Session R25: Superconductivity: Less Common Materials I

Spin triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li0.9Mo6O17

The purple bronze Li0.9Mo6O17 is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four Molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has accidental nodes, i.e. it has more sign changes than required by the point-group symmetry.   

Geometrical structures and electronic properties of Sm, K-doped chrysene

The discovery of superconductivity in potassium-doped picene (KxC22H14) has revitalized the research interest in polycyclic aromatic hydrocarbons (PAHs), and a large variety of PAHs superconductors have been reported afterwards, such as phenanthrene, coronene and 1,2;8, 9-dibenzopentacene. Recently a new PAHs superconductor, Sm-doped chrysene, with Tc ~ 5 K was reported experimentally whose precise nature is still unknown. In this work, crystal structure search and electronic structure of A-doped chrysene, Ax -C18H12 (A=Sm, K), have been studied by the ?rst-principles density-functional theory using the projector augmented wave method based on the generalized gradient approximation implemented in the VASP package. We also include with van der Waals (vdW) corrections in the calculations, thus clarifying the dopant atoms positions and optimized crystal structures of doped superconducting chrysene. Our findings represent a significant step toward the understanding of superconductivity of PAHs.   

Coulomb-induced pairing in a quarter-filled band model for $\kappa$-(BEDT-TTF)$_2$X

$\kappa$-(BEDT-TTF)$_{2}$X is a two dimensional organic charge transfer solid superconductor with a hole density of one half per (BEDT-TTF) molecule. With one hole per dimer of molecules, the material is frequently described using an effective $1/2$-filled band Hubbard model on an anisotropic triangular lattice. Within this effective model a metal to antiferromagnetic (AFM) semiconductor phase transition is found. Calculations beyond the mean field level, however, have shown absence of superconductivity within the model. We present the results of correlated-electron calculations on the $\kappa$-lattice for up to 64 BEDT-TTF molecules using the Constrained Path Monte Carlo (CPMC) and Path Integral Renormalization Group (PIRG) methods over a wide range of carrier density. We show that superconducting pair-pair correlations in this model are enhanced by electron-electron (e-e) interactions for d-wave pairing symmetry uniquely for hole density close to quarter-filling. Our results indicate that this enhancement of superconductivity is not related to the presence of AFM order, but to the strong tendency to spin-singlet formation in the quarter-filled band.   

Quarter-filled systems with frustration: Candidate for correlated electron superconductivity

A necessary condition for superconductivity (SC) driven by electron correlation is that electron electron (e-e) interactions enhance superconducting pair-pair correlations, relative to the non-interacting limit. We present the results of high-precision calculations of superconducting pair-pair correlations on four different frustrated lattices over the complete range of carrier density $0 < \rho < 1$ in each case. We find that pair correlations are enhanced relative to the noninteracting limit only for density $\rho$ equal to or close to $0.5$ ($1/4$ filling). At all other $\rho$ pair correlations are suppressed by interactions. This enhancement is due to the proximity to a spin-gapped paired-electron crystal (PEC) state that occurs at $\rho=0.5$. Our theory explains the pseudogap observed at high temperatures in many organic superconductors. The remarkable bandfilling specificity is an essential ingredient to understanding the mechanism of superconductivity in the two-dimensional organic charge-transfer solids as well as the many different families of other unconventional superconductors that share this bandfilling.   

Quantum critical origin of the superconducting dome and the isotope effect in SrTiO$_3$

We expand the notion that quantum criticality can induce superconductivity, by proposing a concrete mechanism for superconductivity due to quantum ferroelectric fluctuations. To this end, we investigate the origin of superconductivity in doped SrTiO$_3$ (STO) using a combination of density functional and strong coupling theories within the framework of quantum criticality. Our density functional calculations of the ferroelectric soft mode frequency as a function of doping reveal a crossover related to quantum paraelectricity at a doping level coincident with the experimentally observed top of the superconducting dome. Thus, we suggest a model in which the soft mode fluctuations provide the pairing interaction for superconductivity carriers. Within our model, the low doping limit of the superconducting dome is explained by the emergence of the Fermi surface, and the high doping limit by departure from the quantum critical regime. This results in a prediction that the highest critical temperature will increase and shift to lower carrier doping with increasing $^{18}$O isotope substitution, a scenario that is experimentally verifiable. In addition we show a connection between the isotope exponent of superconductivity and the critical exponent pertaining to quantum phase transition.   

Structure and magnetism of oxygen-deficient SrTiO$_3$ surface

Using density functional theory within a fully relaxed spin generalized gradient approximation we have investigated the structural, electronic and magnetic properties of the oxygen-deficient STO surface. We also study the role of the Rashba interaction to explain the observed momentum-spin correlations by spin and angle resolved photoemission spectroscopy.   

Screening of the electron-phonon interaction in STO

Strontium titanate is a bulk insulator that becomes superconducting at remarkably low carrier densities. Even more enigmatic properties become apparent at the strontium titanate/lanthanum aluminate (STO/LAO) interface and it is important to disentangle the effects of reduced dimensionality from the poorly-understood pairing mechanism. Recent experiments\footnote{Z. Wang et al, arXiv:1506.01191} measuring the electronic structure of the analogous strontium titanate surface have found a cross-over as a function of carrier density from a series well-resolved phonon replica bands to a single quasiparticle dispersion, with the crossover occuring at densities that correspond to the disappearance of superconductivity in the STO/LAO system. We interpret these results in a simple analytical model that extends an Engelsberg-Schrieffer theory of electrons coupled to a single longitudinal optic phonon mode to include the effects of electronic screening. As the carrier density increases, the effective dielectric function cuts off the long-range phonon interaction beyond the Thomas-Fermi screening length, eventually leaving only a uniform short-range coupling to the phonon bath. We additionally incorporate the effects of carrier density on the static dielectric properties of the interface.   

A DFT study of electron-phonon mediated superconductivity in doped Mott-Hubbard proxy cubic-tetragonal copper monoxide

We report our preliminary study of electron-phonon mediated Cooper pairing as a component underlying high temperature superconductivity, in the presence of a Hubbard U driven antiferromagnetic ground state, subject to itinerant carrier doping, in the copper oxide perovskites. Our model is based on a proxy CuO fcc cubic-tetragonal structure that contains the basic physics of the electronic structure of copper oxide perovskites readily amenable to numerical analysis. We explore its phase diagram as a function of carrier concentration and coulomb repulsion ranging from the pure Mott-Hubbard AF insulating state to that of a metallic Fermi liquid, focusing on those conditions which might manifest high temperature superconducting behavior. In the Fermi liquid state, we find clear evidence that superconductivity arises from Jahn-Teller instabilities in the CuO bond which guided Bednorz and Mueller on the path to their 1986 discovery.   

The effect of pressure and doping on SrPt$_{\mathrm{3}}$P superconductor: First-principles calculations.

Recently, experiments of resistivity and magnetization on SrPt$_{\mathrm{3}}$P under pressure and doping have been conducted by B. Jawdat et al., (Phys.RevB.91,094514(2015)), it was found that with the increase of pressure, the superconducting transition temperature Tc first increases with the maximal at 0.99 Gpa and then decreases, while the Si doping suppress Tc. In this work, we investigate the electronic and phonon properties of SrPt$_{\mathrm{3}}$P under pressure and partial replacement of P by Si, using first-principles method. When pressure increases from 0 to 0.7 Gpa the electron phonon coupling and Tc increases, the calculated Tc agrees with the experiments. For the doped case, SrPt$_{\mathrm{3}}$P$_{\mathrm{0.5}}$ Si$_{\mathrm{0.5}}$ , an additional hole pocket around M point in Brillouin zone is formed, almost all the phonon modes shifts into lower energy, and the density of states at the Fermi level decreases, which may explains the drop in Tc observed experimentally.   

Real-time study of light-enhanced superconductivity

Resonant pumping of IR-active phonons with lasers enables the ultrafast control of the crystal lattice in solids [1]. It has been shown that transient states with significantly modified electronic properties can be created on picosecond time scales, such as a light-induced state at elevated temperatures with optical properties in close resemblance to those of a superconductor [2]. In our work, we investigate theoretically a situation in which a change of the electronic hopping leads to a modified density of states in real time [3]. This modification, together with electron-phonon coupling, enhances superconductivity if the system is at thermal equilibrium. Our study monitors the out-of-equilibrium time evolution of the electronic momentum distribution and the superconducting order parameter. We show that the condensate dynamics dominates the initial enhancement of superconducting order, and that energy dissipation through electron-phonon scattering helps this enhancement. [1] M. Först et al., Nature Phys. 7, 854 (2011) [2] M. Mitrano et al., arXiv:1505.04529 [3] M. A. Sentef et al., arXiv:1505.07575   

Ising Superconductivity and Majorana Fermions in Transition Metal Dichalcogenides

In monolayer transition metal dichalcogenides (TMDs), electrons in opposite K valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originated from in-plane mirror symmetry breaking, pins the electron spins in out-of-plane directions, and results in the newly discovered Ising superconducting states with strongly enhanced upper critical fields. In this work, we show that the Ising SOC generates equal-spin triplet Cooper pairs with spin polarization in the in-plane directions. Importantly, the spin-triplet Cooper pairs can induce superconducting pairings in a half-metal wire placed on top of the TMD and result in a topological superconductor with Majorana end states. Direct ways to detect equal-spin triplet Cooper pairs and the differences between Ising superconductors and Rashba superconductors are discussed.   

A DMRG Study of MoS$_2$

In a recent work, Hsu, Vaezi, and Kim predicted spatially modulated, topological superconductivity in a class of materials known as transition metal dichalcogenides (TMDs) by studying RG flow.$^1$ Since electrons can readily develop topological superconductivity at low temperatures when spin-degeneracy is lifted, their insight was to exploit the spin-splitting of the TMD valance band in k-space in order to induce p-wave pairing. With experimental efforts currently underway to realize this phenomenon, particularly in monolayer, hole-doped MoS$_2$, it is important to have a non-perturbative check on this result. To this end, we employ a density matrix renormalization group (DMRG) approach to study MoS$_2$. We probe the superconducting susceptibility of the system and explore the properties of its order parameter in order to confirm the predicted FF (Fulde-Ferrell) p$_x$+ip$_y$ phase. A quantitative understanding of the Hamiltonian parameters will provide guidance in experimental efforts to realize this topological superconductor and help ensure that the proposed material will indeed exhibit the expected order. 1.) Y.-T. Hsu, A. Vaezi, E.-A. Kim. Topological modulated superconductivity in monolayer transition metal dichalcogenides, in preparation (2015).   

Superconductivity in quasi-2d organic doped Mott insulators: a superconducting dome without an antiferromagnetic quantum critical point

Layered organic superconductors of the BEDT family are model systems for understanding the interplay of the Mott transition with superconductivity, magnetic order and frustration. Recent experimental studies on a hole-doped compound reveal an enhancement of superconductivity and a rapid crossover between two different conducting phases above the superconducting dome. Using plaquette cellular dynamical mean field theory with state of the art continuous-time quantum Monte Carlo calculations, we study this problem with the two-dimensional Hubbard model on the anisotropic triangular lattice. Phase diagrams are in broad agreement with experiment. As in the case of the cuprates, we find, at finite doping in the unstable normal state, a first-order transition between a pseudogap and a correlated metal. We make several experimental predictions. This work also clearly shows that the superconducting dome in organic superconductors is tied to the Mott transition and its continuation as a transition separating pseudogap phase from correlated metal in doped compounds, as in the cuprates. Contrary to heavy fermions for example, the maximum $T_c$ is definitely not attached to an antiferromagnetic quantum critical point. That can also be verified experimentally.   

\textbf{On the equilibrium of a extremely extended and diluted magneto-matter state subject to its weight. }

Solutions to the force relationship between the magnetic stresses and the self-gravitational force are discussed for a simple homogeneous distribution of matter coalescent to a magnetic field in a cylindrical geometry. Consideration are given to the needed permeability of the medium to make it capable of supporting many times the mass of the Sun, on an extension of several parsecs to kiloparsec. This state of self organization of matter and magnetic field (magneto-matter state) has proven useful interpretation for the explanation of anomalous thermodynamic of the gas of electrons contained in flux-tubes with a twist, low-beta, often observed at 1 AU in the interplanetary medium, Berdichevsky and Shefers, 2015. This state of matter, which most basic property, the freezing in the magnetic field, see e.g., Chew et al, 1956, has proved to exist in the regions where robotic observations in the near and far space perform detailed observations of magnetic fields, and extreme dilute plasma (commonly about 1000 to 0.1 or less ionized particles per cubic cm). This work is in many ways an extension of Alfven work on magnetized space plasmas, Alven, 1942. Berdichevsky, D.B., and K., Schefers, ApJ, 803, 70, 2015, doi: 10.1088/0004-637X/805/1/70 Chew, G.F., M.L., Goldberger, and F.E. Low, 1956, the Royal Soc. London, section Math \textbraceleft $\backslash ${\&}\textbraceright Phys Sc., 236, pp. 112. Alfv$\backslash $'\textbraceleft e\textbraceright n, H (1942). ``Existence of electromagnetic-hydrodynamic waves.'' $\backslash $textit\textbraceleft Nature\textbraceright $\backslash $textbf\textbraceleft 150\textbraceright : 405.. $\backslash $underline \textbraceleft doi\textbraceright :$\backslash $underline \textbraceleft 10.1038/150405d0\textbraceright