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The linear optical properties of semiconducting carbon nanotubes are dominated by quasi-one-dimensional excitons formed by single electron-hole pairs. Hence, the nonlinear response at high pump levels most likely leads to the formation of exciton complexes involving several electron-hole pairs. Such complexes would therefore play an important role in, e.g., lasing applications. We demonstrate here that the biexciton complex is surprisingly stable for nanotubes in a wide diameter range. Theoretical predictions for the signature of such states in pump-probe spectroscopy are presented.

We study the binding energies of singlet trions, i.e. charged excitons, in carbon nanotubes. The problem is modeled, through the effective-mass model, as a three-particle complex on the surface of a cylinder, which we investigate using both one- and two-dimensional expansions of the wave function. The effects of dimensionality and correlation are studied in detail. We find that the Hartree-Fock approximation significantly underestimates the trion binding energy. Combined with band structures calculated using a non-orthogonal nearest neighbour tight binding model, the results from the cylinder model are used to compute physical binding energies for a wide selection of carbon nanotubes. In addition, the dependence on dielectric screening is examined. Our findings indicate that trions are detectable at room temperature in carbon nanotubes with radius below 8{\AA}

This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and Agmon-Combes-Thomas uniform exponential decay estimates.Comment: 35 pages, accepted for publication in Journal of Functional Analysi

Abstract. We provide a constructive proof of exponentially localized Wannier functions and related Bloch frames in 1-and 2-dimensional time-reversal symmetric (TRS) topological insulators. The construction is formulated in terms of periodic TRS families of projectors (corresponding, in applications, to the eigenprojectors on an arbitrary number of relevant energy bands), and is thus model-independent. The possibility to enforce also a TRS constraint on the frame is investigated. This leads to a topological obstruction in dimension 2, related to Z2 topological phases.We review several proposals for Z2 indices that distinguish these topological phases, including the ones by Fu-Kane [FK], Prodan [Pr2], Graf-Porta [GP] and Fiorenza-Monaco-Panati [FMP2]. We show that all these formulations are equivalent. In particular, this allows to prove a geometric formula for the the Z2 invariant of 2-dimensional TRS topological insulators, originally indicated in [FK], which expresses it in terms of the Berry connection and the Berry curvature.

Abstract. Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.

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