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An insulator differs from a metal because of a different organization of the electrons in their ground state. In recent years this feature has been probed by means of a geometrical property, the quantum metric tensor, which addresses the system as a whole, and is therefore limited to macroscopically homogenous samples. Here we show that an analogous approach leads to a localization marker, which can detect the metallic versus insulating character of a given sample region using as the sole ingredient the ground state electron distribution, even in the Anderson case (where the spectrum is gapless). When applied to an insulator with a nonzero Chern invariant, our marker is capable of discriminating the insulating nature of the bulk from the conducting nature of the boundary. Simulations (both model Hamiltonian and first principles) on several test cases validate our theory.

The modern theory of polarization, based on a Berry phase, is currently implemented in most first-principle electronic structure codes. Many KS-DFT calculations have addressed various phenomena (ferroelectricity, piezoelectricity, lattice dynamics, infrared spectra of liquid and amorphous systems) in several materials. Notwithstanding, the KS polarization does not coincide with the exact one, even when ideally implemented with the exact KS crystalline potential. This is at odds with the fact that the KS electrical dipole of a bounded crystallite coincides by definition with the exact one: we analyze this issue from several viewpoints. According to the modern theory, the polarization of a centrosymmetric crystal does not vanish in general; we show that the polarization of a centrosymmetric quasi-1d systems (stereoregular linear polimer) is a topological invariant: ergo in this case the KS polarization coincides with the exact one. © 2018, EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature.

The geometrical intrinsic contribution to the anomalous Hall conductivity (AHC) of a metal is commonly expressed as a reciprocal-space integral: as such, it only addresses unbounded and macroscopically homogeneous samples. Here we show that the geometrical AHC has an equivalent expression as a local property. We define a "geometrical marker" which actually probes the AHC in inhomogeneous systems (e.g. heterojunctions), as well as in bounded samples. The marker may even include extrinsic contributions of geometrical nature., Comment: 4 pages, 4 figures

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY)., The anomalous Hall conductivity of “dirty” ferromagnetic metals is dominated by a Berry-phase contribution which is usually interpreted as an intrinsic property of the Bloch electrons in the pristine crystal. In this work we evaluate the geometric Hall current directly from the electronic ground state with disorder and then recast it as an integral over the crystalline Brillouin zone. The integrand is an effective k-space Berry curvature, obtained by unfolding the Berry curvature from the small Brillouin zone of a large supercell. Therein, disorder yields a net extrinsic Hall contribution, which we argue is related to the elusive side-jump effect. As an example, we unfold the first-principles Berry curvature of an ordered Fe3Co alloy from the original fcc-lattice Brillouin zone onto a bcc-lattice zone with four times the volume. Comparison with the virtual-crystal Berry curvature clearly reveals the symmetry-breaking effects of the substitutional Co atoms., This work was supported by Grants No. MAT2012-33720 from the Ministerio de Economía y Competitividad (Spain), No. CIG-303602 from the European Commission, and ONR Grant No. N00014-12-1-1041 (USA).

The modern expressions for polarization $��$ and orbital magnetization $\M$ are $\k$-space integrals. But a genuine bulk property should also be expressible in $\r$-space, as unambiguous function of the ground-state density matrix, "nearsighted" in insulators, independently of the boundary conditions---either periodic or open. While $��$---owing to its "quantum" indeterminacy---is {\it not} a bulk property in this sense, $\M$ is. We provide its $\r$-space expression for any insulator, even with nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory., Phys. Rev. Lett, in press

International audience; The qualitative difference between insulators and metals stems from the nature of the low-lying excitations, but also--according to Kohn's theory [W. Kohn, Phys. Rev.133, A171 (1964)]--from a different organization of the electrons in their ground state: electrons are localized in insulators and delocalized in metals. We adopt a quantitative measure of such localization, by means of a "localization length" λ, finite in insulators and divergent in metals. We perform simulations over a one-dimensional binary alloy model, in a tight-binding scheme. In the ordered case the model is either a band insulator or a band metal, whereas in the disordered case it is an Anderson insulator. The results show indeed a localized/delocalized ground state in the insulating/metallic cases, as expected. More interestingly, we find a significant difference between the two insulating cases: band versus Anderson. The insulating behavior is due to two very different scattering mechanisms; we show that the corresponding values of λ differ by a large factor for the same alloy composition. We also investigate the organization of the electrons in the many body ground state from the viewpoint of the density matrices and of Boys' theory of localization.

Macroscopic polarization P and magnetization M are the most fundamental concepts in any phenomenological description of condensed media. They are intensive vector quantities that intuitively carry the meaning of dipole per unit volume. But for many years both P and the orbital term in M evaded even a precise microscopic definition, and severely challenged quantum-mechanical calculations. If one reasons in terms of a finite sample, the electric (magnetic) dipole is affected in an extensive way by charges (currents) at the sample boundary, due to the presence of the unbounded position operator in the dipole definitions. Therefore P and the orbital term in M--phenomenologically known as bulk properties--apparently behave as surface properties; only spin magnetization is problemless. The field has undergone a genuine revolution since the early 1990s. Contrary to a widespread incorrect belief, P has nothing to do with the periodic charge distribution of the polarized crystal: the former is essentially a property of the phase of the electronic wavefunction, while the latter is a property of its modulus. Analogously, the orbital term in M has nothing to do with the periodic current distribution in the magnetized crystal. The modern theory of polarization, based on a Berry phase, started in the early 1990s and is now implemented in most first-principle electronic structure codes. The analogous theory for orbital magnetization started in 2005 and is partly work in progress. In the electrical case, calculations have concerned various phenomena (ferroelectricity, piezoelectricity, and lattice dynamics) in several materials, and are in spectacular agreement with experiments; they have provided thorough understanding of the behaviour of ferroelectric and piezoelectric materials. In the magnetic case the very first calculations are appearing at the time of writing (2010). Here I review both theories on a uniform ground in a density functional theory (DFT) framework, pointing out analogies and differences. Both theories are deeply rooted in geometrical concepts, elucidated in this work. The main formulae for crystalline systems express P and M in terms of Brillouin-zone integrals, discretized for numerical implementation. I also provide the corresponding formulae for disordered systems in a single k-point supercell framework. In the case of P the single-point formula has been widely used in the Car-Parrinello community to evaluate IR spectra.

I provide here a comprehensive presentation of the so called 'modern theory of polarization', based on a Berry phase. This theory is implemented as a standard option in most electronic-structure codes for both crystalline and noncrystalline materials, and is routinely used whenever features ot the macroscopic electrical polarization of materials are addressed. Several reviews of the modern theory exist in the literature; with respect to them, the present work has important elements of novelty. In this work I present a formal derivation, starting from the many-body wavefunction at the most general level, and eventually specialising to the case of single-determinant wavefunctions for either disordered or crystalline materials.

We introduce an alternative approach to the first-principles calculation of NMR shielding tensors. These are obtained from the derivative of the orbital magnetization with respect to the application of a microscopic, localized magnetic dipole. The approach is simple, general, and can be applied to either isolated or periodic systems. Calculated results for simple hydrocarbons, crystalline diamond, and liquid water show very good agreement with established methods and experimental results., submitted to Phys. Rev. Lett; second half completely rewritten to address referee's comments

The key formula for computing the orbital magnetization of a crystalline system has been recently found [D. Ceresoli, T. Thonhauser, D. Vanderbilt, R. Resta, Phys. Rev. B {\bf 74}, 024408 (2006)]: it is given in terms of a Brillouin-zone integral, which is discretized on a reciprocal-space mesh for numerical implementation. We find here the single ${\bf k}$-point limit, useful for large enough supercells, and particularly in the framework of Car-Parrinello simulations for noncrystalline systems. We validate our formula on the test case of a crystalline system, where the supercell is chosen as a large multiple of the elementary cell. We also show that--somewhat counterintuitively--even the Chern number (in 2d) can be evaluated using a single Hamiltonian diagonalization., 4 pages, 3 figures; appendix added

First-principles-based methods are used to determine the external dielectric susceptibility (i.e., the polarization response to the external electric field) and the internal susceptibility (i.e., the polarization response to the average internal field) in ferroelectric dots, wires, and films, as a function of the electrical boundary conditions. While the external susceptibility is obviously positive, we find that the internal one is negative over a wide range of boundary conditions for all kinds of nanostructures. A Landau-type phenomenological model provides a rationale for all of our findings.

Within an ab-initio HF scheme, we use both Berry-phase calculations and supercell calculations in order to compute the dynamical charges for lattice dynamics and the electronic dielectric constant for KNbO_3 and BaTiO_3. Comparison with experimental data indicates that HF provides a description of the electronic properties of this material whose accuracy is of the same order as the LDA one. There are however significant differences between the two sets of results, whose origin is scrutinized. Motivated by the study of surface and domain-boundary properties, we also present some results for BaTiO_3 slabs, including both genuinely isolated and periodically repeated slabs with different terminations. The capability of dealing with a genuinely isolated slab is a virtue of the localized-basis implementation adopted here. We demonstrate, amongst other things, the nontrivial dynamical-charge neutrality of BaTiO_3 [001] surfaces., 11 pages, 6 figures. Presented at the Fifth Williamsburg Workshop on First-Principles Calculations for Ferroelectrics

The problem of Fermi-level pinning at semiconductor-metal contacts is readdressed starting from first-principles calculations for Al/GaAs. We give quantitative evidence that the Schottky barrier height is very little affected by any structural distortions on the metal side---including elongations of the metal-semiconductor bond (i.e. interface strain)---whereas it strongly depends on the interface structure on the semiconductor side. A rationale for these findings is given in terms of the interface dipole generated by the ionic effective charges., 5 pages, latex file, 2 postscript figures automatically included

We generalize the Nielsen-Martin stress theorem beyond the local-density approximation (LDA) and present an alternative derivation of the whole theorem. We show that the exchange-correlation stress becomes anisotropic in the most general case: its explicit form is given within a gradient-corrected (GC) scheme. As a test implementation, we use the generalized theorem to achieve fast structural optimization in crystalline Se. In this material LDA predicts a rather poor structure period. Our GC calculation is in much better agreement with the experiment.

The local Zn/Se relative concentration at the interface in ZnSe-GaAs(001) heterostructures synthesized by molecular beam epitaxy was found to be controlled by the Zn/Se flux ratio employed during the early growth stage of ZnSe on GaAs. Correspondingly, the valence band discontinuity varies from 1.20 eV (Zn-rich interface) to 0.58 eV (Se-rich interface). Comparison with the results of first-principles calculations suggests that the observed trend in band offsets is related to the establishment of neutral interfaces with different atomic configurations.

We review in this paper the electronic properties of semiconductor heterojunctions. We focus on interface-specific phenomena, where the conditions of growth—including controlled contamination—may significantly alter the physical properties of the junction. We start outlining the basic concepts of our first-principles theory of the band offsets. We then discuss in some detail the case of Ge/GaAs, where the band offset significantly depends on interface features, owing to the difference in chemical valence which induces electrostatic effects. For this system, sound experimental evidence of noncommutativity of the band offsets has been reached. We then discuss the effects of ultrathin intralayers at heterojunctions and homojunctions, starting with the case of heterovalent implantations, such as GaAs/Ge/GaAs. In these cases, the intralayers control the band offset: the effect has been predicted by our theory and subsequently experimentally observed in several systems. We review some recent measurements and their current interpretation, particularly in relationship with interdiffusion and atomic ordering at the interface. Finally, we discuss the electronic and optical properties of isovalent intralayers, i.e ultrathin quantum wells, such as AlAs/GaAs/AlAs and Si/Ge/Si. We show how the spatial confinement of carriers in an isovalent intralayer strongly enhances interband optical properties and can be used for the optical characterization of semiconductor interfaces at the atomic scale

Band offsets can be modified at semiconductor heterojunctions or created at homojunctions by depositing thin intralayers of group-IV atoms at III-V/III-V polar interfaces. We present here a theoretical study of Si and Ge intralayers deposited along (001) at GaAs and AlAs homojunctions, and at GaAs/AlAs heterojunctions. Our results show that the offset is very sensitive to the coverage and abruptness of the intralayer. A comparison with recent experiments for Si in GaAs/AlAs suggests that Si atoms are confined over two atomic planes for coverages lower than about 0.5 monolayers, whereas for higher coverages Si diffusion occurs.

Nonlinear impurity screening in metals has been widely studied in the literature, and the differences with respect to the linear results have been found to be important. The screening theories available for semiconductors were until very recently obtained in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space, and this prevented the study of nonlinear effects. We present here for the first time an investigation of nonlinear impurity screening in a model semiconductor. The Thomas-Fermi theory of dielectric screening, recently developed by one of us, has been used. Nonlinearity effects are found to be of the same order of magnitude as in metals. A remarkable donoracceptor asymmetry is also found.

The long-standing problem of determining which interface-specific properties affect the band offset at semiconductor heterojunctions is readdressed using a newly developed theoretical approach. The actual interface is considered as a perturbation with respect to a reference periodic system (virtual crystal). By comparison with state-of-the-art self-consistent calculations, we show that linear-response theory provides a very accurate description of the electronic structure of the actual interface in a variety of cases, and sheds light on the mechanisms responsible for the band offset. Results are presented for a number of lattice-matched junctions, both isovalent and heterovalent. It is shown that—within linear response theory—band offsets are genuine bulk properties for isovalent interfaces, whereas they do depend on the atomic structure of the junction for polar interfaces between heterovalent semiconductors. In the latter case, however, the interface-dependent contribution to the offset can be calculated—once the microscopic geometry of the junction is known—from such simple quantities as the lattice parameters and dielectric constants of the constituents. Perspectives for extending the theory to non-lattice-matched systems are also briefly discussed.

We propose a novel ab-initio approach to the problem of band offsets at semiconductor heterojunctions. The actual interface is treated as a perturbation with respect to a periodic crystal: e.g. for the paradygmatic case of the (isovalent and lattice-matched) GaAs/AlAs interface, we take the virtual crystal Ga 1 2 Al 1 2 As as the unperturbed system. The interface electronic charge, which determines the band offsets, is shown to be very well described by linear response theory in this system, and we expect the same to be true in any case where the chemical differences between the constituents on the two sides are small. The numerical value of the valence-band offset obtained in this work is within 0.01 eV from our previous selfconsistent supercell calculations for the (001), (110) and (111) interface, and well within the present experimental error bar. Our main conclusion is that for all those lattice-matched isovalent interfaces where the electronic response to relevant ion substitutions can be described within linear-response theory, the offset is determined by bulk properties only. This means that the offset is independent not only of the growth direction, but even more generally of the abruptness of the interface. For non isovalent interfaces, the linear approach provides a natural way of studying the geometry-dependence of the offsets.