Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and non-linear response properties of materials from first principles. A notable advantage of DFPT over alternative approaches is the possibility of treating incommensurate lattice distortions with an arbitrary wavevector, q, at essentially the same computational cost as the latticeperiodic case. Here we show that q can be formally treated as a perturbation parameter, and used in conjunction with established results of perturbation theory (e.g. the "2n + 1" theorem) to perform a long-wave expansion of an arbitrary response function in powers of the wavevector components. This provides a powerful, general framework to accessing a wide range of spatial dispersion effects that were formerly difficult to calculate by means of first-principles electronic-structure methods. In particular, the physical response to the spatial gradient of any external field can now be calculated at negligible cost, by using the response functions to uniform perturbations (electric, magnetic or strain fields) as the only input. We demonstrate our method by calculating the flexoelectric and dynamical quadrupole tensors of selected crystalline insulators and model systems.
We include the treatment of quadrupolar fields beyond the Fröhlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.
We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense q meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology.
We perform self-consistent Schrödinger-Poisson calculations with exchange and correlation corrections to determine the electron and hole gas in a radial heterojunction formed in a GaAs/AlGaAs core-multi-shell nanowire, which is either n-or p-doped. We show that the electron and hole gases can be tuned to different localizations and symmetries inside the core as a function of the doping density/gate potential. Contrary to planar heterojunctions, conduction electrons do not form a uniform 2D electron gas (2DEG) localized at the GaAs/AlGaAs interface, but rather show a transition between an isotropic, cylindrical distribution deep in the GaAs core (low doping) and a set of six tunnel-coupled quasi-1D channels at the edges of the interface (high doping). Holes, on the other hand, are much more localized at the GaAs/AlGaAs interface. At low doping, they present an additional localization pattern with six separated 2DEGs strips. The field generated by a back-gate may easily deform the electron or hole gas, breaking the sixfold symmetry. Single 2DEGs at one interface or multiple quasi-1D channels are shown to form as a function of voltage intensity, polarity, and carrier type.
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