Session K8: Electrons, Phonons, and Electron Phonon Scattering III

First-principles calculations of mobility

First-principles calculations can be a powerful predictive tool for studying, modeling and understanding the fundamental scattering mechanisms impacting carrier transport in materials. In the past, calculations have provided important qualitative insights, but numerical accuracy has been limited due to computational challenges. In this talk, we will discuss some of the challenges involved in calculating electron-phonon scattering and carrier mobility, and outline approaches to overcome them. Topics will include the limitations of models for electron-phonon interaction, the importance of grid sampling, and the use of Gaussian smearing to replace energy-conserving delta functions. Using prototypical examples of oxides that are of technological importance---SrTiO$_{\mathrm{3}}$ [1], BaSnO$_{\mathrm{3}}$ [2], Ga$_{\mathrm{2}}$O$_{\mathrm{3}}$, and WO$_{\mathrm{3}}$---we will demonstrate computational approaches to overcome these challenges and improve the accuracy. One approach that leads to a distinct improvement in the accuracy is the use of analytic functions for the band dispersion, which allows for an exact solution of the energy-conserving delta function. For select cases, we also discuss direct quantitative comparisons with experimental results. The computational approaches and methodologies discussed in the talk are general and applicable to other materials, and greatly improve the numerical accuracy of the calculated transport properties, such as carrier mobility, conductivity and Seebeck coefficient. This work was performed in collaboration with B. Himmetoglu, Y. Kang, W. Wang, A. Janotti and C. G. Van de Walle, and supported by the LEAST Center, the ONR EXEDE MURI, and NSF. [1] B. Himmetoglu, A. Janotti, H. Peelaers, A. Alkauskas, and C.G. Van de Walle, \textit{Phys. Rev. B} \textbf{90}, 241204 (2014). [2] K. Krishnaswamy, B. Himmetoglu, Y. Kang, A. Janotti, C. G. Van de Walle, \textit{eprint arXiv}:1610.06253 (2016).   

Conditions for $T^{2}$ resistivity from electron-electron scattering

Many complex oxides (including titanates, nickelates and cuprates) exhibit a carrier scattering mechanism with a power law dependence on temperature (resistivity $\rho \propto T^{2})$. By analogy to a similar phenomenon observed in metals at low temperature, this mechanism has often been identified as Fermi-liquid-like electron-electron scattering (Baber scattering). However, other transport signatures in these materials have shown behavior that casts doubt on this simple picture. Careful investigation of electron-electron scattering (both direct and phonon-mediated) reveals that the Baber $T^{2}$ power law rests on several crucial assumptions. In some cases, these assumptions are not satisfied and removing them destroys the power law. We illustrate these issues with two case studies: sodium metal (in which electron-electron scattering gives $T^{2}$ resistivity) and strontium titanate (in which it does not). Our results suggest that an observation of $\rho \propto T^{2}$ is not sufficient evidence for electron-electron scattering. The power law observed in the complex oxides may instead be due to another, as yet undiscovered, mechanism.   

Using sub-Kelvin thermal transport to determine electron-phonon coupling in a metallic thin film

Steady-state thermal transport was measured in a thin film of the alloy Ti$_{0.1}$W$_{0.9}$ for temperatures ranging from approximately 100 mK to 500 mK. The electron temperature was measured using two normal metal-insulator-superconductor (NIS) junction thermometers. The temperature of the normal metal electrons was measured while changing the power applied to the normal metal thin film. The data were compared to the theoretically expected relationship, $P_{ep} = \Sigma\Omega(T_e^n-T_p^n)$, where $\Sigma$ depends on the electron-phonon coupling, and $n$ is effected by the electron mean-free path and the thermal phonon wavevector.   

Temperature-dependence of the forbidden (222) reflection in silicon

Crystals with an $fcc$ lattice like silicon have Bragg scattering at $\mathbf{K}=2\pi(h,k,l)/a$ for integers $hkl$ all even or all odd. The two-atom basis of the diamond structure causes destructive interference whenever $h+k+l$ is an odd multiple of 2; for example, the (222) reflection is nominally forbidden. However, there is not total interference because of tetrahedral rather than spherical scattering symmetry. Such asymmetry arises from anharmonic vibrations and from bonding. Therefore, the weakly allowed (222) X-ray reflection in silicon is useful for studying bond charge. Temperature variation of the (222) X-ray intensity, beyond that expected from anharmonicity, has been measured [1] and studied [1,2]. Previous theories have been somewhat ad hoc, not dealing fully with electron-phonon induced valence charge density thermal shifts. Our formulation of this shift uses full second-order electron-phonon perturbation theory. We include both Fan and Debye-Waller type terms, known to determine band gap thermal shifts. We compare with experiment and with previous theories. [1] J. B. Roberto, B. W. Batterman, and D. T. Keating, Phys. Rev. B $\mathbf{9}$, 2590 (1974). [2] J. R. Chelikowsky and M. L. Cohen, Phys. Rev. Lett. $\mathbf{33}$, 1339 (1974).   

Charge and energy transport at the nanoscale: A DFT perspective

Understanding the interplay between charge and energy transport at the nanoscale paves the way for novel thermoelectric devices, which may prove useful for the development for sustainable energy sources. However, concepts, such as heat flow, temperature and entropy are only well-established at the macroscopic level for slow dynamics. This raises the question about whether these concepts can be employed for small length and short time scales. We will present our recent efforts to use a time-dependent density-functional theory framework, dubbed thermal DFT, in order to generalize temperature and heat or energy flow to the microscopic regime. To this end we will highlight the analogy of the formally exact microscopic equations of motion for charge density and energy density in thermal DFT to the macroscopic equations of motion of hydrodynamics. Furthermore, we will present first result using our approach to compute transient energy energy currents induced by a temperature gradient and show that in the steady-state limit persistent temperature oscillations develop.   

Band gap renormalization and temperature dependence of acene crystals: the case of naphthalene

The band gap is one of the defining properties for semiconductors and insulators. It determines the energy of absorbed light in photovoltaic devices, the color of light emitting materials, or the redox potential for electrochemical reactions. Being able to accurately predict the band gap (its value and the position of the band edge states with respect to the vacuum level) is thus paramount for the design of new optoelectronic materials. Electronic structure theory has made big leaps towards this goal with ever improving functionals within the density functional formalism and many-body theories. The renormalization of the band structure due to electron-phonon interactions becomes equally important at finite as well as zero temperature. However, the computation of electron-phonon renormalization in molecular crystals is challenging, due to the small dispersion of the bands. Through improved algorithms and taking advantage of symmetries, we calculate the electron-phonon coupling in crystalline naphthalene from first principles using van der Waals density functionals, and determine the zero-point renormalization and temperature dependence of the electronic eigenstates within the Allen-Heine-Cardona theory.   

First-principles anharmonic calculations and the dynamic Jahn-Teller effect

First-principles density functional theory methods can be used to investigate the structural configurations, energetics and vibrational motions of solids, including anharmonicity, by using a vibrational self-consistent field (VSCF) method. The possibility of calculating an anharmonic vibrational wavefunction using this method allows anharmonic effects such as the dynamic Jahn-Teller effect to be described accurately. In this work, we apply our VSCF method to an important example of a dynamic Jahn-Teller system, the neutral vacancy in diamond. Our calculations demonstrate that the dynamic Jahn-Teller distorted tetrahedral structure of the vacancy is more stable than the static Jahn-Teller distorted tetragonal structure, in agreement with experimental observations, across a wide range of temperatures. This work opens the way for first-principles treatments of dynamic Jahn-Teller systems in condensed matter. Further examples of systems our method can be applied to are considered as well.   

Temperature renormalization of the electronic and phonon properties of TiSe$_{2}$

We present first-principles studies of the phonon dispersions and the electronic structure of bulk TiSe$_{2}$ as a function of temperature. Above the charge-density-wave (CDW) transition temperature the high-symmetry normal-phase structure is stabilized by anharmonic effects. The transition temperature of the CDW phase is computed to be around 150 K with self-consistent phonon theory [1]. We have also investigated finite-temperature effects on the electronic structure with the molecular dynamics (MD) method. In contrast to zero-temperature band structure which shows a band overlap, MD-averaged band structure shows a small band gap of 76 meV at 300 K. Our results reveal a flat band along the kz direction as observed in ARPES experiments, which is missing in zero temperature calculations. We demonstrate the importance of finite temperature effects on TiSe$_{2}$ and show that fluctuations of the low-energy CDW phase have significant effects on room-temperature properties. [1] T. Tadano and S. Tsuneyuki, Phys. Rev. B \textbf{92}, 054301(2015).   

Band crossing driven by electron phonon coupling

The coupling of charge carriers (electrons or holes) to phonons can lead to the formation of a polaron, a coherent quasi-particle consisting of the charge carrier and the cloud of phonons surrounding it and moving coherently with it. Polarons have been studied extensively in the Holstein model and to a lesser extent in the SSH model, both of which are single band models. However, for many of the materials in which polarons are the low-energy excitations a description with multi-band models is more appropriate. Here we present results obtained with the highly accurate momentum average approximation for the single polaron properties of a two dimensional, three-band model. The model is inspired by the perovskite BaBiO$_3$ and the coupling to phonons modifies the hopping integrals. We find that the electron phonon coupling changes the ground state momentum from $\mathbf{k}=(\pi,\pi)$ to $\mathbf{k}=(\pi,0)$. Furthermore it can lead to the formation of a tilted band crossing point (BCP) and/or shift the location of existing BCPs in the Brillouin zone. These findings are of interest in the light of Dirac or Weyl materials in which BCPs play an important role.   

Lattice dynamics and electron-phonon coupling on Mn$_{1-x}$Fe$_{x}$Si: effect of magnetism

We have studied the electronic, lattice dynamics, and electron-phonon (e-ph) coupling properties of the Mn$_{1-x}$Fe$_x$Si alloy. This system have been analyzed within the framework of density functional perturbation theory, using a mixed-basis pseudopotential method and the virtual crystal approximation (VCA) for modeling the alloy. In particular, the electronic density of states (DOS), the full-phonon dispersion, as well as the electron-phonon coupling ($\lambda$) and the phonon linewidth ($\gamma$) have been calculated with and without the inclusion of spin polarization. While for FeSi is very well known that the effects of magnetism on the lattice dynamics are observed trough the phonon linewidths for specific regions on the zone boundary, on MnSi such detail analysis has not been addressed so far. Thus, the evolution of phonon frequencies and linewidths as a function of Fe-content are presented and discussed in detail, paying special attention the effect of spin-polarization on such properties for the magnetic region on the phase diagram $x < 0.16$.   

Phonon-induced superlattice structures in titanium-oxypnictides superconductors

First-principles electronic and phonon simulations have been carried out within density functional theory (DFT) for layered titanium-oxypnictides, BaTi$_2Pn_2$O ($Pn$ = As, Sb, Bi). We have found a new possibility of orthorhombic $2\times2\times1$ superlattice structure for BaTi$_2$As$_2$O, while that of tetragonal $\sqrt{2}\times\sqrt{2}\times1$ for BaTi$_2$Sb$_2$O and BaTi$_2$Bi$_2$O [1]. It was found that their phonon dispersons and changes of nesting vectors in Fermi surfaces can account for such varieties of superlattice structures even starting with the common undistorted structure when without the charge ordering. This new finding can naturally resolve a discrepancy between experiments and theoretical predictions on the charge ordering of the compounds without any relying on complicated unconventional mechanism proposed recently, which could also affect the understanding of superconductivity on the compounds. [1] K. Nakano, K. Hongo, and R. Maezono, Sci. Rep. 6, 29661 (2016).   

Effect of local correlation on electron phonon coupling in $La_2CuO_4$ using LDA+DMFT

ARPES measurements show a kink in the electron dispersion of $La_2CuO_4$ around 80 meV. The cause of this kink is still under debate. The phonon spectrum is consistent with a kink at that energy but previous studies have demonstrated that the response of the electron-phonon coupling calculated in the framework of density functional theory (DFT) with a GGA functional is too weak to account for the observed kink. However, other works have shown that the electron-phonon coupling can be underestimated by the treatment of LDA/GGA functionals. For this reason, we investigate the effect of the strong local correlation caused by the "d" electrons of Cu on the calculation of electron-phonon matrix elements. The local correlation is added using the dynamic mean-field theory (DMFT) approach within a DFT method. Specific electron-phonon matrix elements are calculated using the Frozen Phonon method.