The tight-binding formulation of the Kronig-Penney model.

Electronic band structure calculations are frequently parametrized in tight-binding form; the latter representation is then often used to study electron correlations. In this paper we provide a derivation of the tight-binding model that emerges from the exact solution of a particle bound in a periodic one-dimensional array of square well potentials. We derive the dispersion for such a model, and show that an effective next-nearest-neighbour hopping parameter is required for an accurate description. An electron-hole asymmetry is prevalent except in the extreme tight-binding limit, and emerges through a "next-nearest-neighbour" hopping term in the dispersion. We argue that this does not necessarily imply next-nearest-neighbour tunneling; this assertion is demonstrated by deriving the transition amplitudes for a two-state effective model that describes a double-well potential, which is a simplified precursor to the problem of a periodic array of potential wells. A next-nearest-neighbour tunneling parameter is required for an accurate description even though there are no such neighbours.

The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model.

Allowing a single electron to hop to next-nearest neighbours (NNN) in addition to the closest atomic sites in the Holstein model, a modified Trugman method is applied to exactly calculate the effect on the polaronic effective mass in one, two, and three dimensions, building on the previous study of the one-dimensional NNN Holstein model. We also present perturbative calculations and a heuristic scaling factor for the coupling strength and ion frequency to nearly map the NNN Holstein model back onto the original Holstein model. When account is taken of the modified electronic bandwidth near the electron energy, we find that including NNN hopping effectively increases the polaron effective mass.

Refractometric sensitivity and thermal stabilization of fluorescent core microcapillary sensors: theory and experiment.

Fluorescent-core microcapillaries (FCMs) present a robust basis for the application of optical whispering gallery modes toward refractometric sensing. An important question concerns whether these devices can be rendered insensitive to local temperature fluctuations, which may otherwise limit their refractometric detection limits, mainly as a result of thermorefractive effects. Here, we first use a standard cylindrical cavity formalism to develop the refractometric and thermally limited detection limits for the FCM structure. We then measure the thermal response of a real device with different analytes in the channel and compare the result to the theory. Good stability against temperature fluctuations was obtained for an ethanol solvent, with a near-zero observed thermal shift for the transverse magnetic modes. Similarly good results could in principle be obtained for any other solvent (e.g., water), if the thickness of the fluorescent layer can be sufficiently well controlled.

Vanishing of interband light absorption in a persistent spin helix state.

Spin-orbit coupling plays an important role in various properties of very different materials. Moreover efforts are underway to control the degree and quality of spin-orbit coupling in materials with a concomitant control of transport properties. We calculate the frequency dependent optical conductivity in systems with both Rashba and Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling is tuned to be equal to the Rashba spin-orbit coupling, the interband optical conductivity disappears. This is taken to be the signature of the recovery of SU(2) symmetry. The presence of the cubic Dresselhaus spin-orbit coupling modifies the dispersion relation of the charge carriers and the velocity operator. Thus the conductivity is modified, but the interband contribution remains suppressed at most but not all photon energies for a cubic coupling of reasonable magnitude. Hence, such a measurement can serve as a diagnostic probe of engineered spin-orbit coupling.

Model of the electron-phonon interaction and optical conductivity of Ba(1-x)K(x)BiO(3) superconductors.

We investigate the physical properties of the Ba(1-x)K(x)BiO(3) compounds with a focus on the optical properties. Results from the simple Holstein model, describing a single band coupled to an oxygen breathing mode with parameters derived from first principles calculations, are in excellent agreement with a broad range of experimental information. It accounts for an insulating parent compound at x=0, with a direct (optical) and an indirect gap, and a metal insulator transition around x=0.38. Strong electron-phonon coupling leads to spectral weight redistribution over a frequency scale much larger than the characteristic phonon frequency and to strongly anharmonic phonons. We find that the metallic phase in the vicinity of phase boundary is close to the polaronic regime.

Modification of ensemble emission rates and luminescence spectra for inhomogeneously broadened distributions of quantum dots coupled to optical microcavities.

We investigate the spontaneous emission modifications when ensembles of quantum dots (QDs) with differing emission frequencies and finite Lorentzian linewidths are coupled to a microcavity. Using contour integrals we develop a general expression for the rate enhancement when neither the emitter nor the cavity resonance can be treated as a delta function. We show that the ensemble cavity-coupled luminescence lifetimes are generally suppressed in the case of spherical cavities and that the spontaneous emission dynamics of the cavity coupled component becomes increasingly stretched as the coupling factor increases. The Q-factor measured from the luminescence spectrum can be much lower than the intrinsic cavity Q-factor, and is in many practical situations limited by the QD spectral width. The mode spectrum observed in the photoluminescence (PL) spectrum can be largely determined by the QD emission linewidth, permitting this parameter to be extracted without requiring single-particle spectroscopy. In the case of Si-QDs, the linewidth cannot be significantly greater than 10 meV in order to observe spherical cavity resonances in the PL spectrum.

Hall conductivity of a spin-triplet superconductor.

We calculate the Hall conductivity for a spin-triplet superconductor, using a generalized pairing symmetry dependent on an arbitrary phase phi. A promising candidate for such an order parameter is Sr2RuO4, whose superconducting order parameter symmetry is still subject to investigation. The value of this phase can be determined through Kerr rotation and dc Hall conductivity measurements. Our calculations impose significant constraints on phi.

Topological change of the Fermi surface in low-density Rashba gases: application to superconductivity.

In this Letter we show how, for small values of the Fermi energy compared to the spin-orbit splitting of Rashba type, a topological change of the Fermi surface leads to an effective reduction of the dimensionality in the electronic density of states in the low charge density regime. We investigate its consequences on the onset of the superconducting instability. We show that the superconducting critical temperature is significantly tuned in this regime by the spin-orbit coupling. We suggest that materials with strong spin-orbit coupling are good candidates for enhanced superconductivity.

Spin-Hall conductivity in electron-phonon coupled systems.

We derive the ac spin-Hall conductivity sigmasH(omega) of two-dimensional spin-orbit coupled systems interacting with dispersionless phonons of frequency omega0. For the linear Rashba model, we show that the electron-phonon contribution to the spin-vertex corrections breaks the universality of sigmasH(omega) at low frequencies and provides a nontrivial renormalization of the interband resonance. On the contrary, in a generalized Rashba model for which the spin-vertex contributions are absent, the coupling to the phonons enters only through the self-energy, leaving the low-frequency behavior of sigmasH(omega) unaffected by the electron-phonon interaction.

Implications of reflectance measurements on the mechanism for superconductivity in MgB2.

Recent optical studies in c-axis oriented superconducting MgB2 films indicate that the electron-phonon coupling is weak. We reinforce this conclusion by examining the raw reflectance data; its frequency dependence is incompatible with strong electron-phonon scattering. This is further strengthened by analysis of the real part of the conductivity, and by the temperature dependence of the effective Drude scattering rate. Using a realistic electron-phonon spectral shape, we find lambda(tr) approximately 0.15. To the extent that lambda(tr) approximately lambda, this disagrees sharply with model calculations, and is far too low to provide the means for T(c) = 39 K. A simple model is constructed with coupling to a high frequency excitation, which is consistent with both the low frequency optical data and the high T(c).