arXiv subjects

Emanuele Maggio

Publications and source records attributed to Emanuele Maggio.

11 recordsLinked to original sources

arXiv2026

Quasi-periodicity enforces Berry phase discontinuity in crystals

The Berry phase of an isolated electronic state is evaluated for different integration paths in reciprocal space, thanks to Riemann-Bloch states providing a consistent description in the whole Brillouin zone. The relationship with the bounded position operator is investigated for the open-path Berry phase and with different form factors of the constituent Gaussian type atomic orbitals (GTOs). When the Berry phase is evaluated over a closed loop in reciprocal space, a regularisation procedure in the complex plane is adopted and additional \textit{quasi}-symmetries are exploited here for the first time in order to rationalise the occurrence of non-analytical jumps as a function of the winding number or of the GTO broadening.

cond-mat.other↗

arXiv2026

Berry Phase of Bloch States through Modular Symmetries

The theoretical identification of crystalline topological materials has enjoyed sustained success in simplified materials models, often by singling out discrete symmetry operations protecting the topological phase. When band structure calculations of realistic materials are considered, complications often arise owing to the requirement of a consistent gauge in the Brillouin zone, or down to the fineness of its sampling. Yet, the Berry phase, acting as topological label, encodes geometrical properties of the system, and it should be easily accessible. Here, an expression for the Berry phase is obtained, thanks to analytical Bloch states constructed from an infinite series of $s$-type Gaussian orbitals. Two contributions in the Berry phase are identified, with one having an immediate geometric interpretation, being equal to the Zak phase. Eigenvalues of a modular symmetry, considered here for the first time in the context of crystalline solid state systems, are put in correspondence with the Zak phase: modular symmetries allow to define a non-trivial action for the spatial inversion also when the system does not have an inversion centre, as for the considered case of space group no. 22 ($F222$), which is known to host symmetry equivalent Bloch states distinguishable by their Berry phase.

cond-mat.mtrl-sci↗

arXiv2025

Exploiting $\vartheta -$functions for the identification of topological materials

An exact analytical expression is derived for Bloch states in three dimensions, based on the only assumption that the electronic wavefunction can be expanded in terms of Gaussian type orbitals. The resulting expression features multidimensional $\vartheta -$functions (and their derivatives) on which the action of discrete space group symmetries is evaluated analytically and contrasted against the symmetry transformations proper of modular forms. We integrate group theoretical arguments with continuity requirements of the Bloch states to produce a viable algorithm for the determination of band inversions in materials with a non-trivial topological electronic band structure; the proposed methodology is then applied to two simplified materials models.

cond-mat.mtrl-sci↗

arXiv2023

Local symmetry groups for arbitrary wavevectors

We present an algorithm for the determination of the local symmetry group for arbitrary k-points in 3D Brillouin zones. First, we test our implementation against tabulated results available for standard high-symmetry points (given by universal fractional coordinates). Then, to showcase the general applicability of our methodology, we produce the irreducible representations for the ``non-universal high-symmetry" points, first reported by Setyawan and Curtarolo [Comput. Mater. Sci. 49, 299 (2010)]. The present method can be regarded as a first step for the determination of elementary band decompositions and symmetry-enforced constraints in crystalline topological materials.

cond-mat.mtrl-sci↗

arXiv2022

LinReTraCe: The Linear Response Transport Centre

We describe the "Linear Response Transport Centre" (LinReTraCe), a package for the simulation of transport properties of solids. LinReTraCe captures quantum (in)coherence effects beyond semi-classical Boltzmann techniques, while incurring similar numerical costs. The enabling algorithmic innovation is a semi-analytical evaluation of Kubo formulae for resistivities and the coefficients of Hall, Seebeck and Nernst. We detail the program's architecture, its interface and usage with electronic-structure packages such as WIEN2k, VASP, and Wannier90, as well as versatile tight-binding settings.

cond-mat.mtrl-sci↗

arXiv2021

Prototypical many-body signatures in transport properties of semiconductors

We devise a methodology for charge, heat, and entropy transport driven by carriers with finite lifetimes. Combining numerical simulations with analytical expressions for low temperatures, we establish a comprehensive and thermodynamically consistent phenomenology for transport properties in semiconductors. We demonstrate that the scattering rate (inverse lifetime) is a relevant energy scale: It causes the emergence of several characteristic features in each transport observable. The theory is capable to reproduce -- with only a minimal input electronic structure -- the full temperature profiles measured in correlated narrow-gap semiconductors. In particular, we account for the previously elusive low-$T$ saturation of the resistivity and the Hall coefficient, as well as the (linear) vanishing of the Seebeck and Nernst coefficient in systems, such as FeSb$_2$, FeAs$_2$, RuSb$_2$ and FeGa$_3$.

cond-mat.str-el↗

arXiv2020

Resistivity saturation in Kondo insulators

Resistivities of heavy-fermion insulators typically saturate below a characteristic temperature $T^*$. For some, metallic surface states, potentially from a non-trivial bulk topology, are a likely source of residual conduction. Here, we establish an alternative mechanism: At low temperature, in addition to the charge gap, the scattering rate turns into a relevant energy scale, invalidating the semiclassical Boltzmann picture. Finite lifetimes of intrinsic carriers limit conduction, impose the existence of a crossover $T^*$, and control - now on par with the gap - the quantum regime emerging below it. We showcase the mechanism with realistic many-body simulations and elucidate how the saturation regime of the Kondo insulator Ce$_3$Bi$_4$Pt$_3$, for which residual conduction is a bulk property, evolves under external pressure and varying disorder. Using a phenomenological formula we derived for the quantum regime, we also unriddle the ill-understood bulk conductivity of SmB$_6$ - demonstrating that our mechanism is widely applicable to correlated narrow-gap semiconductors.

cond-mat.str-el↗

arXiv2017

$GW$ vertex corrected calculations for molecular systems

Hedin's scheme is solved with the inclusion of the vertex function ($GWΓ$) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the self-energy. A diagrammatic analysis shows that the self-energy formed with this four-point vertex does not lead to double counting of diagrams, that can be classified as direct "bubbles" and exchange diagrams. By removing the exchange diagrams from the self-energy, a simpler approximation is obtained, called $GW^{\rm{tc-tc}}$. Very good agreement with expensive wavefunction-based methods is obtained for both approximations.

cond-mat.mtrl-sci↗

arXiv2016

$GW$100: a plane wave perspective for small molecules

In a recent work, van Setten and coworkers have presented a carefully converged $G_0W_0$ study of 100 closed shell molecules [J. Chem. Theory Comput. 11, 5665 (2015)]. For two different codes they found excellent agreement to within few 10 meV if identical Gaussian basis sets were used. We inspect the same set of molecules using the projector augmented wave method and the Vienna ab initio simulation package (VASP). For the ionization potential, the basis set extrapolated plane wave results agree very well with the Gaussian basis sets, often reaching better than 50 meV agreement. In order to achieve this agreement, we correct for finite basis set errors as well as errors introduced by periodically repeated images. For electron affinities below the vacuum level differences between Gaussian basis sets and VASP are slightly larger. We attribute this to larger basis set extrapolation errors for the Gaussian basis sets. For quasi particle (QP) resonances above the vacuum level, differences between VASP and Gaussian basis sets are, however, found to be substantial. This is tentatively explained by insufficient basis set convergence of the Gaussian type orbital calculations as exemplified for selected test cases.

cond-mat.mtrl-sci↗

arXiv2016

Correlation energy for the homogeneous electron gas: exact Bethe-Salpeter solution and new approximate evaluation

The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarisation propagator. The BSE is expected to improve upon the random phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to Møller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlatione energy are compared with Quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarisation propagator. To avoid the occurence of imaginary eigenmodes, an approximation to the BSE kernel is proposed, which allows to completely remove this issue in the low electron density region. We refer to this approximation as the random phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.

cond-mat.mtrl-sci↗

arXiv2015

Singles correlation energy contributions in solids

The random phase approximation to the correlation energy often yields highly accurate results for condensed matter systems. However, ways how to improve its accuracy are being sought and here we explore the relevance of singles contributions for prototypical solid state systems. We set out with a derivation of the random phase approximation using the adiabatic connection and fluctuation dissipation theorem, but contrary to the most commonly used derivation, the density is allowed to vary along the coupling constant integral. This yields results closely paralleling standard perturbation theory. We re-derive the standard singles of Görling-Levy perturbation theory [Görling and Levy, Phys. Rev. A {\bf 50}, 196 (1994)], highlight the analogy of our expression to the renormalized singles introduced by Ren and coworkers [Ren, Tkatchenko, Rinke, and Scheffler, Phys. Rev. Lett. {\bf 106}, 153003 (2011)], and introduce a new approximation for the singles using the density matrix in the random phase approximation. We discuss the physical relevance and importance of singles alongside illustrative examples of simple weakly bonded systems, including rare gas solids (Ne, Ar, Xe), ice, adsorption of water on NaCl, and solid benzene. The effect of singles on covalently and metallically bonded systems is also discussed.

cond-mat.mtrl-sci↗