Dominant Role of Quantum Anharmonicity in the Stability and Optical Properties of Infinite Linear Acetylenic Carbon Chains.

Carbyne, an infinite-length straight chain of carbon atoms, is supposed to undergo a second order phase transition from the metallic bond-symmetric cumulene (═C═C═)∞ toward the distorted insulating polyyne chain (-C≡C-)∞ displaying bond-length alternation. However, recent synthesis of ultra long carbon chains (∼6000 atoms, [Nat. Mater., 2016, 15, 634]) did not show any phase transition and detected only the polyyne phase, in agreement with previous experiments on capped finite carbon chains. Here, by performing first-principles calculations, we show that quantum-anharmonicity reduces the energy gain of the polyyne phase with respect to the cumulene one by 71%. The magnitude of the bond-length alternation increases by increasing temperature, in stark contrast with a second order phase transition, confining the cumulene-to-polyyne transition to extremely high and unphysical temperatures. Finally, we predict that a high temperature insulator-to-metal transition occurs in the polyyne phase confined in insulating nanotubes with sufficiently large dielectric constant due to a giant quantum-anharmonic bandgap renormalization.

The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects.

The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation (SSCHA) method. This technique rigorously describes the full thermodynamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theoretical framework of the SSCHA and its dynamical extension, making particular emphasis on the physical inter pretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calculation to illustrate the potential of the code. Several applications of the method in superconducting hydrides, charge-density-wave materials, and thermoelectric compounds are also reviewed.

Anomalous High-Temperature Superconductivity in YH6.

Pressure-stabilized hydrides are a new rapidly growing class of high-temperature superconductors, which is believed to be described within the conventional phonon-mediated mechanism of coupling. Here, the synthesis of one of the best-known high-TC superconductors-yttrium hexahydride I m 3 ¯ m -YH6 is reported, which displays a superconducting transition at ≈224 K at 166 GPa. The extrapolated upper critical magnetic field Bc2 (0) of YH6 is surprisingly high: 116-158 T, which is 2-2.5 times larger than the calculated value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coefficient 0.4 supports the phonon-assisted superconductivity. Current-voltage measurements show that the critical current IC and its density JC may exceed 1.75 A and 3500 A mm-2 at 4 K, respectively, which is higher than that of the commercial superconductors, such as NbTi and YBCO. The results of superconducting density functional theory (SCDFT) and anharmonic calculations, together with anomalously high critical magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal-Eliashberg and Bardeen-Cooper-Schrieffer theories, and presence of an additional mechanism of superconductivity.

van der Waals driven anharmonic melting of the 3D charge density wave in VSe2.

Understanding of charge-density wave (CDW) phases is a main challenge in condensed matter due to their presence in high-Tc superconductors or transition metal dichalcogenides (TMDs). Among TMDs, the origin of the CDW in VSe2 remains highly debated. Here, by means of inelastic x-ray scattering and first-principles calculations, we show that the CDW transition is driven by the collapse at 110 K of an acoustic mode at qCDW = (2.25 0 0.7) r.l.u. The softening starts below 225 K and expands over a wide region of the Brillouin zone, identifying the electron-phonon interaction as the driving force of the CDW. This is supported by our calculations that determine a large momentum-dependence of the electron-phonon matrix-elements that peak at the CDW wave vector. Our first-principles anharmonic calculations reproduce the temperature dependence of the soft mode and the TCDW onset only when considering the out-of-plane van der Waals interactions, which reveal crucial for the melting of the CDW phase.

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

Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H 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.

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.

Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride.

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.

Quantum Enhancement of Charge Density Wave in NbS2 in the Two-Dimensional Limit.

At ambient pressure, bulk 2H-NbS2 displays no charge density wave instability, which is at odds with the isostructural and isoelectronic compounds 2H-NbSe2, 2H-TaS2, and 2H-TaSe2, and in disagreement with harmonic calculations. Contradictory experimental results have been reported in supported single layers, as 1H-NbS2 on Au(111) does not display a charge density wave, whereas 1H-NbS2 on 6H-SiC(0001) endures a 3 × 3 reconstruction. Here, by carrying out quantum anharmonic calculations from first-principles, we evaluate the temperature dependence of phonon spectra in NbS2 bulk and single layer as a function of pressure/strain. For bulk 2H-NbS2, we find excellent agreement with inelastic X-ray spectra and demonstrate the removal of charge ordering due to anharmonicity. In the two-dimensional limit, we find an enhanced tendency toward charge density wave order. Freestanding 1H-NbS2 undergoes a 3 × 3 reconstruction, in agreement with data on 6H-SiC(0001) supported samples. Moreover, as strains smaller than 0.5% in the lattice parameter are enough to completely remove the 3 × 3 superstructure, deposition of 1H-NbS2 on flexible substrates or a small charge transfer via field-effect could lead to devices with dynamical switching on/off of charge order.

Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe.

Since 2014 the layered semiconductor SnSe in the high-temperature Cmcm phase is known to be the most efficient intrinsic thermoelectric material. Making use of first-principles calculations we show that its vibrational and thermal transport properties are determined by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temperature. Our calculations show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calculate the lattice thermal conductivity obtaining good agreement with experiments only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelectric efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.

Critical Role of the Exchange Interaction for the Electronic Structure and Charge-Density-Wave Formation in TiSe_{2}.

We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe_{2}. In contrast to local approximations in density functional theory, the explicit inclusion of exact, nonlocal exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-density-wave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments.

Orbital magnetization as a local property.

The modern expressions for polarization P and orbital magnetization M are k-space integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the ground-state density matrix, "nearsighted" in insulators, independently of the boundary conditions--either periodic or open. While P--owing to its "quantum" indeterminacy--is not a bulk property in this sense, M is. We provide its r-space expression for any insulator, even with a nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory.