Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions

We study asymptotic behaviour at time infinity of solutions close to the non-zero constant equilibrium for the Gross-Pitaevskii equation in two and three spatial dimensions. We construct a class of global solutions with prescribed dispersive asymptotic behavior, which is given in terms of the linearized evolution

Phase Diagram of the Holstein-Hubbard Two-Leg Ladder

Using a functional renormalization group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization group technique allows us to analyze the problem for both weak and strong electron-phonon coupling. We show that, in contrast results from conventional weak coupling studies, electron-phonon interactions can dominate electron-electron interactions because of retardation effects.Comment: 4 page

Reversible writing of high-mobility and high-carrier-density doping patterns in two-dimensional van der Waals heterostructures

A key feature of two-dimensional materials is that the sign and concentration of their carriers can be externally controlled with techniques such as electrostatic gating. However, conventional electrostatic gating has limitations, including a maximum carrier density set by the dielectric breakdown, and ionic liquid gating and direct chemical doping also suffer from drawbacks. Here, we show that an electron-beam-induced doping technique can be used to reversibly write high-resolution doping patterns in hexagonal boron nitride-encapsulated graphene and molybdenum disulfide (MoS2) van der Waals heterostructures. The doped MoS2 device exhibits an order of magnitude decrease of subthreshold swing compared with the device before doping, whereas the doped graphene devices demonstrate a previously inaccessible regime of high carrier concentration and high mobility, even at room temperature. We also show that the approach can be used to write high-quality p–n junctions and nanoscale doping patterns, illustrating that the technique can create nanoscale circuitry in van der Waals heterostructures