Atomically-thin magnetic crystals have been recently isolated experimentally, greatly expanding the family of two-dimensional materials. In this Article we present an extensive comparative analysis of the electronic and magnetic properties of Cr2Ge2Te6, based on density functional theory (DFT). We first show that the often-used DFT + U approaches fail in predicting the ground-state properties of this material in both its monolayer and bilayer forms, and even more spectacularly in its bulk form. In the latter case, the fundamental gap decreases by increasing the Hubbard-U parameter, eventually leading to a metallic ground state for physically relevant values of U , in stark contrast with experimental data. On the contrary, the use of hybrid functionals, which naturally take into account nonlocal exchange interactions between all orbitals, yields good account of the available ARPES experimental data. We then calculate all the relevant exchange couplings (and the magnetocrystalline anisotropy energy) for monolayer, bilayer, and bulk Cr2Ge2Te6 with a hybrid functional, with super-cells containing up to 270 atoms, commenting on existing calculations with much smaller super-cell sizes. In the case of bilayer Cr2Ge2Te6, we show that two distinct intra-layer secondneighbor exchange couplings emerge, a result which, to the best of our knowledge, has not been noticed in the literature.
We study quantum transport through two-terminal nanoscale devices in contact with two particle reservoirs at different temperatures and chemical potentials. We discuss the general expressions controlling the electric charge current, heat currents, and the efficiency of energy transmutation in steady conditions in the linear regime. With focus in the parameter domain where the electron system acts as a power generator, we elaborate workable expressions for optimal efficiency and thermoelectric parameters of nanoscale devices. The general concepts are set at work in the paradigmatic cases of Lorentzian resonances and antiresonances, and the encompassing Fano transmission function: the treatments are fully analytic, in terms of the trigamma functions and Bernoulli numbers. From the general curves here reported describing transport through the above model transmission functions, useful guidelines for optimal efficiency and thermopower can be inferred for engineering nanoscale devices in energy regions where they show similar transmission functions
We use micro-Raman spectroscopy to study strain profiles in graphene monolayers suspended over SiN membranes micropatterned with holes of non-circular geometry. We show that a uniform differential pressure load ∆P over elliptical regions of free-standing graphene yields measurable deviations from hydrostatic strain conventionally observed in radially-symmetric microbubbles. The top hydrostatic strain ε we observe is estimated to be ≈ 0.7% for ∆P = 1 bar in graphene clamped to elliptical SiN holes with axis 40 and 20 µm. In the same configuration, we report a G± splitting of 10 cm −1 which is in good agreement with the calculated anisotropy ∆ε ≈ 0.6% for our device geometry. Our results are consistent with the most recent reports on the Grüneisen parameters. Perspectives for the achievement of arbitrary strain configurations by designing suitable SiN holes and boundary clamping conditions are discussed.
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