We study the Drude weight, optical conductivity, and flux-periodicity properties of one-dimensional Hubbard chains using Bethe-ansatz, Lanczos, and exact-diagonalization techniques. We find that the Drude weight D is unexpectedly negative for half-filled Hubbard rings with N =4n sites rejecting a strong paramagnetic response, while it is positive (diamagnetic) for half-filled rings of N =4n +2 sites.In both cases at half filling, D vanishes exponentially with N on a length scale set by the inverse of the gap for small U/t. Near half filling, we find that D approaches a constant, positive, diamagnetic value as N increases, indicating metallic behavior. Combining Bethe-ansatz results near half filling with the known U =0 and U = ao limits and Lanczos finite-size extrapolations, we obtain a general picture of D in the thermodynamic limit as a function of band filling and the ratio U/t. We note similarities with the low-frequency integrated spectral weight of certain hole-doped and electron-doped high-T, compounds.We investigate the finite-frequency optical conductivity, finding structure at co= U and, for one hole off half filling, at co~t /U. We find that minima in the energy of a Hubbard ring enclosing a Aux N occur with changes of half a Aux quantum rather than a full Aux quantum when the Coulomb repulsion is turned on. Lastly, we discuss the relationship of the Drude weight computed from open chains to that obtained from rings, and also the effect of arbitrary phases at the ring boundary.
We have studied band-gap renormalization and band filling in Si-doped GaN films with free-electron concentrations up to 1.7 x 10(exp19) cm(-3) , using temperature-dependent photoluminescence (PL) spectroscopy. The low-temperature (2 K) PL spectra showed a line-shape characteristic for momentum nonconserving band-to-band recombination. The energy downshift of the low-energy edge of the PL line with increasing electron concentration n, which is attributed to band-gap renormalization (BGR) effects, could be fitted by a n(1/3) power law with a BGR coefficient of - 4.7 X 10(exp-8) eV cm. The peak energy of the room-temperature band-to-band photoluminescence spectrum was found to decrease as the carrier concentration increases up to about 7 X 10(exp18) cm(-3) followed by a high-energy shift upon further increasing carrier concentration, due to the interplay between the BGR effects and band filling. The room-temperature PL linewidth showed a monotonic increase with carrier concentration, whic h could be described by a n(2/3) power-law dependence
The band-gap narrowing in heavily doped silicon has been studied by optical techniques—namely, photoluminescence and photoluminescence excitation spectroscopy—and by electrical measurements on bipolar transistors. The optical experiments give a consistent set of data for the band-gap narrowing in n- and p-type material at low temperatures as well as at room temperature. A good agreement is found between the optical and electrical data removing the discrepancies existing so far in the literature.
On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard ' partly in view of the sensitivity of the low-frequency conductivity, i.e. , the Drude spectral weight D to the metal-insulator transition.' '" ' For the 1D Hubbard model, we find D at half-filling to vanish exponentially with system size N (up to N =12) on a length scale set by the inverse gap. However, for finitesized rings with N =4n sites D is negative (N =4n +2, D )0), rejecting paramagnetic response and an interesting violation of Lenz's law. Away from half-filling, D tends to a constant diamagnetic value indicating metallic behavior. Recent Bethe-ansatz solutions by Fye, Mar-43 10 517
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