Visibility of graphene flakes on a dielectric substrate

We model the optical visibility of monolayer and bilayer graphene deposited on a silicon/silicon oxide substrate or thermally annealed on the surface of silicon carbide. We consider reflection and transmission setups, and find that visibility is strongest in reflection reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.

Families intersecting on an interval

We shall be interested in the following Erdos-Ko-Rado-type question. Fix some subset B of [n]. How large a family A of subsets of [n] can we find such that the intersection of any two sets in A contains a cyclic translate (modulo n) of B? Chung, Graham, Frankl and Shearer have proved that, in the case where B is a block of length t, we can do no better than to take A to consist of all supersets of B. We give an alternative proof of this result, which is in a certain sense more direct.

Power Dependence of the Photocurrent Lineshape in a Semiconductor Quantum Dot

We propose a kinetic theory to describe the power dependence, $I_{PC}(P)$, of the photocurrent (PC) lineshape in optically pumped quantum dots at low temperatures, in both zero and finite magnetic fields. We show that there is a crossover power $P_c$, determined by the electron and hole tunneling rates, at which the photocurrent spectra become strongly influenced by the dot kinetics, and no longer reflect the exciton lifetime in the dot. For $P>P_c$, we show that the photocurrent saturates due to the slow hole escape rate (in e.g., InGaAs/GaAs dots), whereas the line-width increases with power: $Gamma propto sqrt{P}$. We also analyze to what measure the spin-doublet lineshape of the photocurrent studied in a high magnetic field reflects the degree of circular polarization of the incident light.

Bistability of optically-induced nuclear spin orientation in quantum dots

We demonstrate that bistability of the nuclear spin polarization in optically pumped semiconductor quantum dots is a general phenomenon possible in dots with a wide range of parameters. In experiment, this bistability manifests itself via the hysteresis behavior of the electron Zeeman splitting as a function of either pump power or external magnetic field. In addition, our theory predicts that the nuclear polarization can strongly influence the charge dynamics in the dot leading to bistability in the average dot charge.