Real-Axis Solution of Eliashberg Equations in Various Order-Parameter Symmetries and Tunneling Conductance of Optimally-Doped HTSC

In the present work we calculate the theoretical tunneling conductance curves of SIN junctions involving high-Tc superconductors, for different possible symmetries of the order parameter (s, d, s+id, s+d, anisotropic s and extended s). To do so, we solve the real-axis Eliashberg equations in the case of an half-filled infinite band. We show that some of the peculiar characteristics of HTSC tunneling curves (dip and hump at eV > Delta, broadening of the gap peak, zero bias and so on) can be explained in the framework of the Migdal-Eliashberg theory. The theoretical dI/dV curves calculated for the different symmetries at T=4 K are then compared to various experimental tunneling data obtained in optimally-doped BSCCO, TBCO, HBCO, LSCO and YBCO single crystals. To best fit the experimental data, the scattering by non-magnetic impurities has to be taken into account, thus limiting the sensitivity of this procedure in determining the exact gap symmetry of these materials. Finally, the effect of the temperature on the theoretical tunneling conductance is also discussed and the curves obtained at T=2 K are compared to those given by the analytical continuation of the imaginary-axis solution.Comment: 6 pages, 3 figures, Proceedings of SATT10 Conference, to be published in Int. J. Mod. Phys.

Anomalous screening of an electrostatic field at the surface of niobium nitride

The interaction between an electric field and the electric charges in a material is described by electrostatic screening, which in metallic systems is commonly thought to be confined within a distance of the order of the Thomas-Fermi length. The validity of this picture, which holds for surface charges up to $\sim 10^{13}\,\mathrm{cm^{-2}}$, has been recently questioned by several experimental results when dealing with larger surface charges, such as those routinely achieved via the ionic gating technique. Whether these results can be accounted for in a purely electrostatic picture is still debated. In this work, we tackle this issue by calculating the spatial dependence of the charge carrier density in thin slabs of niobium nitride via an ab initio density functional theory approach in the field-effect transistor configuration. We find that perturbations induced by surface charges $\lesssim 10^{14}\,\mathrm{cm^{-2}}$ are mainly screened within the first layer, while those induced by larger surface charges $\sim 10^{15}\,\mathrm{cm^{-2}}$ can penetrate over multiple atomic layers, in reasonable agreement with the available experimental data. Furthermore, we show that a significant contribution to the screening of large fields is associated not only to the accumulation layer of the induced charge carriers at the surface, but also to the polarization of the pre-existing charge density of the undoped system.Comment: 8 pages, 4 figure

Towards the insulator-to-metal transition at the surface of ion-gated nanocrystalline diamond films

Hole doping can control the conductivity of diamond either through boron substitution, or carrier accumulation in a field-effect transistor. In this work, we combine the two methods to investigate the insulator-to-metal transition at the surface of nanocrystalline diamond films. The finite boron doping strongly increases the maximum hole density which can be induced electrostatically with respect to intrinsic diamond. The ionic gate pushes the conductivity of the film surface away from the variable-range hopping regime and into the quantum critical regime. However, the combination of the strong intrinsic surface disorder due to a non-negligible surface roughness, and the introduction of extra scattering centers by the ionic gate, prevents the surface accumulation layer to reach the metallic regime.Comment: 5 pages, 4 figure

Mapping multi-valley Lifshitz transitions induced by field-effect doping in strained MoS2 nanolayers

Gate-induced superconductivity at the surface of nanolayers of semiconducting transition metal dichalcogenides (TMDs) has attracted a lot of attention in recent years, thanks to the sizeable transition temperature, robustness against in-plane magnetic fields beyond the Pauli limit, and hints to a non-conventional nature of the pairing. A key information necessary to unveil its microscopic origin is the geometry of the Fermi surface hosting the Cooper pairs as a function of field-effect doping, which is dictated by the filling of the inequivalent valleys at the K/K$^{\prime}$ and Q/Q$^{\prime}$ points of the Brillouin Zone. Here, we achieve this by combining Density Functional Theory calculations of the bandstructure with transport measurements on ion-gated 2H-MoS$_{2}$ nanolayers. We show that, when the number of layers and the amount of strain are set to their experimental values, the Fermi level crosses the bottom of the high-energy valleys at Q/Q$^{\prime}$ at doping levels where characteristic kinks in the transconductance are experimentally detected. We also develop a simple 2D model which is able to quantitatively describe the broadening of the kinks observed upon increasing temperature. We demonstrate that this combined approach can be employed to map the dependence of the Fermi surface of TMD nanolayers on field-effect doping, detect Lifshitz transitions, and provide a method to determine the amount of strain and spin-orbit splitting between sub-bands from electric transport measurements in real devices.Comment: 8 pages, 4 figure

A model for critical current effects in point-contact Andreev-reflection spectroscopy

It is well known that point-contact Andreev reflection spectroscopy provides reliable measurements of the energy gap(s) in a superconductor when the contact is in the ballistic or nearly-ballistic regime. However, especially when the mean free path of the material under study is small, obtaining ballistic contacts can be a major challenge. One of the signatures of a Maxwell contribution to the contact resistance is the presence of "dips" in the differential conductance, associated to the sudden appearance of a Maxwell term, in turn due to the attainment of the critical current of the material in the contact region. Here we show that, using a proper model for the $R(I)$ of the material under study, it is possible to fit the experimental curves (without the need of normalization) obtaining the correct values of the gap amplitudes even in the presence of such dips, as well as the temperature dependence of the critical current in the contact. We present a test of the procedure in the case of Andreev-reflection spectra in Mg$_{0.75}$Al$_{0.25}$B$_2$ single crystals.Comment: 7 pages, 5 figure

Towards the insulator-to-metal transition at the surface of ion-gated nanocrystalline diamond films

Hole doping can control the conductivity of diamond either through boron substitution, or carrier accumulation in a field-effect transistor. In this work, we combine the two methods to investigate the insulator-to-metal transition at the surface of nanocrystalline diamond films. The finite boron doping strongly increases the maximum hole density which can be induced electrostatically with respect to intrinsic diamond. The ionic gate pushes the conductivity of the film surface away from the variable-range hopping regime and into the quantum critical regime. However, the combination of the strong intrinsic surface disorder due to a non-negligible surface roughness, and the introduction of extra scattering centers by the ionic gate, prevents the surface accumulation layer to reach the metallic regime.Comment: 5 pages, 4 figure

Multi-Valley Superconductivity In Ion-Gated MoS2 Layers

Layers of transition metal dichalcogenides (TMDs) combine the enhanced effects of correlations associated with the two-dimensional limit with electrostatic control over their phase transitions by means of an electric field. Several semiconducting TMDs, such as MoS$_2$, develop superconductivity (SC) at their surface when doped with an electrostatic field, but the mechanism is still debated. It is often assumed that Cooper pairs reside only in the two electron pockets at the K/K' points of the Brillouin Zone. However, experimental and theoretical results suggest that a multi-valley Fermi surface (FS) is associated with the SC state, involving 6 electron pockets at the Q/Q' points. Here, we perform low-temperature transport measurements in ion-gated MoS$_2$ flakes. We show that a fully multi-valley FS is associated with the SC onset. The Q/Q' valleys fill for doping$\gtrsim2\cdot10^{13}$cm$^{-2}$, and the SC transition does not appear until the Fermi level crosses both spin-orbit split sub-bands Q$_1$ and Q$_2$. The SC state is associated with the FS connectivity and promoted by a Lifshitz transition due to the simultaneous population of multiple electron pockets. This FS topology will serve as a guideline in the quest for new superconductors.Comment: 12 pages, 7 figure

Cluster charge-density-wave glass in hydrogen-intercalated TiSe2_{2}

The topotactic intercalation of transition-metal dichalcogenides with atomic or molecular ions acts as an efficient knob to tune the electronic ground state of the host compound. A representative material in this sense is 1$T$-TiSe$_{2}$, where the electric-field-controlled intercalations of lithium or hydrogen trigger superconductivity coexisting with the charge-density wave phase. Here, we use the nuclear magnetic moments of the intercalants in hydrogen-intercalated 1$T$-TiSe$_{2}$ as local probes for nuclear magnetic resonance experiments. We argue that fluctuating mesoscopic-sized domains nucleate already at temperatures higher than the bulk critical temperature to the charge-density wave phase and display cluster-glass-like dynamics in the MHz range tracked by the $^{1}$H nuclear moments. Additionally, we observe a well-defined independent dynamical process at lower temperatures that we associate with the intrinsic properties of the charge-density wave state. In particular, we ascribe the low-temperature phenomenology to the collective phason-like motion of the charge-density wave being hindered by structural defects and chemical impurities and resulting in a localized oscillating motion.Comment: 9 pages, 4 figure

Strong band-filling-dependence of the scattering lifetime in gated MoS2 nanolayers induced by the opening of intervalley scattering channels

Gated molybdenum disulphide (MoS2) exhibits a rich phase diagram upon increasing electron doping, including a superconducting phase, a polaronic reconstruction of the bandstructure, and structural transitions away from the 2H polytype. The average time between two charge-carrier scattering events - the scattering lifetime - is a key parameter to describe charge transport and obtain physical insight in the behavior of such a complex system. In this work, we combine the solution of the Boltzmann transport equation (based on ab-initio density functional theory calculations of the electronic bandstructure) with the experimental results concerning the charge-carrier mobility, in order to determine the scattering lifetime in gated MoS2 nanolayers as a function of electron doping and temperature. From these dependencies, we assess the major sources of charge-carrier scattering upon increasing band filling, and discover two narrow ranges of electron doping where the scattering lifetime is strongly suppressed. We indentify the opening of additional intervalley scattering channels connecting the simultaneously-filled K/K' and Q/Q' valleys in the Brillouin zone as the source of these reductions, which are triggered by the two Lifshitz transitions induced by the filling of the high-energy Q/Q' valleys upon increasing electron doping.Comment: 10 pages, 6 figure

Possible charge-density-wave signatures in the anomalous resistivity of Li-intercalated multilayer MoS2

We fabricate ion-gated field-effect transistors (iFET) on mechanically exfoliated multilayer MoS$_2$. We encapsulate the flake by Al$_2$O$_3$, leaving the device channel exposed at the edges only. A stable Li$^+$ intercalation in the MoS$_2$ lattice is induced by gating the samples with a Li-based polymeric electrolyte above $\sim$ 330 K and the doping state is fixed by quenching the device to $\sim$ 300 K. This intercalation process induces the emergence of anomalies in the temperature dependence of the sheet resistance and its first derivative, which are typically associated with structural/electronic/magnetic phase transitions. We suggest that these anomalies in the resistivity of MoS$_2$ can be naturally interpreted as the signature of a transition to a charge-density-wave phase induced by lithiation, in accordance with recent theoretical calculations.Comment: 8 pages, 4 figure