Showing papers by "Francesco Mauri published in 2020"

Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride

Abstract: The discovery of superconductivity at 200 kelvin in the hydrogen sulfide system at high pressures1 demonstrated the potential of hydrogen-rich materials as high-temperature superconductors. Recent theoretical predictions of rare-earth hydrides with hydrogen cages2,3 and the subsequent synthesis of LaH10 with a superconducting critical temperature (Tc) of 250 kelvin4,5 have placed these materials on the verge of achieving the long-standing goal of room-temperature superconductivity. Electrical and X-ray diffraction measurements have revealed a weakly pressure-dependent Tc for LaH10 between 137 and 218 gigapascals in a structure that has a face-centred cubic arrangement of lanthanum atoms5. Here we show that quantum atomic fluctuations stabilize a highly symmetrical [Formula: see text] crystal structure over this pressure range. The structure is consistent with experimental findings and has a very large electron-phonon coupling constant of 3.5. Although ab initio classical calculations predict that this [Formula: see text] structure undergoes distortion at pressures below 230 gigapascals2,3, yielding a complex energy landscape, the inclusion of quantum effects suggests that it is the true ground-state structure. The agreement between the calculated and experimental Tc values further indicates that this phase is responsible for the superconductivity observed at 250 kelvin. The relevance of quantum fluctuations calls into question many of the crystal structure predictions that have been made for hydrides within a classical approach and that currently guide the experimental quest for room-temperature superconductivity6-8. Furthermore, we find that quantum effects are crucial for the stabilization of solids with high electron-phonon coupling constants that could otherwise be destabilized by the large electron-phonon interaction9, thus reducing the pressures required for their synthesis.

Weak Dimensionality Dependence and Dominant Role of Ionic Fluctuations in the Charge-Density-Wave Transition of NbSe_{2}.

Abstract: Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H ${\mathrm{NbSe}}_{2}$. While scanning tunneling experiments on single layers grown by molecular beam epitaxy measure a charge-density-wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By employing a nonperturbative approach to deal with anharmonicity, we calculate from first principles the temperature dependence of the phonon spectra both for bulk and monolayer. In both cases, the charge-density-wave transition temperature is estimated as the temperature at which the phonon energy of the mode driving the structural instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Environmental factors could motivate the disagreement between the transition temperatures reported by experiments. Our analysis also demonstrates the predominance of ionic fluctuations over electronic ones in the melting of the charge-density-wave order.

Anharmonicity and doping melt the charge density wave in single-layer TiSe2

Abstract: Low-dimensional systems with a vanishing band gap and a large electron-hole interaction have been proposed to be unstable toward exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe2. We find that, contrary to the bulk case and to the generally accepted picture, in single-layer TiSe2, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has weak effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain TCDW ≈ 440 K for an isolated and undoped single layer and TCDW ≈ 364 K for an electron-doping n = 4.6 × 1013 cm-2, close to the experimental result of 200-280 K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe2.

Phonon collapse and van der Waals melting of the 3D charge density wave of VSe$_2$

Abstract: Among transition metal dichalcogenides (TMDs), VSe$_2$ is considered to develop a purely 3-dimensional (3D) charge-density wave (CDW) at T$_{CDW}$=110 K. Here, by means of high resolution inelastic x-ray scattering (IXS), we show that the CDW transition is driven by the collapse of an acoustic mode at the critical wavevector \textit{q}$_{CDW}$= (2.25 0 0.7) r.l.u. and critical temperature T$_{CDW}$=110 K. The softening of this mode starts to be pronounced for temperatures below 2$\times$ T$_{CDW}$ and expands over a rather wide region of the Brillouin zone, suggesting a large contribution of the electron-phonon interaction to the CDW formation. This interpretation is supported by our first principles calculations that determine a large momentum-dependence of the electron-phonon interaction, peaking at the CDW wavevector, in the presence of nesting. Fully anharmonic {\it ab initio} calculations confirm the softening of one acoustic branch at \textit{q}$_{CDW}$ as responsible for the CDW formation and show that van der Waals interactions are crucial to melt the CDW. Our work also highlights the important role of out-of-plane interactions to describe 3D CDWs in TMDs.

Theory of the thickness dependence of the charge density wave transition in 1 T-TiTe2

Abstract: Computational resources were granted by PRACE (Project No. 2017174186) and from IDRIS, CINES and TGCC (Grant eDARI 91202 and Grand Challenge Jean Zay). M C, F M, J S Z and L M acknowledge support from the European Union’s Horizon 2020 research and innovation programme Graphene Flagship under grant agreement No 881603.. M C and J S Z acknowledge support from Agence nationale de la recherche (Grant No. ANR-19-CE24-0028). F M and L M acknowledge support by the MIUR PRIN-2017 program, project number 2017Z8TS5B.

Long-Range Rhombohedral-Stacked Graphene through Shear

Abstract: The discovery of superconductivity and correlated electronic states in the flat bands of twisted bilayer graphene has raised a lot of excitement. Flat bands also occur in multilayer graphene flakes...

Hybrid-functional electronic structure of multilayer graphene

Abstract: Multilayer graphene with rhombohedral and Bernal stacking is supposed to be metallic, as predicted by density functional theory calculations using semilocal functionals. However, recent angular resolved photoemission and transport data have questioned this point of view. In particular, rhombohedral flakes are suggested to be magnetic insulators, a view supported also by hybrid-functional calculations. Bernal flakes composed of an even number of layers are insulating (for $N\ensuremath{\le}6$), while those composed of an odd number of layers are pseudogapped (for $N\ensuremath{\le}7$). Here, by systematically benchmarking with plane-waves codes, we develop very accurate all-electron Gaussian basis sets for graphene multilayers, allowing a precise description of the electronic structure in the 100 meV energy range from the Fermi energy at the hybrid-functional level. We find, in agreement with our previous calculations, that rhombohedral stacked multilayers are gapped and magnetic. However, the valence band curvature and the details of the electronic structure at the $\ensuremath{\sim}10\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ scale show a dependence on the basis set. A substantially extended basis set is needed to describe the long-range interlayer interactions and, consequently, to correctly reproduce the effective mass of the valence band top at the $K$ point. In the case of Bernal stacking, we show that exact exchange gaps the flakes composed by four layers and opens pseudogaps for $N=3$, 6, 7, 8. However, the gap or pseudogap size and its behavior as a function of thickness are not compatible with experimental data. Moreover, hybrid functionals lead to a metallic solution for five layers and a magnetic ground state for five, six, and eight layers. Magnetism is very weak with practically no effect on the electronic structure and the magnetic moments are mostly concentrated in the central layers. Our hybrid-functional calculations on trilayer Bernal graphene are in excellent agreement with $GW$ results. For thicker multilayers, our calculations are a benchmark for many-body theoretical modeling of the low energy electronic structure.

Ab-initio energetics of graphite and multilayer graphene: stability of Bernal versus rhombohedral stacking

Abstract: There has been a lot of excitement around the observation of superconductivity in twisted bilayer graphene, associated to flat bands close to the Fermi level. Such correlated electronic states also occur in multilayer rhombohedral stacked graphene (RG), which has been receiving increasing attention in the last years. In both natural and artificial samples however, multilayer stacked Bernal graphene (BG) occurs more frequently, making it desirable to determine what is their relative stability and under which conditions RG might be favored. Here, we study the energetics of BG and RG in bulk and also multilayer stacked graphene using first-principles calculations. It is shown that the electronic temperature, not accounted for in previous studies, plays a crucial role in determining which phase is preferred. We also show that the low energy states at room temperature consist of BG, RG and mixed BG-RG systems with a particular type of interface. Energies of all stacking sequences (SSs) are calculated for N = 12 layers, and an Ising model is used to fit them, which can be used for larger N as well. In this way, the ordering of low energy SSs can be determined and analyzed in terms of a few parameters. Our work clarifies inconsistent results in the literature, and sets the basis to studying the effect of external factors on the stability of multilayer graphene systems in first principles calculations.

Bending rigidity and sound propagation in graphene

Abstract: Despite the interest raised by graphene and 2D materials, their mechanical and acoustic properties are still highly debated. Harmonic theory predicts a quadratic dispersion for the flexural acoustic mode. Such a quadratic dispersion leads to diverging atomic fluctuations and a constant linewidth of in-plane acoustic phonon modes at small momentum, which implies that graphene cannot propagate sound waves. Many works based on membrane theory questioned the robustness of the quadratic dispersion, arguing that the anharmonic phonon-phonon interaction linearizes it, which implies a divergent bending rigidity (stiffness) in the long wavelength limit. However, these works are based on effective low-energy models that explicitly break the rotational invariance. Here we show that rotational symmetry protects the quadratic flexural dispersion against phonon-phonon interaction, and that the bending stiffness of graphene is unaffected by temperature and quantum fluctuations. Nevertheless, our non-perturbative anharmonic calculations predict that sound propagation coexists with such a quadratic dispersion. Since our conclusions are universal properties of membranes, they apply not just to graphene, but to all 2D materials.

Theory of the thickness dependence of the charge density wave transition in 1T-TiTe$_2$

Abstract: Most metallic transition metal dichalcogenides undergo charge density wave (CDW) instabilities with similar or identical ordering vectors in bulk and in single layer, albeit with different critical temperatures. Metallic 1T-TiTe$_2$ is a remarkable exception as it shows no evidence of charge density wave formation in bulk, but it displays a stable $2\times2$ reconstruction in single-layer form. The mechanism for this 3D-2D crossover of the transition is still unclear, although strain from the substrate and the exchange interaction have been pointed out as possible formation mechanisms. Here, by performing non-perturbative anharmonic calculations with gradient corrected and hybrid functionals, we explain the thickness behaviour of the transition in 1T-TiTe$_2$. We demonstrate that the occurrence of the CDW in single-layer TiTe$_2$ occurs from the interplay of non-perturbative anharmonicity and an exchange enhancement of the electron-phonon interaction, larger in the single layer than in the bulk. Finally, we study the electronic and structural properties of the single-layer CDW phase and provide a complete description of its electronic structure, phonon dispersion as well as infrared and Raman active phonon modes.

Weak Dimensionality Dependence of the Charge Density Wave Transition in NbSe$_2$

Abstract: Contradictory experiments have been reported about the dimensionality effect on the charge density wave transition in 2H NbSe$_2$. While scanning tunnelling experiments on single layers grown by molecular beam epitaxy measure a charge density wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By calculating from first principles the charge density wave temperature, we determine that the intrinsic charge density wave is barely affected by dimensionality as suggested by the scanning tunnelling experiments. The transition temperature is estimated by calculating the temperature dependence of the phonon spectra within a non-perturbative approach to deal with anharmonicity and determining at which temperature the phonon energy of the mode driving the instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Our results demonstrate that the charge density wave melts due to the ionic contribution to the entropy, not the electronic one, and underline that environmental factors, such as sample preparation or the substrate, have a large impact on the transition temperatures.

Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride

Abstract: 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 $\\lambda\\sim3.5$. 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].