Chemically-exfoliated single-layer MoS2_2 : stability, lattice dynamics and catalytic adsorption from first principles

Chemically and mechanically exfoliated MoS$_2$ single-layer samples have substantially different properties. While mechanically exfoliated single-layers are mono-phase (1H polytype with Mo in trigonal prismatic coordination), the chemically exfoliated samples show coexistence of three different phases, 1H, 1T (Mo in octahedral coordination) and 1T$^{'}$ (a distorted $2\times 1$ 1T-superstructure). By using first-principles calculations, we investigate the energetics and the dynamical stability of the three phases. We show that the 1H phase is the most stable one, while the metallic 1T phase, strongly unstable, undergoes a phase transition towards a metastable and insulating 1T$^{'}$ structure composed of separated zig-zag chains. We calculate electronic structure, phonon dispersion, Raman frequencies and intensities for the 1T$^{'}$ structure. We provide a microscopical description of the J$_1$, J$_2$ and J$_3$ Raman features first detected more then $20$ years ago, but unexplained up to now. Finally, we show that H adsorbates, that are naturally present at the end of the chemical exfoliation process, stabilize the 1T$^{\prime}$ over the 1H one.Comment: 7 Pages, 8 Pictures, To appear on Phys. Rev.

Phonon-assisted magnetic Mott-insulating state in the charge density wave phase of single-layer 1TNbSe2

We study the structural, electronic and vibrational properties of single-layer 1TNbSe$_2$ from first principles. Within the generalized gradient approximation, the 1T polytype is highly unstable with respect to the 2H. The DFT+U method improves the stability of the 1T phase, explaining its detection in experiments. A charge density wave occurs with a $\sqrt{13}\times\sqrt{13}~R30^{\circ}$ periodicity, in agreement with STM data. At $U=0$, the David-star reconstruction displays a flat band below the Fermi level with a marked d$_{z^2-r^2}$ orbital character of the central Nb. The Hubbard interaction induces a magnetic Mott insulating state. Magnetism distorts the lattice around the central Nb atom in the star, reduces the hybridization between the central Nb d$_{z^2-r^2}$ orbital and the neighbouring Se p-states and lifts in energy the flat band becoming non-bonding. This cooperative lattice and magnetic effect amplifies the Mott gap. Single-layer 1TNbSe$_2$ is then a phonon-assisted spin-$1/2$ Magnetic Mott insulator.Comment: 6 pages, 9 picture

Projector augmented wave calculation of x-ray absorption spectra at the L2,3 edges

We develop a technique based on density functional theory and the projector augmented wave method in order to obtain the x-ray absorption cross section at a general edge, both in the electric dipole and quadrupole approximations. The method is a generalization of Taillefumier et al., PRB 66, 195107 (2002). We apply the method to the calculation of the Cu L2,3 edges in fcc copper and cuprite (Cu2O), and to the S L2,3 edges in molybdenite (2H-MoS2). The role of core-hole effects, modeled in a supercell approach, as well as the decomposition of the spectrum into different angular momentum channels are studied in detail. In copper we find that the best agreement with experimental data is obtained when core-hole effects are neglected. On the contrary, core-hole effects need to be included both in Cu2O and 2H-MoS2. Finally we show that a non-negligible component of S L2,3 edges in 2H-MoS2 involves transition to states with s character at all energy scales. The inclusion of this angular momentum channel is mandatory to correctly describe the angular dependence of the measured spectra. We believe that transitions to s character states are quantitatively significant at the L2,3 edges of third row elements from Al to Ar.Comment: 12 pages, 10 picture

Possibility of superconductivity in graphite intercalated with alkaline earths investigated with density functional theory

Using density functional theory we investigate the occurrence of superconductivity in AC$_6$ with A=Mg,Ca,Sr,Ba. We predict that at zero pressure, Ba and Sr should be superconducting with critical temperatures (T$_c$) 0.2 K and 3.0 K, respectively. We study the pressure dependence of T$_c$ assuming the same symmetry for the crystal structures at zero and finite pressures. We find that the SrC$_6$ and BaC$_6$ critical temperatures should be substantially enhanced by pressure. On the contrary, for CaC$_6$ we find that in the 0 to 5 GPa region, T$_c$ weakly increases with pressure. The increase is much smaller than what shown in several recent experiments. Thus we suggest that in CaC$_6$ a continous phase transformation, such as an increase in staging, occurs at finite pressure. Finally we argue that, although MgC$_6$ is unstable, the synthesis of intercalated systems of the kind Mg$_x$Ca$_{1-x}$C$_y$ could lead to higher critical temperatures.Comment: 9 page

Charge density wave and superconducting dome in TiSe2 from electron-phonon interaction

At low temperature TiSe2 undergoes a charge density wave instability. Superconductivity is stabilized either by pressure or by Cu intercalation. We show that the pressure phase diagram of TiSe2 is well described by first-principles calculations. At pressures smaller than 4 GPa charge density wave ordering occurs, in agreement with experiments. At larger pressures the disappearing of the charge density wave is due to a stiffening of the short-range force-constants and not to the variation of nesting with pressure. Finally we show that the behavior of Tc as a function of pressure is entirely determined by the electron-phonon interaction without need of invoking excitonic mechanisms. Our work demonstrates that phase-diagrams with competing orders and a superconducting dome are also obtained in the framework of the electron-phonon interaction.Comment: 4 pages, 7 picture

Electronic structure of heavily-doped graphene: the role of foreign atom states

Using density functional theory calculations we investigate the electronic structure of graphene doped by deposition of foreign atoms. We demonstrate that, as the charge transfer to the graphene layer increases, the band structure of the pristine graphene sheet is substantially affected. This is particularly relevant when Ca atoms are deposed on graphene at CaC$_{6}$ stoichiometry. Similarly to what happens in superconducting graphite intercalated compounds, a Ca bands occurs at the Fermi level. Its hybridization with the C states generates a strong non-linearity in one of the $\pi^{*}$ bands below the Fermi level, at energies comparable to the graphene E$_{2g}$ phonon frequency. This strong non-linearity, and not manybody effects as previously proposed, explains the large and anisotropic values of the apparent electron-phonon coupling measured in angular resolved photoemission.Comment: 4 pages, 2 figures, see also M. Calandra and F. Mauri,arXiv:0707.146

Charge density wave and spin 1/21/2 insulating state in single layer 1T-NbS2_2

In bulk samples and few layer flakes, the transition metal dichalcogenides NbS$_2$ and NbSe$_2$ assume the H polytype structure with trigonal prismatic coordination of the Nb atom. Recently, however, single and few layers of 1T-NbSe$_2$ with octahedral coordination around the transition metal ion were synthesized. Motivated by these experiments and by using first-principles calculations, we investigate the structural, electronic and dynamical properties of single layer 1T-NbS$_2$. We find that single-layer 1T-NbS$_2$ undergoes a $\sqrt{13}\times\sqrt{13}$ star-of-David charge density wave. Within the generalized gradient approximation, the weak interaction between the stars leads to an ultraflat band at the Fermi level isolated from all other bands. The spin-polarized generalized gradient approximation stabilizes a total spin $1/2$ magnetic state with opening of a $0.15$ eV band gap and a $0.21\mu_B$ magnetic moment localized on the central Nb in the star. Within GGA+U, the magnetic moment on the central Nb is enhanced to $0.41\mu_{B}$ and a larger gap occurs. Most important, this approximation gives a small energy difference between the 1T and 1H polytypes (only $+0.5$ mRy/Nb), suggesting that the 1T-polytype can be synthesized in a similar way as done for single layer 1T-NbSe$_2$. Finally we compute first and second nearest neighbors magnetic inter-star exchange interactions finding $J_1$=9.5~K and $J_2$=0.4~K ferromagnetic coupling constants

Superconductivity in C6Ca

Using density functional theory we demonstrate that superconductivity in C6Ca is due to a phonon-mediated mechanism with electron-phonon coupling 0.83 and phonon-frequency logarithmic-average 24.7 meV. The calculated isotope exponents are 0.24 for Ca and 0.26 for C. Superconductivity is mostly due C vibrations perpendicular and Ca vibrations parallel to the graphite layers. Since the electron-phonon couplings of these modes are activated by the presence of an intercalant Fermi surface, the occurrence of superconductivity in graphite intercalated compounds requires a non complete ionization of the intercalant.Comment: 4 pages, 3 figure

Electronic structure and magnetic properties of few-layer Cr2_2Ge2_2Te6_6: the key role of nonlocal electron-electron interaction effects

Atomically-thin magnetic crystals have been recently isolated experimentally, greatly expanding the family of two-dimensional materials. In this Article we present an extensive comparative analysis of the electronic and magnetic properties of ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$, based on density functional theory (DFT). We first show that the often-used ${\rm DFT}+U$ approaches fail in predicting the ground-state properties of this material in both its monolayer and bilayer forms, and even more spectacularly in its bulk form. In the latter case, the fundamental gap {\it decreases} by increasing the Hubbard-$U$ parameter, eventually leading to a metallic ground state for physically relevant values of $U$, in stark contrast with experimental data. On the contrary, the use of hybrid functionals, which naturally take into account nonlocal exchange interactions between all orbitals, yields good account of the available ARPES experimental data. We then calculate all the relevant exchange couplings (and the magneto-crystalline anisotropy energy) for monolayer, bilayer, and bulk ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$ with a hybrid functional, with super-cells containing up to $270$ atoms, commenting on existing calculations with much smaller super-cell sizes. In the case of bilayer ${\rm Cr}_2{\rm Ge}_2{\rm Te}_6$, we show that two distinct intra-layer second-neighbor exchange couplings emerge, a result which, to the best of our knowledge, has not been noticed in the literature.Comment: 13 pages, 6 figures, 3 table

High-TcT_c superconductivity in weakly electron-doped HfNCl

We investigate the magnetic and superconducting properties in electron-doped Li$_x$HfNCl. HfNCl is a band insulator that undergoes an insulator to superconductor transition upon doping at $x\approx0.13$. The persistence of the insulating state for $x<0.13$ is due to an Anderson transition probably related to Li disorder. In the metallic and superconducting phase, Li$_x$HfNCl is a prototype two-dimensional two-valley electron gas with parabolic bands. By performing a model random phase approximation approach as well as first-principles range-separated Heyd-Scuseria-Ernzerhof (HSE06) calculations, we find that the spin susceptibility $\chi_s$ is strongly enhanced in the low doping regime by the electron-electron interaction. Furthermore, in the low doping limit, the exchange interaction renormalizes the intervalley electron-phonon coupling and results in a strong increase of the superconducting critical temperature for $x<0.15$. On the contrary, for $x>0.15$, $T_c$ is approximately constant, in agreement with experiments. At $x=0.055$ we found that $T_c$ can be as large as 40 K, suggesting that the synthesis of cleaner samples of Li$_x$HfNCl could remove the Anderson insulating state competing with superconductivity and generate a high-$T_c$ superconductor.Comment: 8 pages, 6 figure