Session C22: Electrons, Phonons, and Electron-Phonon Scattering II

Controlling electron-phonon scattering with metamaterial plasmonic structures

Electron-plasmon scattering can be faster than electron-phonon scattering. While in metals plasmons occur in the UV range, phonons dominate behavior at much lower frequencies (far IR range), and this typically decouples these phenomena. In metamaterial plasmonic structures, however, plasma effects can be tuned down to the far IR range, allowing for their interference with phonons. It was recently shown, that such interference can protect hot electron energy induced in a solar cell, from dissipation into heat [1]. In this work we explore the possibility of using such an effect to control the electron-phonon interaction and transport in semiconductors. We demonstrate, that this could lead to a novel path to enhancing the electrical and thermal conductivities and the thermoelectric figure of merit. [1] Hot electron plasmon-protected solar cell, J. Kong, A.H. Rose, C. Yang, J. M. Merlo, M.J. Burns, M. Naughton, and K. Kempa, Opt. Express 23, A1087-A1095 (2015) doi:10.1364/OE.23.0A1087   

Temperature-dependence of electron bands in wurtzite GaN, including non-adiabatic (Polaron) contributions

We study the temperature dependence of the band gap of wurtzite structure GaN [1]. Virtual interband electron-phonon scattering is accounted properly by adiabatic (Allen-Heine-Cardona) theory. The correct way to avoid an unphysical divergence, is to use a non-adiabatic treatment for intraband scattering by small $q$ polar optical phonons [2,3]. This is equivalent to including Fr\"ohlich polaron effects. The $T=0$ zero-point weak-coupling polaron shift ($-\alpha\hbar\omega$) is well known, but finite $T$ effects are less studied. We also calculate the $T$ dependence of the band mass (both polaron and adiabatic contributions). We compare results from an {\it ab-initio} density-functional approach with those obtained starting from the traditional Fr\"ohlich Hamiltonian approach. [1] M. Cardona and … Kremer, Thin Solid Films {\bf 571}, 680 (2014). [2] S. Ponc\'e {\it et al.}, The Journal of Chemical Physics {\bf 143}, 102813 (2015) [3] C. Verdi and F. Giustino, Phys. Rev. Lett. {\bf 115}, 176401 (2015)   

Anti-ferromagnetism enables electron-phonon coupling in iron-based superconductors

We show that a generic form of an anti-ferromagnetic wavefunction opens strong electron-phonon coupling channels in the iron-based superconductors. In the non-magnetic state these channels exist locally on a single iron atom, but are cancelled out between two iron atoms in the primitive unit cell. Our findings are mostly based on symmetry and are relevant for any iron-based superconductor. This work was supported by NSF Grant No. DMR15-1508412 and the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Computational resources have been provided by the DOE at Lawrence Berkeley National Laboratory's NERSC facility.   

Acoustic Faraday rotation in Weyl semimetals

We investigate the phonon problems in Weyl semimetals, from which both the phonon Berry curvature and the phonon Damping could be obtained. We show that even without a magnetic field, the degenerate transverse acoustic modes could also be split due to the adiabatic curvature. In three dimensional case, acoustic Faraday rotation shows up. And furthermore, since the attenuation procedure could distinguish the polarized mode, single circularly polarized acoustic wave could be realized. We study the mechanism in the novel time reversal symmetry broken Weyl semimetal. New effects rise because of the linear dispersion, which give enlightenment in the measurement of this new kind of three-dimensional material.   

Strong enhancement of $s$-wave superconductivity near a quantum critical point of (Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Ir$_{4}$\-Sn$_{13}$ and (Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Rh$_{4}$\-Sn$_{13}$

We report microscopic studies by muon spin rotation as a function of pressure of the ~(Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Ir$_{4}$\-Sn$_{13}$ and (Ca$_{1-x}$Sr$_{x}$)$_{3}$\-Rh$_{4}$\-Sn$_{13}$ cubic compounds, which display superconductivity and a structural phase transition associated with the formation of a charge density wave (CDW)[1]. In Ca$_{3}$\-Ir$_{4}$\-Sn$_{13}$ we find a strong enhancement of the superfluid density and a dramatic increase of the pairing strength above a pressure of $\approx 1.6 $ GPa giving direct evidence of the presence of a quantum critical point separating a superconducting phase coexisting with CDW from a pure superconducting phase [2]. The superconducting order parameter in both phases has the same $s$-wave symmetry. Similar behavior is found in the other family. In spite of the conventional phonon-mediated BCS character of these weakly correlated 3-4-13 systems, the dependence of the effective superfluid density on the critical temperature put these compounds in the ``Uemura'' plot close to unconventional superconductors. These systems exemplify that conventional BCS superconductors can also display characteristics of unconventional superconductors. [1] S.K. Goh et al. Phys. Rev. Lett. 114, 097002 (2015). [2] P.K. Biswas et al., Phys. Rev. B (2015).   

Ambient Pressure Structural Quantum Critical Point in the Phase Diagram of (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$

The quasiskutterudite superconductor Sr$_3$Rh$_4$Sn$_{13}$ features a pronounced anomaly in electrical resistivity at $T^*\sim$ 138 K. The anomaly is caused by a second-order structural transition, which can be tuned to 0 K by applying physical pressure and chemical pressure via the substitution of Ca for Sr. A broad superconducting dome is centered around the structural quantum critical point. Detailed analysis of the tuning parameter dependence of $T^*$ as well as insights from lattice dynamics calculations strongly support the existence of a structural quantum critical point at ambient pressure when the fraction of Ca is 0.9 ($x_c$=0.9). This establishes the (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ series as an important system for exploring the physics of structural quantum criticality and its interplay with the superconductivity, without the need of applying high pressures. Refs: Swee K. Goh {\it et al.}, Phys. Rev. Lett. {\bf 114}, 097002 (2015); Wing Chi Yu {\it et al.}, Phys. Rev. Lett. (in press, 2015)   

Pressure-enhanced superconductivity in A15-type Nb3Ge via increased Fermi surface nesting

The A15-type superconductors are the most widely used superconductors in industrial applications yet the physics behind maximizing the superconducting transition temperature is still not completely understood. The highest transition temperatures found to date have recently been reported for high-pressure hydride materials and it is believed that they too are BCS-type phonon-mediated superconductors, just like the A15-type superconductors. Understanding the electron-phonon coupling has therefore been brought front stage in the search to understand the mechanisms for optimizing high-temperature superconductors. Using a multi-faceted suite of high-pressure techniques we found that Nb3Ge has an isostructural phase transition at high pressure that correlates directly with a bandstructure change seen in high-pressure magnetotransport measurements. Our results suggest that A15-type superconductivity is not only phonon-mediated but that the degree of Fermi surface nesting is a controlling parameter for maximizing the superconducting transition temperature.   

Strong Coupling Superconductivity in the Vicinity of the Structural Quantum Critical Point in (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$

The family of the superconducting quasiskutterudites (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$ features a structural quantum critical point at $x_c=0.9$, around which a dome-shaped variation of the superconducting transition temperature $T_c$ is found. In this talk, we present the specific heat data for the normal and the superconducting states of the entire series straddling the quantum critical point. Our analysis indicates a significant lowering of the effective Debye temperature on approaching $x_c$, which we interpret as a result of phonon softening accompanying the structural instability. Furthermore, a remarkably large enhancement of $2\Delta/k_BT_c$ and $\Delta C/\gamma T_c$ beyond the Bardeen-Cooper-Schrieffer values is found in the vicinity of the structural quantum critical point. Reference: Wing Chi Yu et al. Phys. Rev. Lett. (in press, 2015)   

Investigation of the superconducting and normal state properties of the filled-skutterudite system PrPt$_{\mathrm{4}}$Ge$_{\mathrm{12}}$ via chemical substitution.

We report a systematic chemical substitution study on the unconventional superconductor system PrPt$_{\mathrm{4}}$Ge$_{\mathrm{12}}$, which Sb ions are substituted for Ge. Polycrystalline samples of PrPt$_{\mathrm{4}}$Ge$_{\mathrm{12-}}_{x}$Sb$_{x}$ up to $x=$ 5 were synthesized and investigated by means of x-ray diffraction, electrical resistivity, magnetic susceptibility, and specific heat measurements. We observed a suppression of superconductivity with increasing Sb substitutions and evidence for a weak ``rattling'' mode associated with the Pr ions, characterized by a value of $\Theta_{\mathrm{E}} \sim$ 60 K. As part of a systematic study of the effect of various elemental substitutions on the properties of PrPt$_{\mathrm{4}}$Ge$_{\mathrm{12}}$, measurements of the superconducting and normal state properties of the Pr$_{1-x}$Eu$_x$Pt$_4$Ge$_{12}$ system are currently being performed. This work was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Grant No. DE-FG02-04-ER46105 (characterization and physical properties measurements), and the National Science Foundation under Grant No. DMR 1206553 (low-temperature measurements).   

First principles study of the electron-phonon coupling on the light-actinides Ac-Th alloy: effect of spin-orbit coupling

We have studied the electronic, lattice dynamics, and electron-phonon (e-ph) properties of the Ac$_{1-x}$Th$_x$ actinide alloy. This system have been studied within the framework of density functional perturbation theory, using a mixed-basis pseudopotential method and the virtual crystal approximation (VCA) for modeling the alloy. The electronic density of states (DOS), the full-phonon dispersion as well as the Eliashberg spectral function ($\alpha^2F(\omega)$) and the electron-phonon coupling ($\lambda$) parameter have been calculated with and without the inclusion of spin-orbit coupling (SOC). For Ac the observed effects of SOC on $\alpha^2F(\omega)$ are very minor. However, as Th-content increases on the alloy the SOC influence is more important. Such evolution has its roots on a continuous increase of density of states at the Fermi level ($N(E_F)$) difference between schemes, as well as a steady hardening of the SOC full phonon dispersion. The evolution of $\lambda$ as a function of Th-content for both schemes is presented and discussed on the light of SOC effects on the electronic and vibrational properties.   

Truncated phase-space approach to polaron response

A method is presented to obtain the linear response coefficients of a system coupled to a bath. The method is based on a systematic truncation of the Liouville equation for the reduced distribution function in the Weyl representation. Explicit expressions for the conductivity of the Fröhlich polaron are obtained, and the discrepancy between the Kadanoff and the Feynman-Hellwarth-Iddings-Platzman mobility is elucidated. We argue why both approaches require a correction. Finally, we show how due to the system-bath coupling, the external perturbation induces a retarded internal field which dynamically screens the external force. Whereas the effect on the dc-mobility is of second order, dynamical properties such as the effective mass and the optical absorption are modified in first order.   

First-Principles Calculation of forces and phonons in solid

We have developed a multiple scattering theory approach to calculate Hellmann-Feynman forces and phonons via the calculation of the force constant and dynamical matrix. To demonstrate the accuracy and validity of our approach we compare with the ELK code, which is a full potential Linear Augmented Plane Wave (FLAPW) based method. As we will show our forces and phonon dispersion curves are in good agreement with the FLAPW code. This work lays the foundation for developing a first principles approach for calculation of phonons in substitutionally disordered materials.   

Phonon and magnon dispersions of incommensurate spin ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$

There are a variety of compounds consisting of two or more interpenetrating sublattices with lattice periods incommensurate at least along one crystal axis. One example is spin ladder compound Sr$_{14}$Cu$_{24}$O$_{41}$ consisting of incommensurate spin ladder and spin chain sublattices. It has been predicted that unique phonon modes occur in these compounds due to the relative motion of the sublattices. In the low-wavelength limit, there is only one longitudinal acoustic mode due to the rigid translation of both sublattices. In addition, one extra pseudo-acoustic mode is present due to relative sliding motions of the two sublattices. Although the theoretical aspects of the lattice dynamics of incommensurate compounds have been studied, there have been few experimental investigations on their phonon dynamics. In this work, single crystals of Sr$_{14}$Cu$_{24}$O$_{41\, }$are grown by the traveling solvent floating zone method. The phonon dispersion of Sr$_{14}$Cu$_{24}$O$_{41}$ is studied through inelastic neutron scattering measurements in order to better understand its phonon dynamics. In addition, its magnon dispersion$_{\, }$is investigated and correlated to the large directional magnon thermal conductivity. The measurements reveal a wealth of intriguing features on phonons and magnons in the spin ladder compound.   

High Temperature Superconductivity at High Pressures for H3SixP(1-x), H3PxS(1-x) and H3ClxS(1-x)

Recent experimental and computational works have established the occurrence of superconducting temperatures,Tc, around 200K at corresponding 200GPa pressures in hydrogen-based sulfur compounds. In this work we have investigated the effects of phosphorus and chlorine substitutions of sulfur on Tc, as well as the effect of hydrogen vacancies. In addition, we have explored the superconductivity-relevant parameters in the H3SixP(1-x) system. In executing this work we have used the virtual-crystal-approximation and performed a systematic set of LAPW calculations for many different concentrations of the sulfur component. From the densities of states and the scattering phase-shifts at the Fermi level, we calculated electron-ion matrix elements and estimated the electron-phonon coupling constants for different concentrations as well as Tc. We find that the high values of Tc correlate with the position of the Fermi level with respect to peaks(van Hove singularities) in the density of electronic states of these materials.   

Effect of van Hove singularities on high-Tc superconductivity in H3S

One of interesting open questions for the high-Tc superconductivity in sulfur hydrides is why some of the H3S phases under high pressures are so special. Recently, it has been pointed out that the presence of the van Hove singularities (vHs) around the Fermi level is crucial. Interestingly, such vHs are always absent in H2S, for which Tc is estimated to be much lower. Although there have been quantitative calculations of Tc based on the Migdal-Eliashberg theory, the effect of the vHs on the superconductivity is yet to be fully understood. This is because the energy dependence of the density of states (DOS) has been neglected to simplify the Eliashberg equation. In this study, we perform a calculation beyond the constant DOS approximation. In contrast with the conventional calculations, this approach with a sufficiently large number of Matsubara frequencies enables us to calculate Tc self-consistently without introducing the empirical pseudo Coulomb potential. We show that the constant DOS approximation seriously overestimates (underestimates) Tc by \textasciitilde 60 K (\textasciitilde 10 K) for H3S (H2S). We then consider the effect of the anharmonicity of the phonon and the energy shift due to the zero-point motion. Eventually, Tc is estimated to be 180 K for H3S and 35 K for H2S, which successfully explains the pressure dependence of Tc observed in the experiment.