Topological insulators represent unique phases of matter with insulating bulk and conducting edge or surface states, immune to small perturbations such as backscattering due to disorder. This stems from their peculiar band structure, which provides topological protections. While conventional tools (pressure, doping etc.) to modify the band structure are available, time periodic perturbations can provide tunability by adding time as an extra dimension enhanced to the problem. In this short review, we outline the recent research on topological insulators in non equilibrium situations. Firstly, we introduce briefly the Floquet formalism that allows to describe steady states of the electronic system with an effective time-independent Hamiltonian. Secondly, we summarize recent theoretical work on how light irradiation drives semi-metallic graphene or a trivial semiconducting system into a topological phase. Finally, we show how photons can be used to probe topological edge or surface states.Comment: 7 pages, 4 figures, comments are welcom

Time-periodic perturbations can be used to engineer topological properties of matter by altering the Floquet band structure. This is demonstrated for the helical edge state of a spin Hall insulator in the presence of monochromatic circularly polarized light. The inherent spin structure of the edge state is influenced by the Zeeman coupling and not by the orbital effect. The photocurrent (and the magnetization along the edge) develops a finite, helicity-dependent expectation value and turns from dissipationless to dissipative with increasing radiation frequency, signalling a change in the topological properties. The connection with Thouless' charge pumping and nonequilibrium zitterbewegung is discussed, together with possible experiments.

The synthesis of a unique isotope engineered system, double-wall carbon nanotubes with natural carbon outer and highly 13C enriched inner walls, is reported from isotope enriched fullerenes encapsulated in single-wall carbon nanotubes (SWCNTs). The material allows the observation of the D line of the highly defect-free inner tubes that can be related to a curvature induced enhancement of the electron-phonon coupling. Ab initio calculations explain the inhomogeneous broadening of inner tube Raman modes due to the distribution of different isotopes. Nuclear magnetic resonance shows a significant contrast of the isotope enriched inner SWCNTs compared to other carbon phases and provides a macroscopic measure of the inner tube mass content. The high curvature of the small diameter inner tubes manifests in an increased distribution of the chemical shift tensor components.

The analysis of the Raman scattering cross section of the radial breathing modes of double-wall carbon nanotubes allowed to determine the optical transitions of the inner tubes. The Raman lines are found to cluster into species with similar resonance behavior. The lowest components of the clusters correspond well to SDS wrapped HiPco tubes. Each cluster represents one particular inner tube inside different outer tubes and each member of the clusters represents one well defined pair of inner and outer tubes. The number of components in one cluster increases with decreasing of the inner tube diameter and can be as high as 14.

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We report on the spin dynamics of 13C isotope enriched inner walls in double-wall carbon nanotubes using 13C nuclear magnetic resonance. Contrary to expectations, we find that our data set implies that the spin-lattice relaxation time (T1) has the same temperature (T) and magnetic field (H) dependence for most of the inner-wall nanotubes detected by NMR. In the high-temperature regime (T approximately > or = 150 K), we find that the T and H dependence of 1/T1T is consistent with a 1D metallic chain. For T approximately < or = 150 K we find a significant increase in 1/T1T with decreasing T, followed by a sharp drop below approximately = 20 K. The data clearly indicate the formation of a gap in the spin excitation spectrum, where the gap value 2delta approximately = 40 K (congruent to 3.7 meV) is H independent.

High filling of single wall carbon nanotubes (SWCNT) with C60 and C70 fullerenes in solvent is reported at temperatures as low as 69 o C. A 2 hour long refluxing in n-hexane of the mixture of the fullerene and SWCNT results in a high yield of C60,C70@SWCNT, fullerene peapod, material. The peapod filling is characterized by TEM, Raman and electron energy loss spectroscopy and X-ray scattering. We applied the method to synthesize the temperature sensitive (N@C60:C60)@SWCNT as proved by electron spin resonance spectroscopy. The solvent prepared peapod samples can be transformed to double walled nanotubes enabling a high yield and industrially scalable production of DWCNT.

Abstract. A detailed investigation of the Raman response of the inner tube radial breathing modes (RBMs) in double-wall carbon nanotubes is reported. It revealed that the number of observed RBMs is two to three times larger than the number of possible tubes in the studied frequency range. This unexpected increase in Raman lines is attributed to a splitting of the inner tube response. It is shown to originate from the possibility that one type of inner tube may form in different types of outer tubes and the fact that the inner tube RBM frequency depends on the diameter of the enclosing tube. Finally, a comparison of the inner tube RBMs and the RBMs of tubes in bundles gave clear evidence that the interaction in a bundle is stronger than the interaction between inner and outer tubes.