plateau at zero energy is four times that at finite energy. The number of Dirac points and the zero energy Hall step are only determined by the existence of RSO coupling, but are independent of the strength of the coupling. The robustness of these phenomena suggests equivalence between the RSO coupling and the topological effect in bilayer coupling.

Nanophysics in graphene: neutrino physics in quantum rings and superlattices

Electrons in graphene at low energy obey a two-dimensional Dirac equation, closely analogous to that of neutrinos. As a result, quantum mechanical effects when the system is confined or subjected to potentials at the nanoscale may be quite different from what happens in conventional electronic systems. In this article, we review recent progress on two systems where this is indeed the case: quantum rings and graphene electrons in a superlattice potential. In the former case, we demonstrate that the spectrum reveals signatures of 'effective time-reversal symmetry breaking', in which the spectra are most naturally interpreted in terms of effective magnetic flux contained in the ring, even when no real flux is present. A one-dimensional superlattice potential is shown to induce strong band-structure changes, allowing the number of Dirac points at zero energy to be manipulated by the strength and/or period of the potential. The emergence of new Dirac points is shown to be accompanied by strong signatures in the conduction properties of the system.