arXiv subjects

Raffaele Resta

Publications and source records attributed to Raffaele Resta.

34 records · Page 2Linked to original sources

arXiv2016

Metal-insulator transition in disordered systems from the one-body density matrix

The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered systems. In particular, for non-interacting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based on the static conductivity, which is only sensible within periodic boundary conditions. We exemplify the method by considering a simple lattice model, known to have a metal-insulator transition as a function of the disorder strength and demonstrate that the transition point can be obtained accurately from the one-body density matrix. The approach has a general {\it ab-initio} formulation and can be applied to realistic disordered materials by standard electronic structure methods.

cond-mat.dis-nn↗

arXiv2016

Orbital Magnetization in Insulators: Bulk vs. Surface

The orbital magnetic moment of a finite piece of matter is expressed in terms of the one-body density matrix as a simple trace. We address a macroscopic system, insulating in the bulk, and we show that its orbital moment is the sum of a bulk term and a surface term, both extensive. The latter only occurs when the transverse conductivity is nonzero and owes to conducting surface states. Simulations on a model Hamiltonian validate our theory.

cond-mat.mes-hall↗

arXiv2016

Irrelevance of the boundary on the magnetization of metals

The macroscopic current density responsible for the mean magnetization $\mathbf{M}$ of a uniformly magnetized bounded sample is localized near its surface. In order to evaluate $\mathbf{M}$ one needs the current distribution in the whole sample: bulk and boundary. In recent years it has been shown that the boundary has no effect on $\mathbf{M}$ in insulators: therein, $\mathbf{M}$ admits an alternative expression, not based on currents. $\mathbf{M}$ can be expressed in terms of the bulk electron distribution only, which is "nearsighted" (exponentially localized); this virtue is not shared by metals, having a qualitatively different electron distribution. We show, by means of simulations on paradigmatic model systems, that even in metals the $\mathbf{M}$ value can be retrieved in terms of the bulk electron distribution only.

cond-mat.mes-hall↗

arXiv2014

How disorder affects the Berry-phase anomalous Hall conductivity: the view from k space

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 a generalized 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 Fe3Co ordered 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.

cond-mat.mtrl-sci↗

arXiv2013

Orbital Magnetization as a Local Property

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.

cond-mat.mes-hall↗

arXiv2012

Mapping topological order in coordinate space

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the corresponding topological order can be mapped by means of a "topological marker", defined in $\r$-space, and which may vary in different regions of the same sample. Notably, this applies equally well to periodic and open boundary conditions. Simulations over a model Hamiltonian validate our theory.

cond-mat.str-el↗

arXiv2011

Zone-Center Dynamical Matrix in Magnetoelectrics

In ordinary dielectrics the dynamical matrix at the zone center in general is a nonanalytic function of degree zero in the wavevector q. Its expression (for a crystal of arbitrary symmetry) is well known and is routinely implemented in first principle calculations. The nonanalytic behavior occurs in polar crystals and owes to the coupling of the macroscopic electric field E to the lattice. In magnetoelectric crystals both electric and magnetic fields, E and H, are coupled to the lattice, formally on equal footing. We provide the general expression for the zone center dynamical matrix in a magnetoelectric, where the E and H couplings are accounted for in a symmetric way. As in the ordinary case, the dynamical matrix is a nonanalytic function of degree zero in q, and is exact in the harmonic approximation. For the sake of completeness, we address other issues, and in particular we solve a problem which might arise in first-principle implementations, where-differently than here-the basic fields are E and B (not H).

cond-mat.mtrl-sci↗

arXiv2011

Lyddane-Sachs-Teller relationship in linear magnetoelectrics

In a linear magnetoelectric the lattice is coupled to electric and magnetic fields: both affect the longitudinal-transverse splitting of zone-center optical phonons on equal footing. A response matrix relates the macroscopic fields (D,B) to (E,H) at infrared frequencies. It is shown that the response matrices at frequencies 0 and \infty fulfill a generalized Lyddane-Sachs-Teller relationship. The rhs member of such relationship is expressed in terms of weighted averages over the longitudinal and transverse excitations of the medium, and assumes a simple form for an harmonic crystal.

cond-mat.mtrl-sci↗

arXiv2010

The Insulating State of Matter: A Geometrical Theory

In 1964 W. Kohn published the milestone paper "Theory of the insulating state'", according to which insulators and metals differ in their ground state. Even before the system is excited by any probe, a different organization of the electrons is present in the ground state and this is the key feature discriminating between insulators and metals. However, the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent developments. The many-body ground wavefunction of any insulator is characterized by means of geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among them, it is the quantum metric which sharply characterizes the insulating state of matter. The theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators

cond-mat.mtrl-sci↗

arXiv2008

Role of dipolar correlations in the IR spectra of water and ice

We report simulated infrared spectra of deuterated water and ice using Car-Parrinello molecular dynamics with maximally localized Wannier functions. Experimental features are accurately reproduced within the harmonic approximation. By decomposing the lineshapes in terms of intra and intermolecular dipole correlation functions we find that short-range intermolecular dynamic charge fluctuations associated to hydrogen bonds are prominent over the entire spectral range. Our analysis reveals the origin of several spectral features and identifies network bending modes in the far IR range.

cond-mat.soft↗

arXiv2005

Electron Localization in the Quantum-Hall Regime

The theory of the insulating state discriminates between insulators and metals by means of a localization tensor, which is finite in insulators and divergent in metals. In absence of time-reversal symmetry, this same tensor acquires an offdiagonal imaginary part, proportional to the dc transverse conductivity, leading to quantization of the latter in two-dimensional systems. I provide evidence that electron localization--in the above sense--is the common cause for both vanishing of the dc longitudinal conductivity and quantization of the transverse one in quantum-Hall fluids.

cond-mat.mes-hall↗

arXiv2001

Electron localization in the insulating state: application to crystalline semiconductors

We measure electron localization in different materials by means of a ``localization tensor'', based on Berry phases and related quantities. We analyze its properties, and we actually compute such tensor from first principles for several tetrahedrally coordinated semiconductors. We discuss the trends in our calculated quantity, and we relate our findings to recent work by other authors. We also address the ``hermaphrodite orbitals'', which are localized (Wannier-like) in a given direction, and delocalized (Bloch-like) in the two orthogonal directions: our tensor is related to the optimal localization of these orbitals. We also prove numerically that the decay of the optimally localized hermaphrodite orbitals is exponential.

cond-mat.mtrl-sci↗

arXiv2000

What makes an insulator different from a metal?

The insulating state of matter is characterized by the excitation spectrum, but also by qualitative features of the electronic ground state. The insulating ground wavefunction in fact: (i) displays vanishing dc conductivity; (ii) sustains macroscopic polarization; and (iii) is localized. The idea that the insulating state of matter is a consequence of electron localization was first proposed in 1964 by W. Kohn. I discuss here a novel definition of electron localization, rather different from Kohn's, and deeply rooted in the modern theory of polarization. In fact the present approach links the two features (ii) and (iii) above, by means of essentially the same formalism. In the special case of an uncorrelated crystalline solid, the localization of the many-body insulating wavefunction is measured - according to our definition - by the spread of the Wannier orbitals; this spread diverges in the metallic limit. In the correlated case, the novel approach to localization is demonstrated by means of a two-band Hubbard model in one dimension, undergoing a transition from band insulator to Mott insulator.

cond-mat.mtrl-sci↗

arXiv1999

Macroscopic Polarization from Electronic Wavefunctions

The dipole moment of any finite and neutral system, having a square-integrable wavefunction, is a well defined quantity. The same quantity is ill-defined for an extended system, whose wavefunction invariably obeys periodic (Born-von Karman) boundary conditions. Despite this fact, macroscopic polarization is a theoretically accessible quantity, for either uncorrelated or correlated many-electron systems: in both cases, polarization is a rather "exotic" observable. For an uncorrelated-either Hartree-Fock or Kohn-Sham-crystalline solid, polarization has been expressed and computed as a Berry phase of the Bloch orbitals (since 1993). The case of a correlated and/or disordered system received a definitive solution only very recently (1998): this latest development allows us present here the whole theory from a novel, and very general, viewpoint. The modern theory of polarization is even relevant to the foundations of density functional theory in extended systems.

cond-mat.mtrl-sci↗

arXiv1997

The effects of interface morphology on Schottky barrier heights: a case study on Al/GaAs(001)

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.

cond-mat.mtrl-sci↗

arXiv1997

Dynamical-charge neutrality at a crystal surface

For both molecules and periodic solids, the ionic dynamical charge tensors which govern the infrared activity are known to obey a dynamical neutrality condition. This condition enforces their sum to vanish (over the whole finite system, or over the crystal cell, respectively). We extend this sum rule to the non trivial case of the surface of a semiinfinite solid and show that, in the case of a polar surface of an insulator, the surface ions cannot have the same dynamical charges as in the bulk. The sum rule is demonstrated through calculations for the Si-terminated SiC(001) surface.

cond-mat.mtrl-sci↗