arXiv subjects

Francesco Belli

Publications and source records attributed to Francesco Belli.

15 recordsLinked to original sources

arXiv2026

Anharmonicity and Nonadiabaticity in Hydride Superconductors

We study superconductivity in representative hydrides using anharmonic phonons, electron-phonon vertex corrections, and full-bandwidth Eliashberg theory. The high-pressure binary hydrides H3S, YH6, and YH9 must be treated with both anharmonic and nonadiabatic corrections, whereas the ambient-pressure PdH/PdD/PdT series is strongly anharmonic but remains adiabatic, reproducing the inverse isotope effect without sizable vertex contributions. LaBeH8 exhibits weak anharmonicity, while vertex corrections reduce the critical temperature (Tc) by approximately 4 K, leaving the predicted Tc above experiment. To identify when treatments beyond harmonic, adiabatic Migdal-Eliashberg theory are required, we introduce the anharmonic renormalization $A_{\lambda}$ and the vertex ratio $R_{V}$ as material-specific diagnostics.

cond-mat.supr-con↗

arXiv2026

Structural and Vibrational Properties of D$_3$Se from First Principles: Anharmonic Quantum and Isotope Effects

Hydrogen-rich superconductors have garnered considerable interest following the discovery of hot superconductivity in high pressure H$_3$S, reviving prospects for room temperature superconductors under high-pressures. Using H$_3$Se as a reference system, we investigate the vibrational and superconducting properties of D$_3$Se in the Im\bar{3}m phase across 60-200 GPa by combining first-principles calculations with the stochastic self-consistent harmonic approximation to treat ionic quantum and anharmonic effects. These effects introduce significant renormalization to the phonon spectra and stabilize the lattice down to at least 70 GPa, well below the harmonic prediction of >110 GPa. Ultimately, the phonon renormalizations alter the electron-phonon coupling, introducing a decrease in the superconducting critical temperature by about 3-16 K across the studied pressure range with respect to standard calculations. Including anharmonic phonons within the Migdal-Eliashberg theory yields $T_c \approx 154$ K at 75 GPa (with ${\mu}^* = 0.1$, ${\lambda} = 3.0$), highlighting D3Se as a promising high-Tc superconductor at moderate pressures. Examining the role of anharmonicity in the isotope effect, we find that at 200 GPa it suppresses the isotope coefficient $\alpha$ to 0.29 one third below the harmonic value (0.44) which approaches the BCS limit of 0.5. This dramatic reduction demonstrates that anharmonicity fundamentally governs the isotope effect on this system. The stark discrepancy between anharmonic and harmonic descriptions underscores the need for targeted experimental efforts to resolve the origin of the persistent theory-experiment discrepancy in compressed hydrides.

cond-mat.supr-con↗

arXiv2025

Real-space understanding of electron-phonon coupling in superconducting hydrides

Electron-phonon coupling is at the origin of conventional superconductivity, enabling the pairing of electrons into Cooper pairs. The electron-phonon matrix elements depend on the electronic eigenstates and, in the standard linear approximation, on the first derivative of the potential felt by the electrons with respect to ionic perturbations. Here, we focus on the derivatives of the potential with a twofold aim: to assess their contribution to the overall coupling and to analyze the limitations of neglecting higher-order derivatives. Several real-space functions are proposed to do the analysis, and are computed for some well-known superconductors. Our results show that, in hydrides, the derivatives of the potential tend to be larger in regions of high electron localization, explaining the success of electronic descriptors previously described to correlate with the critical temperature. The new functions introduced here are able to tell apart structures with similar types of bonding but very different critical temperatures, such as H3S and H3Se Im-3m phases, where electronic descriptors alone fail. Moreover, they provide a method to discriminate promising superconductors from conventional low-$T_c$ materials. Interestingly, our descriptors are capable of easily estimating the impact of higher-order terms in the electron-phonon coupling. In fact, we capture the limitations of the linear approximation expected for PdH, and predict an even more important non-linear behavior in other hydrides.

cond-mat.supr-con↗

arXiv2025

Refining Tc Prediction in Hydrides via Symbolic-Regression-Enhanced Electron-Localization-Function-Based Descriptors

Hydrogen-based materials are able to possess extremely high superconducting critical temperatures, \tc s, due to hydrogen's low atomic mass and strong electron-phonon interaction. Recently, a descriptor based on the Electron Localization Function (ELF) has enabled the rapid estimation of the \tc\ of hydrogen-containing compounds from electronic networking properties, but its applicability has been limited by the small size and homogeneity of the training dataset used. Herein, the model is re-examined compiling a publicly available combined dataset of 244 binary and ternary hydride superconductors. Our analysis shows that though ELF-based networking remains a valuable descriptor, its predictive power declines with increasing compositional complexity. However, by introducing the molecularity index, defined as the highest value of the ELF at which two hydrogen atoms connect, and applying symbolic regression, the accuracy of the predictions can be substantially enhanced. These results establish a more robust framework for assessing superconductivity in hydride materials, facilitating accelerated screening of novel candidates through integration with crystal structure prediction methods or high-throughput searches.

physics.comp-ph↗

arXiv2025

A chemical bonding based descriptor for predicting the impact of quantum nuclear and anharmonic effects on hydrogen-based superconductors

Quantum nuclear effects (QNEs) can significantly alter a material's crystal structure and phonon spectra, impacting properties such as thermal conductivity and superconductivity. However, predicting a priori whether these effects will enhance or suppress superconductivity, or destabilize a structure, remains a grand challenge. Herein, we address this unresolved problem by introducing a descriptor, based upon the integrated crystal orbital bonding index (iCOBI), to predict the influence of QNEs on a crystal lattice's dynamic stability, phonon spectra and superconducting properties. We find that structures with atoms in symmetric chemical bonding environments exhibit greater resilience to structural perturbations induced by QNEs, while those with atoms in asymmetric bonding environments are more susceptible to structural alterations, resulting in enhanced superconducting critical temperatures.

cond-mat.supr-con↗

arXiv2024

Quantum Anharmonic Effects on the Superconductivity of I-43m CH4-H3S at High Pressures: a First-Principles Study

Making use of first-principles calculations we analyze the effect of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of I-43m CH4-H3S, one of the lowest enthalpy structures in the C-S-H system, in the 150-300 GPa pressure range within the stochastic self-consistent harmonic approximation. We predict a correction to the crystal structure, which is formed by an H3S lattice and CH4 molecules, the phonon spectra, and the pressure-dependent superconducting critical temperatures, which have been estimated in previous calculations without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for the lattice dynamics. Our results show that quantum ionic fluctuations have an impact on the distance between H atoms and S atoms in the H3S host lattice, pushing it towards more symmetric bonds, while the methane molecules are barely affected. According to our anharmonic phonon spectra, this structure is dynamically stable above 150 GPa, which is 30 GPa lower than the pressure at which the harmonic approximation predicts the emergence of an instability. As a consequence of the strong anharmonic enhancement of the phonon frequencies, the electron-phonon coupling constant is suppressed by 46% at 200 GPa, and even more at lower pressures. As a result, the superconducting critical temperature is overestimated by around 50 K at 200 GPa, such that it falls below 150 K in the whole pressure range studied. Our results underline that ternary hydrides are subject to strong anharmonic effects on their structural, vibrational, and superconducting properties.

cond-mat.mtrl-sci↗

arXiv2024

Efficient Modelling of Anharmonicity and Quantum Effects in PdCuH$_2$ with Machine Learning Potentials

Quantum nuclear effects and anharmonicity impact a wide range of functional materials and their properties. One of the most powerful techniques to model these effects is the Stochastic Self-Consistent Harmonic Approximation (SSCHA). Unfortunately, the SSCHA is extremely computationally expensive, prohibiting its routine use. We propose a protocol that pairs machine learning interatomic potentials, which can be tailored for the system at hand via active learning, with the SSCHA. Our method leverages an upscaling procedure that allows for the treatment of supercells of up to thousands of atoms with practically minimal computational effort. The protocol is applied to PdCuH$_x$ ($x = 0-2$) compounds, chosen because previous experimental studies have reported superconducting critical temperatures, $T_\text{c}$s, as high as 17~K at ambient pressures in an unknown hydrogenated PdCu phase. We identify a $P4/mmm$ PdCuH$_2$ structure, which is shown to be dynamically stable only upon the inclusion of quantum fluctuations, as being a key contributor to the measured superconductivity. For this system, our methodology is able to reduce the computational expense for the SSCHA calculations by $\sim$96\%. The proposed protocol opens the door towards the routine inclusion of quantum nuclear motion and anharmonicity in materials discovery.

cond-mat.supr-con↗

arXiv2024

Quantum Stabilization and Flat Hydrogen-based Bands of Nitrogen-doped Lutetium Hydride

We explore electronic and structural properties of Fm$\overline{3}$m Lu-H-N structures with specific N,H ordering as plausible candidates for near-ambient superconductivity possibly originating from their remarkably narrow hydrogen-based bands at the Fermi level. Although LuH$_{2.875}$N$_{0.125}$ exhibits an instability persisting up to 17 GPa, it is anharmonically stable near ambient pressure when accounting for quantum nuclear effects. The presence of flat bands near $E_\text{F}$ is understood to arise from destructive\ quantum interference between N-p and surrounding H-s orbitals, with certain types of defects leaving the flat bands unaffected. The results suggest there is an optimal pressure near ambient where the superconducting $T_{\text{c}}$ is maximized in this structure by anharmonically-stabilized low-frequency and non-adiabatically coupled high-frequency hydrogen modes. Despite the metastability of this structure, its electronic properties and dynamical stability when calculated beyond a classical harmonic approach can explain the reported near-ambient superconductivity in Lu-H-N.

cond-mat.supr-con↗

arXiv2023

Phase Boundaries, Isotope Effect and Superconductivity of Lithium Under Hydrostatic Conditions

We present theoretical and experimental studies of superconductivity and low temperature structural phase boundaries in lithium. We mapped the structural phase diagram of 6Li and 7Li under hydrostatic conditions between 5 top 55GPa and within the temperature range of 15 to 75K, observing the FCC-hR1-cI16 phase transitions. 6Li and 7Li show some differences at the structural boundaries, with a potential shift of the phase boundaries of 6Li to lower pressures. Density functional theory calculations and topological analysis of the electron density elucidates the superconducting properties and interatomic interactions within these phases of lithium.

cond-mat.supr-con↗

arXiv2023

Superconductivity in CH4 and BH4- Containing Compounds Derived from the High-Pressure Superhydrides

Inspired by the synthesis of the high-pressure Fm-3m LaH10 superconducting superhydride, systematic density functional theory (DFT) calculations are performed to study ternaries that could be derived from it by replacing two of the hydrogen atoms with boron or carbon and varying the identity of the electropositive element. Though many of the resulting alkali-metal and alkaline-earth MC2H8 phases are predicted to be dynamically stable at mild pressures, their superconducting critical temperatures (Tcs) are low because their metallicity results from the filling of an electride-like band. Substitution with a trivalent element leads to phases with substantial metal d-character at the Fermi level whose Tcs are typically above 40 K. Among the MB2H8 phases examined, KB2H8, RbB2H8 and CsB2H8 are predicted to be dynamically stable at very mild pressures, and their stability is rationalized by a DFT-Chemical Pressure analysis that elucidates the role of the M atom size. Quantum anharmonic effects strongly affect the properties of KB2H8, the highest predicted Tc compound, near 10 GPa, but molecular dynamics simulations reveal it would decompose below its Tc at this pressure. Nonetheless, at ca. 50 GPa KB2H8 is predicted to be thermally stable with a superconducting figure of merit surpassing that of the recently synthesized LaBeH8.

cond-mat.supr-con↗

arXiv2022

Impact of ionic quantum fluctuations on the thermodynamic stability and superconductivity of LaBH$_8$

The recent prediction of a metastable high-symmetry Fm$\bar{3}$m phase of LaBH$_8$ gives hopes to reach high superconducting critical temperatures at affordable pressures among ternary hydrogen-rich compounds. Making use of first-principles calculations within density functional theory and the stochastic self-consistent harmonic approximation, we determine that ionic quantum fluctuations drive the system dynamically unstable below 77 GPa, a much higher pressure than the 45 GPa expected classically. Quantum anharmonic effects stretch the covalent B-H bond in the BH$_8$ units of the structure and, consequently, soften all hydrogen-character modes. Above 77 GPa Fm$\bar{3}$m LaBH$_8$ remains metastable and, interestingly, its superconducting critical temperature is largely enhanced by quantum anharmonic effects, reaching critical temperatures around 170 K at the verge of the dynamical instability. Our results suggest that low pressure metastable phases with covalently bonded symmetric XH$_8$ units will be destabilized by ionic quantum fluctuations.

cond-mat.mtrl-sci↗

arXiv2021

Quantum anharmonic enhancement of superconductivity in $P6_3/mmc$ ScH$_6$ at high pressures: a first-principles study

Making use of first-principles calculations, we analyze the effect of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of P63/mmc ScH6 in the 100-160 GPa pressure range within the stochastic self-consistent harmonic approximation. We predict a strong correction to the crystal structure, the phonon spectra, and the superconducting critical temperatures, which have been estimated in previous calculations without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for the lattice dynamics. Quantum ionic fluctuations have a large impact on the H2 molecular-like units present in the crystal by increasing the hydrogen-hydrogen distance about a 5%. According to our anharmonic phonon spectra, this structure will be dynamically stable at least above 85 GPa, which is 45 GPa lower than the pressure given by the harmonic approximation. Contrary to many superconducting hydrogen-rich compounds, where quantum ionic effects and the consequent anharmonicity tend to lower the superconducting critical temperature, our results show that it can be enhanced in P63/mmc ScH6 by approximately a 15%. We attribute the enhancement of the critical temperature to the stretching of the H$_2$ molecular-like units and the associated increase of the electron-phonon interaction. Our results suggest that quantum ionic effects increase the superconducting critical temperature in hydrogen-rich materials with H2 units by increasing the hydrogen-hydrogen distance and, consequently, the electron-phonon interaction.

cond-mat.supr-con↗

arXiv2021

Strong correlation between bonding network and critical temperature in hydrogen-based superconductors

Recent experimental discoveries show that hydrogen-rich compounds can reach room temperature superconductivity, at least at high pressures. Also that there exist metallic hydrogen-abundant systems with critical temperatures of few Kelvin, or even with no trace of superconductivity at all. By analyzing through first-principles calculations the structural and electronic properties of more than one hundred compounds predicted to be superconductors in the literature, we determine that the capacity of creating a bonding network of connected localized units is the key to enhance the critical temperature in hydrogen-based superconductors, explaining the large variety of critical temperatures of superconducting hydrogen-rich materials. We define a magnitude named as the {\it networking value}, which correlates well with the predicted critical temperature, much better than any other descriptor analyzed thus far. This magnitude can be easily calculated for any compound by analyzing isosurfaces of the electron localization function. By classifying the studied compounds according to their bonding nature, we observe that the {\it networking value} correlates with the critical temperature for all bonding types. Our analysis also highlights that systems with weakened covalent bonds are the most promising candidates for reaching high critical temperatures. The discovery of the positive correlation between superconductivity and the bonding network offers the possibility of screening easily hydrogen-based compounds and, at the same time, sets clear paths for chemically engineering better superconductors.

cond-mat.supr-con↗

arXiv2021

Strong Anharmonic and Quantum Effects in Pm-3n AlH3 Under High Pressure: A First-Principles Study

Motivated by the absence of experimental superconductivity in the metallic Pm-3n phase of AlH3 despite the predictions, we reanalyze its vibrational and superconducting properties at pressures above 99 GPa making use of first-principles techniques. In our calculations based on the self-consistent harmonic approximation method that treats anharmonicity beyond perturbation theory, we predict a strong anharmonic correction to the phonon spectra and demonstrate that the superconducting critical temperatures predicted in previous calculations based on the harmonic approximation are strongly suppressed by anharmonicity. The electron-phonon coupling concentrates on the lowest-energy hydrogen-character optical modes at the X point of the Brillouin zone. As a consequence of the strong anharmonic enhancement of their frequency, the electron-phonon coupling is suppressed by at least a 30%. The suppression in λ makes Tc smaller than 4.2 K above 120 GPa, which is well consistent with the experimental evidence. Our results underline that metal hydrides with hydrogen atoms in interstitial sites are subject to huge anharmonic effects.

cond-mat.supr-con↗

arXiv2019

Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride

The discovery of superconductivity at 200 K in the hydrogen sulfide system at large pressures [1] was a clear demonstration that hydrogen-rich materials can be high-temperature superconductors. The recent synthesis of LaH$_{10}$ with a superconducting critical temperature (T$_{\text{c}}$) of 250 K [2,3] places these materials at the verge of reaching the long-dreamed room-temperature superconductivity. Electrical and x-ray diffraction measurements determined a weakly pressure-dependent T$_{\text{c}}$ for LaH$_{10}$ between 137 and 218 gigapascals in a structure with a face-centered cubic (fcc) arrangement of La atoms [3]. Here we show that quantum atomic fluctuations stabilize in all this pressure range a high-symmetry Fm-3m crystal structure consistent with experiments, which has a colossal electron-phonon coupling of $λ\sim3.5$. Even if ab initio classical calculations neglecting quantum atomic vibrations predict this structure to distort below 230 GPa yielding a complex energy landscape with many local minima, the inclusion of quantum effects simplifies the energy landscape evidencing the Fm-3m as the true ground state. The agreement between the calculated and experimental T$_{\text{c}}$ values further supports this phase as responsible for the 250 K superconductivity. The relevance of quantum fluctuations in the energy landscape found here questions many of the crystal structure predictions made for hydrides within a classical approach that at the moment guide the experimental quest for room-temperature superconductivity [4,5,6]. Furthermore, quantum effects reveal crucial to sustain solids with extraordinary electron-phonon coupling that may otherwise be unstable [7].

cond-mat.supr-con↗