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Register a new userCarbon Nanotubes Band Assignation, Topology, Bloch States and Selection Rules
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Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the single-wall carbon nanotubes are established. The complete set of quantum numbers consists of quasi momenta (angular and linear or helical) and parities with respect to the z-reversal symmetries and, for achiral tubes, the vertical plane. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the same set of quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g. allowed interband transitions, conductivity, Raman tensor, etc.
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We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital components (pseudospins) pick up nonzero winding numbers (topological invariants) around the extremal k-point, the optical strength and nature (i.e., helicity) of the excitonic states are dictated by the optical matrix element winding number, a unique and heretofore unrecognized characteristic. We illustrate these findings in three gapped graphene systems - monolayer graphene with inequivalent sublattices and biased bi- and tri-layer graphene, where the pseudospin textures manifest into a unique optical matrix element winding pattern associated with different valley and photon circular polarization. This winding-number physics leads to novel exciton series and optical selection rules, with each valley hosting multiple bright excitons coupled to light of different helicity. This valley-exciton selective circular dichroism can be unambiguously detected using optical spectroscopy.
We investigate the spectrum of finite-length carbon nanotubes in the presence of onsite and nearest-neighbor superconducting pairing terms. A one-dimensional ladder-type lattice model is developed to explore the low-energy spectrum and the nature of the electronic states. We find that zero energy edge states can emerge in zigzag class carbon nanotubes as a combined effect of curvature-induced Dirac point shift and strong superconducting coupling between nearest-neighbor sites. The chiral symmetry of the system is exploited to define a winding number topological invariant. The associated topological phase diagram shows regions with nontrivial winding number in the plane of chemical potential and superconducting nearest-neighbor pair potential (relative to the onsite pair potential). A one-dimensional continuum model reveals the topological origin of the zero energy edge states: A bulk-edge correspondence is proven, which shows that the condition for nontrivial winding number and that for the emergence of edge states are identical. For armchair class nanotubes, the presence of edge states in the superconducting gap depends on the nanotubes boundary shape. For the minimal boundary condition, the emergence of the subgap states can also be deduced from the winding number.
We derive the generalized magneto-absorption spectra for curved graphene nanorib- bons and carbon nanotubes by using the Peierls tight-binding model. The main spectral characteristics and the optical selection rules result from the cooperative or competitive relationships between the geometric structure and a magnetic field. In curved ribbons, the dominant selection rule remains unchanged during the variation of the curvature. When the arc angle increases, the prominent peaks are split, with some even vanishing as the angle exceeds a critical value. In carbon nanotubes, the angular-momentum coupling induces extra selection rules, of which more are revealed due to the increase of either (both) of the factors: tube diameter and field strength. Particularly once the two factors exceed certain critical values, the optical spectra could reflect the quasi-Landau-level structures. The identifying features of the spec- tra provide insight into optical excitations for curved systems with either open or closed boundary condition.
We have calculated the effects of structural distortions of armchair carbon nanotubes on their electrical transport properties. We found that the bending of the nanotubes decreases their transmission function in certain energy ranges and leads to an increased electrical resistance. Electronic structure calculations show that these energy ranges contain localized states with significant $sigma$-$pi$ hybridization resulting from the increased curvature produced by bending. Our calculations of the contact resistance show that the large contact resistances observed for SWNTs are likely due to the weak coupling of the NT to the metal in side bonded NT-metal configurations.
We have observed large-amplitude coherent phonon oscillations of radial breathing modes (RBMs) in single-walled carbon nanotubes excited through the lowest-energy (E11) interband transitions. In contrast to the previously-studied coherent phonons excited through higher-energy (E22) transitions, these RBMs show comparable intensities between (n-m) mod 3 = 1 and -1 nanotubes. We also find novel non-resonantly excited RBMs over an excitation range of ~300 meV above the E11 transition, which we attribute to multi-phonon replicas arising from strong exciton-phonon coupling.
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