Snake states in graphene quantum dots in the presence of a p-n junction

We investigate the magnetic interface states of graphene quantum dots that contain p-n junctions. Within a tight-binding approach, we consider rectangular quantum dots in the presence of a perpendicular magnetic field containing p-n, as well as p-n-p and n-p-n junctions. The results show the interplay between the edge states associated with the zigzag terminations of the sample and the snake states that arise at the p-n junction, due to the overlap between electron and hole states at the potential interface. Remarkable localized states are found at the crossing of the p-n junction with the zigzag edge having a dumb-bell shaped electron distribution. The results are presented as function of the junction parameters and the applied magnetic flux.Comment: 13 pages, 23 figures, to be appeared in Phys. Rev.

Weakly holomorphic modular forms in prime power levels of genus zero

Let $M_k^\sharp(N)$ be the space of weight $k$, level $N$ weakly holomorphic modular forms with poles only at the cusp at $\infty$. We explicitly construct a canonical basis for $M_k^\sharp(N)$ for $N\in\{8,9,16,25\}$, and show that many of the Fourier coefficients of the basis elements in $M_0^\sharp(N)$ are divisible by high powers of the prime dividing the level $N$. Additionally, we show that these basis elements satisfy a Zagier duality property, and extend Griffin's results on congruences in level 1 to levels 2, 3, 4, 5, 7, 8, 9, 16, and 25

The split-operator technique for the study of spinorial wavepacket dynamics

The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagating wave functions describing Schr\"odinger particles, namely, charge carriers in semiconductor nanostructures within the effective mass approximation, in the presence of Zeeman effect, as well as of Rashba and Dresselhaus spin-orbit interactions. We also demonstrate that simple modifications to the expanded technique allow us to calculate the time evolution of wave packets describing Dirac particles, which are relevant for the study of transport properties in graphene.Comment: 19 pages, 4 figure

Gas expulsion in highly substructured embedded star clusters

We investigate the response of initially substructured, young, embedded star clusters to instantaneous gas expulsion of their natal gas. We introduce primordial substructure to the stars and the gas by simplistically modelling the star formation process so as to obtain a variety of substructure distributed within our modelled star forming regions. We show that, by measuring the virial ratio of the stars alone (disregarding the gas completely), we can estimate how much mass a star cluster will retain after gas expulsion to within 10% accuracy, no matter how complex the background structure of the gas is, and we present a simple analytical recipe describing this behaviour. We show that the evolution of the star cluster while still embedded in the natal gas, and the behavior of the gas before being expelled, are crucial processes that affect the timescale on which the cluster can evolve into a virialized spherical system. Embedded star clusters that have high levels of substructure are subvirial for longer times, enabling them to survive gas expulsion better than a virialized and spherical system. By using a more realistic treatment for the background gas than our previous studies, we find it very difficult to destroy the young clusters with instantaneous gas expulsion. We conclude that gas removal may not be the main culprit for the dissolution of young star clusters.Comment: 19 pages, 8 figures, 2 tables. Accepted for publication in MNRA