Session W21: Focus Session: Search for New Superconductors- Electron-Phonon Coupling

Correlation-enhanced electron-phonon coupling produces high-temperature superconductors

The microscopic origin of superconductivity has been established in numerous classes of materials. In elemental metals it results from the exchange of phonons whereas in copper oxides and iron pnictides it is intimately connected to magnetism. On the other hand, the cause of superconductivity in a large third class of isotropic high temperature superconductors is still mysterious and subject of debate. In this talk, we will demonstrate that dynamical correlations among electrons enhance their coupling to phonons in a large number of superconductors, raising significantly the previously underestimated theoretical superconducting critical temperature T$_c$ of up to a few Kelvin to their experimental values of tens of Kelvin. The mechanism we propose is quite general, explains the magnitude and the doping dependence of superconductivity in many materials such as the celebrated Ba$_{1-x}$K$_x$BiO$_3$ ($T_C$=32 K) compounds and the electron-doped $\beta$-HfNCl compounds ($T_c$ = 25.5 K) and can be used to design other high temperature superconductors which have not yet been synthesized. We will also propose a few novel materials which are good superconductors in our theory and can be easily synthesized and tested by experiments.   

Spectral properties of correlated systems with electron-phonon coupling

Results from a variety of experiments, including single particle probes such as ARPES and STM, and multi-particle spectroscopies such as optical and Raman responses, have revealed the importance of the electron-phonon interaction in strongly correlated electron materials. We present a determinant quantum Monte Carlo study of the single-band Hubbard-Holstein model, which treats electron-electron and electron-phonon interactions on an equal footing. We focus on the behavior of the single- and multi-particle dynamical properties of the model, such as the spectral function and optical conductivity, as a function of electron-phonon coupling and Hubbard U.   

Vibrational spectrum and electron-phonon coupling of doped solid picene from first principles

The search for new intercalated hydrocarbon superconductors was initiated by the report of a superconducting critical temperature ($T_c$) of 18 K in K- and Rb- doped picene (C$_{22}$H$_{14}$), followed by phenanthrene, coronene and di-benz-picene (27 K). These compounds, formed by justappoxed benzene rings, bear a strong resemblance both to fullerenes and intercalated graphites. Using first-principles linear response calculations have performed calculations of the phonon spectrum and electron-phonon (ep) interaction, we have shown that the coupling of the high-energy C bond-stretching phonons to the $\pi$ molecular orbitals for a doping of ~3 electrons per picene molecule is sufficiently strong to reproduce the experimental Tc of 18 K within Migdal-Eliashberg theory. For hole doping, we predicted a similar coupling leading to a maximum Tc of 6 K. However, we argue that, due to its molecular nature, picene may belong to the same class of strongly correlated $ep$ superconductors as fullerides [1]. Our results are in agreement with estimates based on molecular orbital models;we also discuss possible reasons and implications of the discrepancy with linear response calculations that include explicitely the dopant.   

Strong Correlation Physics in Aromatic Hydrocarbon Superconductors

We show, by means of ab-initio calculations, that electron-electron correlations play an important role in doped aromatic hydrocarbon superconductors, including potassium doped picene with $T_c = 18K$ [1], coronene and phenanthrene [2]. For the case of picene the inclusion of exchange interactions by means of hybrid functionals reproduces the correct gap for the undoped compound and predicts an antiferromagnetic state for $x=3$, where superconductivity has been observed [3]. The latter finding is compatible with a sizable value of the correlation strength. The differences between the different compounds are analyzed and results of Dynamical Mean-Field Theory including both correlation effects and electron-phonon interactions are presented. Finally we discuss the consequences of strong correlations in an organic superconductor in relation to the properties of Cs$_3$C$_{60}$, in which electron correlations drive an antiferromagnetic state [4] but also lead to an enhancement of superconductivity [5]. \\ 1. R. Mitsuhashi et al. Nature 464, 76 (2010)\\ 2. X.F. Wang et al, Nat. Comm. 2, 507 (2011)\\ 3. G. Giovannetti and M. Capone, Phys. Rev. B 83, 134508 (2011)\\ 4. Y. Takabayashi et al., Science 323, 1585 (2009)\\ 5. M. Capone et al. Rev. Mod. Phys. 81, 943 (2009   

Transport Anomalies and Possible High Tc Superconductivity in interconnected multiwall carbon nanotube sheets doped by ion implantation

Ion implantation offers an alternative doping method. In searching for superconductivity,we describe here the ion-implantation doping of MWCNT interconnected networks by boron and other dopants (phosphorous, sulfur, arsenic) and report transport anomalies in oriented networks of ion implanted MWCNT sheets as compared to cross coated (non-oriented multilayer MWCNT sheets). The strong drop of resistance R(T) with temperature decrease starting at T$_{c1}$= 50-60 K and even at higher T is reminiscent of inhomogeneous superconducting islands appearing in the non-SC matrix. An unusual anomaly of the 4-terminal resistance is observed in many samples, R(T) becoming negative at lower T$<$ T$_{c2} \quad \sim $ 10-20 K, This negative resistance is found to be associated with unusual I-V curves with s-shape at low T $<$ Tc2 and R(T) shows nonlinear dependence on excitation current and other features that are studied carefully in MWCNTs with different lengths and densities. This negative-resistance behavior gives a hint for the possible incorporation of superconducting areas and can be explained in terms of an imbalanced resistance bridge.   

Large Magnetoresistance and low temperature Transport anomalies in Ion implanted HOPG

Strong positive magnetoresistance (MR) was found in highly oriented pyrolytic graphite (HOPG) upon ion implantation by boron and phosphorous. Similar effects, but with smaller amplitude, are induced by carbon ion implantation, but due to structural disorder and defect formation without carrier concentration increase. The magnetic field dependence of the MR is linear at high fields with no sign of saturation, but different contact geometries result in a wide range of parameters. Two possible explanations of strong MR are suggested and analyzed. While the MR remains large at all temperatures, plots of R(T) in constant field show a drop at lower T. Future experiments will clarify the origin of the R(T) drop, in particular, whether this might be interpreted as the onset of inhomogeneous superconductivity, as proposed in some previous work, or could be explained in the context of strong linear MR effects seen in high-mobility, disordered materials.   

Quantiative reliability of the Migdal-Eliashberg theory for strong coupling superconductors

The Migdal-Eliashberg (ME) theory for strong electron-phonon coupling and retardation effects of the Morel-Anderson type form the basis for the quantitative understanding of conventional superconductors. The validity of the ME theory for values of the electron-phonon coupling strength $\lambda>1$ has been questioned by model studies. By distinguishing bare and effective parameters, and by comparing the ME theory with the dynamical mean field theory (DMFT), we clarify the range of applicability of the ME theory. Specifically, we show that ME theory is very accurate as long as the product of effective parameters, $\lambda \omega_{\rm ph}/D$, where $\omega_{\rm ph}$ is an appropriate phonon scale and $D$ an electronic scale, is small enough [1]. The effectiveness of retardation effects is usually considered based on the lowest order diagram in the perturbation theory. We analyze these effects to higher order and find modifications to the usual result for the Coulomb pseudo-potential $\mu^*$. Retardation effects are weakened due to a reduced effective bandwidth. Comparison with the non-perturbative DMFT corroborates our findings~[2]. \\[4pt] [1] J Bauer, J E Han, and O Gunnarsson, Phys. Rev. B. 84, 184531 (2011).\\[0pt] [2] J Bauer, J E Han, and O Gunnarsson, in preparation (2011).   

Influence of Surface Termination of Boron-Doped Diamond on Superconducting Property

In 2004, a heavily boron-doped diamond was found to be a superconductor Since then, a superconducting diamond has attracted considerable attention, mainly explored for fundamental properties and a theoretical basis. Meanwhile, it is known that the surface of diamond is easily modified by a chemical treatment, and the physical properties, such as surface conductivity, could be modulated through the surface modification. Here, we report modulation of superconducting properties of a heavily boron-doped diamond by tuning the surface electronic state. A heavily boron-doped diamond was prepared onto a silicon wafer substrate by a microwave plasma-assisted chemical vapor deposition method. The surface of a boron-doped diamond was changed between hydrogen- and oxygen-termination by thermal and electrochemical reactions, respectively. As a result, the critical current and the diamagnetic magnetization value could be modulated in a reversible manner between the hydrogen- and oxygen-terminated diamonds with maintenance of the superconducting transition temperature. It is assumed that the carrier density at grain boundaries would change due to the induced dipole moment via surface modification, resulting in modulation of the magnetic flux pinning effect at grain boundaries.   

Energy landscape of fullerene materials: A comparion of boron to boron nitride and carbon

After the discovery of the C60 fullerene some 25 years ago, many more hollow and endohedrally doped structures made out of various elements have been proposed theoretically. However, since no other fullerenes have been synthesized up to date, the question arises whether experimentalists have just not yet found a way to synthesize these theoretically predicted fullerenes, or whether they do not exist at all in nature. Following the theoretical discovery of the $B_{80}$ fullerene by Szwacki et al, various other fullereneand stuffed fullerene structures were proposed but none of them could be synthesized in the laboratory yet. Using the minima hopping global geometry optimization method on the density functional potential energy surface we show that the energy landscape of boron clusters is glass like. Medium size boron clusters exhibit many structures which are lower in energy than the cages. This is in contrast to carbon and boron nitride systems which can be clearly identified as structure seekers. The differences in the potential energy landscape explain why carbon and boron nitride systems are found in nature whereas pure boron fullerenes have not been found. We thus present a methodology which can make predictions on the feasibility of the synthesis of new nano structures.   

Light element ternary compounds -- searching for new superconductors in the ``upper left corner''

We propose here a new class of ternary compounds, composed entirely of light elements drawn from the upper left corner of the Periodic Table, as a new family of superconductors with the promise of high transition temperatures ($T_c$). In this explorative computational study, we have investigated stoichiometric 1:1:1 compounds of lithium, beryllium, and boron. We find layered metallic phases that are thermodynamically stable at P=1 atm, with still others stabilized at relatively low pressures and hence in principle accessible to synthesis and experimental characterization. At high pressures, close packed structures are again stabilized and a metal-to-insulator transition is predicted. Superconducting transition temperatures for the most structurally attractive metallic phases are estimated using BCS theory. An outlook on other stoichiometries, as well as the incorporation of different constituents, Mg instead of Be in particular, is given.   

Progress on Determining the alpha-beta Phase Boundary of Elemental Boron

Recently, it was reported that the phase boundary between alpha-boron and beta-boron has been directly determined using high-pressure and temperature experiments down to P$\sim $4GPa and T$\sim $1400K [Scientific Reports 1, \textbf{96} (2011)]. Based on linear extrapolation of their results to lower pressure and temperature, these authors proposed that at P=0GPa alpha-boron is the stable form below about T$\sim $933(20)K, in conflict with the recent theoretical works based on DFT total energy calculations [JACS \textbf{129}, 2458 (2007); PRB \textbf{77}, 064113 (2008); JACS \textbf{131}, 1903 (2009) ], where it was concluded that beta-boron is the most stable at all temperature below melting temperature and down to zero Kelvin. At the talk, we show that the theoretical alpha-beta boundary obtained with a few approximations agrees well with the aforementioned experimental results within the error bars except for the lowest $P, T$ point, and in this case, the ground state is still beta-boron [submitted]. We will also discuss on the recent experimental efforts in measuring the specific heat of boron allotropes that lead to a tentative conclusion supporting the aforementioned DFT results.   

Calculation of electron-phonon coupling in Arsenic under pressure

Elemental As undergoes a structural transformation from a rhombohedral A7 phase to a simple cubic (sc) phase at around 25 GPa as pressure is increased. At pressures near this phase transformation, As is superconducting, with a maximum superconducting transition temperature $T_c$ of about 2.5 $K$. Experiments indicate that this maximum $T_c$ occurs at the transition pressure for structural transformation, and the increase in $T_c$ as the transition pressure is approached has been attributed to phonon softening. In this work, we calculate from first principles the electronic structure, phonon dispersions, and electron-phonon coupling constant $\lambda$ for As in the A7 and sc phases at various pressures near the A7 to sc transition. Using these detailed quantitative calculations, we explain the trends in $T_c$ as function of pressure in terms of phonon softening, electronic density of states, and electron-phonon matrix elements. We discuss the implications of these results for finding new superconducting materials.   

Physical properties of heavily boron doped silicon

The discovery of superconductivity (SC) in heavily boron doped silicon in 2006 by [1] occurred shortly after diamond in 2004 by [2]. However, the SC in these 2 materials occurs differently. For diamond, the SC is obtained for a boron concentration close to the metal-insulator transition (MIT), while for silicon, the onset of superconductivity is obtained well above the MIT threshold. The aim of this study is to determine the influence of different parameters that impact the SC, such as the doping concentration nB, or the thickness of the layer. Interpolation between resistivity measurements of Tc(nB) and ab initio calculations of the electron phonon coupling $\lambda $(nB) showed a complete mismatch of the dependency of $\lambda $(Tc) with the BSC MacMillan exponential law. The results obtained suggest rather a power law dependence such as $\lambda $ $\alpha $ Tc$^{2}$. This dependency suggests a fractal dimension of the superconducting wave function as reported by Feigel'man et al. [3]. \\[4pt] [1] E. Bustarret \textit{et al}., Nature (London) 444, 465 (2006).\\[0pt] [2] E. Ekimov \textit{et al.} (2004).\textit{ Nature} \textbf{428}: 542\\[0pt] [3] Feigel'man et al., arXiv:1002.0859   

Eliashberg-McMillan Parameters of Polysulfur Nitride, (SN)$_{x}$

Thirty-seven years following the discovery of superconductivity in polysulfur nitride, (SN)$_{x}$ remains the lone conducting polymer exhibiting this phenomenon. The transition temperature is only 0.3 -- 0.4 K, and details of its origin remain largely unknown, although it very likely arises from conventional phonon-mediated BCS pairing of normal state carriers. In pursuit of such a possible mechanism, we have performed density functional theory (DFT) investigations of the phonon and electron-phonon dispersion relationships in (SN)$_{x}$, and will present values for the coupling strength of the latter along with an estimate of T$_{C}$.   

Probing electronic order via coupling to phonons in Bi2Sr2CuO6 (Bi2201)

Recent work on several members of the cuprate family of high-temperature superconductors has revealed the occurrence of broken lattice translational, rotational, and time reversal symmetries in various materials at low temperatures. We report on measurements of acoustic phonons on Bi$_2$(La,Sr)$_2$CuO$_{6+\delta}$, which reveal a coupling to an underlying electronic density-wave state. Longitudinal acoustic phonons are found to be anomalously broadened at a wavevector of q $\approx$ 1/4 rlu along the Cu-O direction. At low temperatures a disparity between the scattered intensity at positive and negative energy transfer is seen. These measurements indicates a breaking of time reversal and inversion symmetry in the bulk.