We investigate the influence of a periodic weak modulation along the x direction on the electrical and thermal properties of a two-dimensional electron gas in the presence of a perpendicular magnetic field. The modulation lifts the degeneracy of the Landau levels and leads to one-dimensional magnetic bands whose bandwidth oscillates as a function of the magnetic field. At weak magnetic fields this gives rise to the Weiss oscillations in the magnetoresistance, discovered recently, which have a very weakly temperature-dependent amplitude and a period proportional to Qn"when n, is the electron density.Diffusion-current contributions, proportional to the square of the bandwidth, dominate p"", and collisional contributions, varying approximately as the square of the density of states, dominate p» The result is that p""and p» oscillate out of phase as observed. Asymptotic analytical expressions are presented for the conductivity tensor. Similar oscillations, of much smaller amplitude, occur in the thermodynamic quantities, such as the magnetization, the susceptibility, and the specific heat. We also predict oscillations in the Ha11 resistance, the cyclotron resonance position, the linewidth, as well as in the thermal conductivity and thermopower.The components of the thermal-resistance tensor have a magnetic-field dependence similar to that of the electrical-resistivity tensor.

We investigate the stability, the dynamical properties and melting of a two-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in a bi-layer structure. Compared to the single-layer WC, this system shows a rich phase diagram. Five different crystalline phases are stable; the energetically favoured structure can be tuned by changing either the inter-layer distance or the particle density. Phase boundaries consist of both continuous and discontinuous transitions. We calculated the phonon excitations of the system within the harmonic approximation and we evaluated the melting temperature of the bi-layer WC by use of a modified Lindemann criterion, appropriate to 2D systems. We minimized the harmonic free-energy of the system with respect to the lattice geometry at different values of temperature/inter-layer distance and we found no temperature-induced structural phase transition.68.65.+g -Layer structures: multilayer, and superlattices 63.20.Dj -Phonon states and bands, normal modes, and phonon dispersion 64.70.Dv -Solid-liquid transitions Typeset using REVT E X

Schweigert, Schweigert, and Peeters Reply: Rinn and Maass [1] claim that the Brownian dynamics (BD) simulation results of Schweigert et al. [2] are analyzed incorrectly. Furthermore, they claim that the definition for the intershell diffusion coefficient ͑D u ͒ used by Schweigert et al. [2] makes sense only when the particles remain in the same shell.The whole misunderstanding is based on the fact that Rinn et al. [1] believe that one needs to follow the trajectory of each individual particle in order to calculate D u . Within such an approach, one is in trouble when a particle jumps from one shell to another shell. In order to remove this switching of particles between shells they analyzed their data in two different ways: (1) ignoring shell jumps (open symbols in Fig. 2 of Ref. [1]); and (2) taking care of shell jumps (solid symbols in Fig. 2 of Ref. [1]).When Rinn et al. ignored shell jumps they found a very large "unrealistic" reduction of D u with decreasing G , 20. Notice that for G , 20 the diffusion coefficient D u attains values which are even smaller than in the G . 100 region, where the rigid crystal phase sets in. On physical grounds, this makes no sense.In their second approach, Rinn et al. calculated D u by "taking care of shell jumps." It is not clear what they mean with this and how they calculated D u . Did they remove the particles which performed a shell jump from their calculation of D u ? If so, it is not surprising that the results are different from those of Schweigert et al. [2]. As explained in Refs. [2,3], the radial fluctuations (and shell jumps) are essential for the stabilization of the intershell (or angular) diffusion in the reentrant region. The numerical results of Rinn et al. (solid symbols in Fig. 2 of Ref. [1]) saturate for G , 20 which is hard to understand physically.

No abstract

Recently, rhenium disulfide (ReS 2) monolayers were experimentally extracted by conventional mechanical exfoliation technique from as-grown ReS 2 crystals. Unlike the well-known members of transition metal dichalcogenides (TMDs), ReS 2 crystallizes in a stable distorted-1T structure and lacks an indirect to direct gap crossover. Here we present an experimental and theoretical study of the formation, energetics, and stability of the most prominent lattice defects in monolayer ReS 2. Experimentally, irradiation with 3-MeV He +2 ions was used to break the strong covalent bonds in ReS 2 flakes. Photoluminescence measurements showed that the luminescence from monolayers is mostly unchanged after highly energetic α particle irradiation. In order to understand the energetics of possible vacancies in ReS 2 we performed systematic first-principles calculations. Our calculations revealed that the formation of a single sulfur vacancy has the lowest formation energy in both Re and S rich conditions and a random distribution of such defects are energetically more preferable. Sulfur point defects do not result in any spin polarization whereas the creation of Re-containing point defects induce magnetization with a net magnetic moment of 1-3µ B. Experimentally observed easy formation of sulfur vacancies is in good agreement with first-principles calculations.