First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling.

The combination of spin-orbit coupling with interactions results in many exotic phases of matter. In this Letter, we investigate the superconducting pairing instability of the two-dimensional extended Hubbard model with both Rashba and Dresselhaus spin-orbit coupling within the mean-field level at both zero and finite temperature. We find that both first- and second-order time-reversal symmetry breaking topological gapped phases can be achieved under appropriate parameters and temperature regimes due to the presence of a favored even-parity s+id-wave pairing even in the absence of an external magnetic field or intrinsic magnetism. This results in two branches of chiral Majorana edge states on each edge or a single zero-energy Majorana corner state at each corner of the sample. Interestingly, we also find that not only does tuning the doping level lead to a direct topological phase transition between these two distinct topological gapped phases, but also using the temperature as a highly controllable and reversible tuning knob leads to different direct temperature-driven topological phase transitions between gapped and gapless topological superconducting phases. Our findings suggest new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superconductors in a simple but realistic microscopic model.

Mixed temperature-dependent order parameters in the extended Hubbard model.

The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this model, we show that these symmetries are often dependent on temperature. The critical points of this functional are constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of symmetry transitions below T c. Understanding the nature of these transitions is crucial to assessing the symmetry of unconventional superconductors.

Reappraising the Luminescence Lifetime Distributions in Silicon Nanocrystals.

The luminescence dynamics in ensembles of nanocrystals are complicated by a variety of processes, including the size-dependence of the radiative and non-radiative rates in inhomogeneous broadened samples and interparticle interactions. This results in a non-exponential decay, which for the specific case of silicon nanocrystals (SiNCs) has been widely modeled with a Kohlrausch or "stretched exponential" (SE) function. We first derive the population decay function for a luminescence decay following exp[- (t/τ)ß]. We then compare the distributions and mean times calculated by assuming that either the luminescence decay or the population decay follows this function and show that the results are significantly different for ß much below 1. We then apply these two types of SE functions as well as other models to the luminescence decay data from two thermally grown SiNC samples with different mean sizes. The mean lifetimes are strongly dependent on the experimental setup and the chosen fitting model, none of which appears to adequately describe the ensemble decay dynamics. Frequency-resolved spectroscopy (FRS) techniques are then applied to SiNCs in order to extract the lifetime distribution directly. The rate distribution has a half width of ~ 0.5 decades and mainly resembles a somewhat high-frequency-skewed lognormal function. The combination of TRS and FRS methods appear best suited to uncovering the luminescence dynamics of NC materials having a broad emission spectrum.