Session L8: Electrons, Phonons, and Electron Phonon Scattering IV

Anomalous phonon/heat transport in low dimensional micro/nano materials

When system dimension and size go down, many interesting phenomena can happen. Both experimental and numerical works in recent years have shown that phonon/heat transport in low (quasi 1D and 2D) dimensional nano structures like nanotube, nanowire, polymer chain, graphene, and other 2D materials show anomalous behavior: (a) heat conduction due to phonons does not follow the Fourier law; (b) heat transports may break down the reciprocal principle, namely heat flows asymmetrically. (c) negative differential thermal resistance will arise, namely the larger the temperature drops, the smaller the heat current. Issues (b) and (c) can be used to build up useful phononic thermal devices like thermal diode and thermal transistor, which lay the foundation of a new emerging field -- phononics. In this talk, I will focus on issue (a) and present a general theoretical understanding of the anomalous phonon/heat transport. More specifically, I will discuss how the anomalous thermal transport - a macroscopic phenomenon -- is connected with the anomalous energy diffusion - a microscopic process.   

Revisiting the theory of disordered alloy thermal conductivity

Current understanding of the phonon contributions to alloy thermal conductivity (TC) is based on the phonon gas model (PGM) and the virtual crystal approximation (VCA). Using this theoretical framework, good agreement is obtained in some cases, but there are many instances where it fails -- both quantitatively and qualitatively. Here, we reexamine the conventional theory and note that a critical assumption is that all of the phonons/normal modes of vibration resemble plane waves with well-defined velocities. Instead, we show that in a random alloy, the character of the normal modes changes dramatically within the first 2{\%} impurity concentration, beyond which they more closely resemble the modes found in amorphous materials. We then utilize a new theory that can treat modes with any character and experimentally confirm its new insights. The results indicate that mode character is critical and has significant implications for phonon interactions with neutrons, electrons and photons, since the momentum of non-propagating phonons is currently unknown.   

Thermal Conductivity within Nanoparticle Powder Beds

Non-equilibrium molecular dynamics is utilized to compute thermal transport properties within nanoparticle powder beds. In the realm of additive manufacturing of metals, the electronic contribution to thermal conduction is critical. To this end, our simulations incorporate the two temperature model, coupling a continuum representation of the electronic thermal contribution and the atomic phonon system. The direct method is used for conductivity determination, wherein thermal gradients between two different temperature heat flux reservoirs are calculated. The approach is demonstrated on several example cases including 304L stainless steel. The results from size distribution variations of mono/poly-disperse systems are extrapolated to predict values at the micron length scale, along with bulk properties at infinite system sizes. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Nonequilibrium dynamics of electrons and phonons: tailoring the transport properties of Carbon Nanotubes with encapsulated nanowires.

Rapid saturation of electronic current in carbon nanotubes (CNTs) under bias voltage has been observed in several recent experimental and theoretical studies [1-5] This effect, caused by scattering with lattice vibrations, limits otherwise promising applications of CNTs in nanoelectronics. Here we propose a mechanism to enhancement electrical performance of metallic CNTs by encapsulation of one-dimensional nanowires. Although experimental studies of such structures are increasingly common [6-9], our first-principles study combined with the coupled electron-phonon dynamics is the first to explicitly demonstrate their enhanced functional performance relative to an empty metallic CNT. References: [1] A. Javey et al Phys. Rev. Lett., 92(10):106804, 2004. [2] J.-Y. Park et al Nano Lett., 4(3):517, 2004. [3] Z. Yao et al. Phys. Rev. Lett., 84(13):2941, 2000. [4] M. Amer et al Nano Res., 5(3):172, 2012. [5] M. Lazzeri et al. Phys. Rev. Lett., 95(23):236802, 2005. [6] J. H. Spencer et al ACS Nano, 8(9):9044, 2014.[7] R. Carter et al Dalton Transactions, 43(20):7391, 2014.[8] E. Philp et al Nat Mater, 2(12):788, 2003.[9] R. Senga et al. Nat Mater, 13(11): 1050, 2014.   

Hypersonic hybridization band gaps in structures based on polymer-tethered colloids.

Phononic hybridization gaps, originating from the anti-crossing between local resonant and propagating modes, are robust to structural disorder and occur at wavelengths much larger than the size of the resonant unit. Here, polymer-tethered colloidal particles (particle brush) were used to fabricate hybridization gap structures harnessing the anisotropic elasticity across their solid particle-polymer interface. Brillouin light spectroscopy was employed to record the dispersion diagram for longitudinal and transverse phonons as a function of grafting density and polymer length. Frequency band gap width and position decreased with polymer volume fraction at roughly constant grafting density but increased with decreasing grafting density at constant volume fraction. Modeling of the phononic band diagrams using the layered-multiple scattering formalism revealed the importance of the boundary conditions and differences of the polymer elastic moduli from their isotropic bulk values. These intriguing findings were discussed in terms of structural and particle brush topology effects and complemented by the elastic excitations of the individual particle brush systems. The results point to new opportunities to harness efficient self-assembly methods for the fabrication of phononic materials.   

Surface States Mediated Interfacial Thermal Conductance across Metal-nonmetal Interfaces

The thermal transport mechanisms across metal-nonmetal interfaces are of great interest. We point out that the interfacial thermal conductance across metal-nonmetal interfaces could be determined by the electron-phonon interaction mediated by the surface states near the interface. Our calculation results show that the interfacial thermal conductance across Pb/Pt/Al/Au-diamond interfaces are only slightly different among these metals. The reason is the pinning of Fermi energy near the interface. Our results are in good agreement with the experimental results of the thermal boundary conductance of metal-diamond interfaces observed by Stoner et al. [Phys. Rev. Lett. 68, 1563 (1992)] and by Hohensee et al. [Nature Commun. 6, 6578 (2015)].   

Ultrafast Structure Control through Nonlinear Phononics

Utilizing ultrashort THz light pulses to manipulate the state of matter becomes an emerging approach in condensed matter science. Here we present an approach[1] to actively control the transient structural distortion arising from non-linear phononics in ErFeO3. Using density functional theory, we calculate the structural properties as input to an anharmonic phonon model that describes the response of the system to a pulsed optical excitation. We find that a trilinear coupling of two orthogonal infrared-active phonons to a Raman-active phonon causes a transient distortion of the lattice. The direction of the distortion is determined by the polarization of the exciting light, suggesting a route to nonlinear phononic lattice control and switching. Since the occurrence of the coupling is determined by the symmetry of the system we propose that it is a universal feature of orthorhombic and tetragonal perovskites. Finally, we discuss our findings with respect to experiments of T. Nova et al.[2] as pathway to manipulate the spin system by non-linear phonon excitations. [1] D. M. Juraschek, M. Fechner, and N. A. Spaldin, arXiv 1607.01653 (2016). [2] T. F. Nova, et al., Nature Phys. doi:10.1038/nphys3925 (2016)   

Redirection and splitting of sound waves by a periodic chain of thin perforated cylindrical shells

A perforated metallic cylindrical shell in air is a weak scatterer of sound, and so is a periodic chain of shells. However, in a narrow region of frequencies the transmission of a normally incident acoustic wave through the chain exhibits a sharp minimum due to excitation of a leaky wave which propagates along the chain. This wave is a weakly-decaying eigenmode with either symmetric profile and anomalous dispersion, or with antisymmetric profile and normal dispersion. At normal incidence, only the symmetric eigenmode can be excited, but for slightly oblique incidence both modes can be excited at close frequencies. These modes allow effective 90$^{\circ}$-redirection of sound, and since the mode with anomalous dispersion propagates in the “wrong” direction, an incoming signal containing two harmonics will be split into two beams propagating along the chain in opposite directions. A rigorous scattering theory is developed for finite and infinite chains of shells, and theoretical and numerical calculations of the transmission coefficient and redirected field pattern are presented.   

Efficient Computation of Anharmonic Force Constants via q-space, with Application to Graphene

We present a new approach for extracting anharmonic force constants from a sparse sampling of the anharmonic dynamical tensor. We calculate the derivative of the energy with respect to q-space displacements (phonons) and strain, which guarantees the absence of supercell image errors. Central finite differences provide a well-converged quadratic error tail for each derivative, separating the contribution of each anharmonic order. These derivatives populate the anharmonic dynamical tensor in a sparse mesh that bounds the Brillouin Zone, which ensures comprehensive sampling of q-space while exploiting small-cell calculations for efficient, high-throughput computation. This produces a well-converged and precisely-defined dataset, suitable for big-data approaches. We transform this sparsely-sampled anharmonic dynamical tensor to real-space anharmonic force constants that obey full space-group symmetries by construction. Machine-learning techniques identify the range of real-space interactions. We show the entire process executed for graphene, up to and including the fifth-order anharmonic force constants. This method successfully calculates strain-based phonon renormalization in graphene, even under large strains, which solves a major shortcoming of previous potentials.   

Strong negative thermal expansion in metal carbides using the quasi-harmonic approximation

Negative thermal expansion (NTE) is a very rare but important property found in materials in which they shrink upon heating. Negative and positive thermal expansion substances can be combined to synthesize zero thermal expansion composites. There are very few compounds with very strong NTE for a wide range of temperatures. For instance, network structured compounds such as (Zr,Hf)W$_2$O$_8$, show an isotropic NTE for a wide range of temperature larger than $1000$ K. However, strong NTE materials without a network structure are very rare. Here, we have studied the thermal expansion of transition metal carbides using the quasi-harmonic approximation. Their phonon dispersion curves show low energy (less than 8 meV) transverse acoustic modes observed as intense and sharp peaks in their phonon density of states. These compounds present large negative Gr\"uneisen parameters for their transverse acoustic bands, which is reflected in the intense NTE behavior from close to 0 K to more than $1000$ K.   

Effects of vdW and Electrostatic Interactions on Phonon Velocity and Thermal Transport in Polymers

Bulk amorphous polymers typically have a low thermal conductivity (\textasciitilde 0.2 W/mK). This low thermal conductivity is believed to be due to weak inter-chain interactions, e.g., van der Waals and electrostatic. Heat transfer along polymer chains, however, is considered very robust due to strong covalent bonds between the atoms. In this work we show that this explanation does not give a clear picture of precisely what contributes to heat transfer in various polymers with different structures. Here we show that the abundance of vdW and electrostatic interactions can greatly impact heat transfer in polymers at room temperature. Through molecular dynamics calculations, we show that the propagation velocities of acoustic phonons at moderate frequencies (\textasciitilde 1THz), which contribute significantly to heat transfer at room temperature, are much higher when non-bonding interactions are present in the system versus when they are excluded. This relationship has important implications for designing amorphous polymers with high thermal conductivity.   

Controlling instabilities during gold nanoribbon crystallization

This paper describes the electrochemical growth of branchless gold nanoribbons with $\sim $40 nm thicknesses, $\sim $300 nm widths, and greater than 100 $\mu $m lengths (giving length-to-thickness aspect ratios of well over 10$^{\mathrm{3}})$. These structures are useful for opto-electronic studies and as nanoscale electrodes. Growing these ultra-long, branchless, crystalline structures requires controlling the Mullins-Sekerka instability, which is necessary for maintaining the template-free growth of the ribbon but has the unwanted effect of inducing side-branching. The 0.75-1.0 V voltage amplitude range is optimal for branchless ribbon growth. Reduced amplitudes induce no growth, possibly due to the reversible redox chemistry of gold at reduced amplitudes, whereas elevated amplitudes, or excess electrical noise, induce significant side-branching. An electrochemical, linear stability analysis illustrates how voltage amplitude and excess noise cause side-branching. Limitations of this linear theory will be discussed. An outcome of this study is the controlled application of electrical noise in order to produce targeted structures, such as Y-shaped nanoribbons. This research was supported by the NSF (IIA-1430493) and NIH (1R21EY026392).