Intersubband decay of 1-D exciton resonances in carbon nanotubes

We have studied intersubband decay of E22 excitons in semiconducting carbon nanotubes experimentally and theoretically. Photoluminescence excitation line widths of semiconducting nanotubes with chiral indicess (n, m) can be mapped onto a connectivity grid with curves of constant (n-m) and (2n+m). Moreover, the global behavior of E22 linewidths is best characterized by a strong increase with energy irrespective of their (n-m) mod(3)= \pm 1 family affiliation. Solution of the Bethe-Salpeter equations shows that the E22 linewidths are dominated by phonon assisted coupling to higher momentum states of the E11 and E12 exciton bands. The calculations also suggest that the branching ratio for decay into exciton bands vs free carrier bands, respectively is about 10:1.Comment: 4 pages, 4 figure

Ultrafast photocurrent measurement of the escape time of electrons and holes from carbon nanotube PN junction photodiodes

Ultrafast photocurrent measurements are performed on individual carbon nanotube PN junction photodiodes. The photocurrent response to sub-picosecond pulses separated by a variable time delay {\Delta}t shows strong photocurrent suppression when two pulses overlap ({\Delta}t = 0). The picosecond-scale decay time of photocurrent suppression scales inversely with the applied bias VSD, and is twice as long for photon energy above the second subband E22 as compared to lower energy. The observed photocurrent behavior is well described by an escape time model that accounts for carrier effective mass.Comment: 8 pages Main text, 4 Figure

Double point self-intersection surfaces of immersions

A self-transverse immersion of a smooth manifold M^{k+2} in R^{2k+2} has a double point self-intersection set which is the image of an immersion of a smooth surface, the double point self-intersection surface. We prove that this surface may have odd Euler characteristic if and only if k is congruent to 1 modulo 4 or k+1 is a power of 2. This corrects a previously published result by Andras Szucs. The method of proof is to evaluate the Stiefel-Whitney numbers of the double point self-intersection surface. By earier work of the authors these numbers can be read off from the Hurewicz image h(\alpha ) in H_{2k+2}\Omega ^{\infty }\Sigma ^{\infty }MO(k) of the element \alpha in \pi _{2k+2}\Omega ^{\infty }\Sigma ^{\infty }MO(k) corresponding to the immersion under the Pontrjagin-Thom construction.Comment: 22 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper4.abs.htm

Exercises with the universal R-matrix

Using the formula for the universal $R$-matrix proposed by Khoroshkin and Tolstoy, we give a detailed derivation of $L$-operators for the quantum groups associated with the generalized Cartan matrices $A_1^{(1)}$ and $A_2^{(1)}$.Comment: 36 page