arXiv subjects

Raffaele Resta

Publications and source records attributed to Raffaele Resta.

At least 19 recordsLinked to original sources

arXiv2025

Intrinsic nonlinear Hall effect beyond Bloch geometry

The theory of the intrinsic Hall effect, both linear and nonlinear, is rooted in a geometry which is defined in the Bloch-vector parameter space; the formal expressions are mostly derived from semiclassical concepts. When disorder and interaction are considered there is no Bloch vector to speak of; one needs a more general quantum geometry, defined in a different parameter space. The nonlinear Hall effect is a fundamental geometric response of the many-body ground state, not a band-structure peculiarity. The higher-level geometrical formulation of the intrinsic Hall effect provides very compact expressions, which have the additional virtue -- in the Bloch special case -- of yielding the known results in a straightforward way: the logic is not concealed by the algebra.

cond-mat.mtrl-sci↗

arXiv2025

Quantum geometry and adiabaticity in molecules and in condensed matter

The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the adiabatic evolution of a generic observable obtains simply as its expectation value over the instantaneous eigenstate. As a general principle there is an additional adiabatic term, of quantum-geometrical nature, which is the relevant one for several static or adiabatic observables. This is shown explicitly for the cases of polarizability and infrared tensors (in molecules and condensed matter); rotational g factor and magnetizability (in molecules only). Quantum geometry allows for a transparent derivation and a compact expression for these observables, alternative to the well known sum-over-states Kubo formulas.

quant-ph↗

arXiv2025

Nonadiabatic quantum geometry and optical conductivity

The ground-state quantum geometry is at the root of several static and adiabatic properties, while genuinely dynamic properties are routinely addressed via Kubo formulae, whose essential entries are the excited states. It is shown here that the ground-state metric-curvature tensor evolves in time by means of a causal unitary operator, which by construction elucidates the geometrical effect of the excited states in compact form. In the condensed-matter case the generalized tensor encompasses the whole conductivity tensor at arbitrary frequencies in both insulators and metals, with the exception of the Drude term in the metallic case; the latter is shown to be eminently nongeometrical.

cond-mat.mtrl-sci↗

arXiv2024

Geometrical theory of the shift current in presence of disorder and interaction

The electric field of light induces--in a non centrosymmetric insulator--a dc current, quadratic in the field magnitude, and called "shift current". When addressed from a many-electron viewpoint, the shift current has a simple explanation and a simple formulation as well, deeply rooted in quantum geometry. The basic formula is then specialized to the independent-electron case, first for a disordered system in a supercell formulation, and then for a crystalline system. In the latter case the known shift-current formula is retrieved in a very transparent way.

cond-mat.mtrl-sci↗

arXiv2023

Drude weight in presence of nonlocal potentials

The nonlocal potential contributes an extra term to the velocity operator; I show here that such term affects the formal expression of the Drude weight in a nontrivial way. Notably, the present main result fixes a disturbing discrepancy in the Dreyer-Coh-Stengel sum rule [Phys. Rev. Lett. {\bf 128}, 095901 (2022)].

cond-mat.mtrl-sci↗

arXiv2023

Adiabatic observables and Berry curvatures in insulators and metals

A sharp definition of what "adiabatic" means is given; it is then shown that the time-dependent expectation value of a quantum-mechanical observable in the adiabatic limit can be expressed -- in many cases -- by means of the appropriate Berry curvature. Condensed-matter observables belonging to this class include: Born effective charges in insulators and in metals, quantized Faraday charges in electrolytes, and linear dc conductivities (longitudinal and transverse). Remarkably, the adiabatic limit is well defined even in metals, despite the absence of a spectral gap therein. For all of the above observables the explicit Berry-curvature expressions are derived in a general many-body setting, which also allows for compact and very transparent notations and formulas. Their conversion into band-structure formulas in the independent-electron crystalline case is straightforward.

cond-mat.mes-hall↗

arXiv2022

Molecular Berry curvatures and the adiabatic response tensors

Adiabatic transport in a many-electron system is expressed in terms of the appropriate Berry curvature, owing to the Niu-Thouless theory [J. Phys A {\bf 17}, 2453 (1984)]; the main equation is very compact and very general. I address here three paradigmatic adiabatic response tensors -- -the atomic polar tensor, the atomic axial tensor, and the rotational $g$ factor -- and I show that, for all of them, the known formulas do not need an independent proof. They are just case studies of the general expression, for different choices the curvature's two arguments.

cond-mat.mtrl-sci↗

arXiv2021

Theory of nonlinear dc conductivity, longitudinal and transverse

Kohn's theory of Drude conductivity, established in a many-body framework, addresses even systems with disorder and correlation, besides the ordinary band metals (i.e. crystalline systems of independent electrons). Kohn's theory is here extended to nonlinear dc conductivities of arbitrary order, longitudinal and transverse. The results are then reformulated in a band-structure framework, and their relationships to the semiclassical theory of nonlinear electron transport are elucidated.

cond-mat.mtrl-sci↗

arXiv2021

Faraday law, oxidation numbers, and ionic conductivity: The role of topology

Faraday's experiment measures -- within a modern view -- the charge adiabatically transported over a macroscopic distance by a given nuclear species in insulating liquids: the reason why it is integer is deeply rooted in topology. Whole numbers enter chemistry in a different form: atomic oxidation states. They are not directly measurable, and are determined instead from an agreed set of rules. Insulating liquids are a remarkable exception: Faraday's experiment indeed measures the oxidation numbers of each dissociated component in the liquid phase, whose topological values are unambiguous. Ionic conductivity in insulating liquids is expressed in terms of the autocorrelation function of the fluctuating charge current at a given temperature in zero electric field; topology plays a major role in this important observable as well. The existing literature deals with the above issues by adopting the independent-electron framework; here I provide the many-body generalization of all the above findings, which furthermore allows for compact and very transparent notations and formulas.

cond-mat.mtrl-sci↗

arXiv2021

Linear and nonlinear Hall conductivity in presence of interaction and disorder

The theory of the nonlinear Hall effect has been established by I. Sodemann and L. Fu [Phys. Rev. Lett. 115, 216806 (2015)] in a semiclassical framework: therein, the effect appears as a geometrical property of Bloch electrons, originating from their anomalous velocity. Here I present a more general theory, addressing correlated and/or noncrystalline systems as well, where the expressions of both linear and nonlinear Hall conductivities originate from the many-electron anomalous velocity. The independent-electron results are retrieved as special cases.

cond-mat.mtrl-sci↗

arXiv2021

Perspective: From the dipole of a crystallite to the polarization of a crystal

The quantum-mechanical expression for the polarization of a crystalline solid does not bear any resemblance to the (trivial) expression for the dipole of a bounded crystallite; and in fact it has been proved via a conceptually different path. Here I show how to alternatively define the dipole of a bounded sample in a somewhat unconventional way; from such formula, the crystalline polarization formula -- as routinely implemented in electronic-structure codes -- follows almost seamlessly.

cond-mat.mtrl-sci↗

arXiv2020

Drude weight in systems with open boundary conditions

A many-electron conducting system undergoes free acceleration in response to a macroscopic field. The Drude weight $D$---also called charge stiffness---measures the adiabatic (inverse) inertia of the electrons; the $D$ formal expression requires periodic boundary conditions. When instead a bounded sample is addressed within open boundary conditions, no current flows and a constant (external) field only polarizes the sample: the Faraday cage effect. Nonetheless a low-frequency field induces forced oscillations: we show here that the low-frequency linear response of the bounded system is dominated by the adiabatic inertia and allows an alternative evaluation of $D$. Simulations on model one-dimensional systems demonstrate our main message.

cond-mat.mes-hall↗

arXiv2020

Geometry and topology in many-body physics

Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework, beyond band-structure theory. The formalism allows dealing with the general case of disordered and/or correlated many-electron systems.

cond-mat.str-el↗

arXiv2020

X-ray circular dichroism versus orbital magnetization

The x-ray magnetic circular dichroism (XMCD) sum rule yields an extremely useful ground-state observable, which provides a quantitative measure of spontaneous time-reversal symmetry breaking (T-breaking) in a given material. I derive here its explicit expression within band-structure theory, in the general case: trivial insulators, topological insulators, and metals. Orbital magnetization provides a different measure of T-breaking in the electronic ground state. The two observables belong to the class of "geometrical" observables; both are local and admit a "density" in coordinate space. In both of them one could include/exclude selected groups of bands, in order to acquire element-specific information about the T-breaking material. Only in the case of an isolated flat band the contributions to the two observables coincide. Finally, I provide the corresponding geometrical formula-in a different Hilbert space-for a many-body interacting system.

cond-mat.mtrl-sci↗

arXiv2020

Chern number and orbital magnetization in ribbons, polymers, and layered materials

The modern theory of orbital magnetization addresses crystalline materials at the noninteracting level: therein the observable is the k-space integral of a geometrical integrand. Alternatively, magnetization admits a local representation in r space, i.e. a "density" which may address noncrystalline and/or inhomogeneous materials as well; the Chern number admits an analogous density. Here we provide the formulation for ribbons, polymers, and layered materials, where both k-space and r-space integrations enter the definition of the two observables.

cond-mat.mes-hall↗

arXiv2019

Local theory of the insulating state

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 vs. insulating character of a given sample region using as sole ingredient the ground state electron distribution, even in the Anderson case (where the spectrum is gapless). When applied to an insulator with 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-principle) on several test cases validate our theory.

cond-mat.mes-hall↗

arXiv2017

Geometrical meaning of the Drude weight and its relationship to orbital magnetization

At the mean-field level the Drude weight is the Fermi-volume integral of the effective inverse mass tensor. I show here that the deviation of the inverse mass from its free-electron value is the real symmetric part of a geometrical tensor, which is naturally endowed with an imaginary antisymmetric part. The Fermi-volume integral of the latter yields the orbital magnetization. The novel geometrical tensor has a very compact form, and looks like a close relative of the familiar metric-curvature tensor. The Fermi-volume integral of each of the two tensors provides (via real and imaginary parts) a couple of macroscopic observables of the electronic ground-state. I discuss the whole quartet, for both insulating and metallic crystals.

cond-mat.mtrl-sci↗

arXiv2017

Locality of the anomalous Hall conductivity

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.

cond-mat.mes-hall↗