Boltzmann Transport in Nanostructures as a Friction Effect

Surface scattering is the key limiting factor to thermal transport in dielectric crystals as the length scales are reduced or when temperature is lowered. To explain this phenomenon, it is commonly assumed that the mean free paths of heat carriers are bound by the crystal size and that thermal conductivity is reduced in a manner proportional to such mean free paths. We show here that these conclusions rely on simplifying assumptions and approximated transport models. Instead, starting from the linearized Boltzmann transport equation in the relaxon basis, we show how the problem can be reduced to a set of decoupled linear differential equations. Then, the heat flow can be interpreted as a hydrodynamic phenomenon, with the relaxon gas being slowed down in proximity of a surface by friction effects, similar to the flux of a viscous fluid in a pipe. As an example, we study a ribbon and a trench of monolayer molybdenum disulphide, describing the procedure to reconstruct the temperature and thermal conductivity profile in the sample interior and showing how to estimate the effect of nanostructuring. The approach is general and could be extended to other transport carriers, such as electrons, or extended to materials of higher dimensionality and to different geometries, such as thin films

AiiDA: Automated Interactive Infrastructure and Database for Computational Science

Computational science has seen in the last decades a spectacular rise in the scope, breadth, and depth of its efforts. Notwithstanding this prevalence and impact, it is often still performed using the renaissance model of individual artisans gathered in a workshop, under the guidance of an established practitioner. Great benefits could follow instead from adopting concepts and tools coming from computer science to manage, preserve, and share these computational efforts. We illustrate here our paradigm sustaining such vision, based around the four pillars of Automation, Data, Environment, and Sharing. We then discuss its implementation in the open-source AiiDA platform (http://www.aiida.net), that has been tuned first to the demands of computational materials science. AiiDA's design is based on directed acyclic graphs to track the provenance of data and calculations, and ensure preservation and searchability. Remote computational resources are managed transparently, and automation is coupled with data storage to ensure reproducibility. Last, complex sequences of calculations can be encoded into scientific workflows. We believe that AiiDA's design and its sharing capabilities will encourage the creation of social ecosystems to disseminate codes, data, and scientific workflows.Comment: 30 pages, 7 figure

Thermal transport in low dimensions

Lattice vibrations are the microscopic mechanism responsible for a large, if not dominant, contribution to heat transport in crystalline insulators. These vibrations are described in terms of phonons, collective excitations (or quasiparticles) in the form of waves of atomic displacements inside a crystal. Phonons are traditionally considered to be the quasiparticles responsible for carrying heat through the material. Heat transport is considered as a flux of a phonon gas, diffusing from hot areas (high phonon densities) to cold areas (low phonon densities) in an attempt to reestablish equilibrium, with phonon collisions being the source of heat flux dissipation. However, as dimensionality is reduced, the motion of phonons stimulated by temperature perturbations becomes correlated and this gas-like picture of thermal transport in terms of phonons becomes invalid. In this Thesis, we lay out an interpretation of thermal transport in 2D materials based on the Boltzmann transport equation in the form of collective excitations of phonons. These collective phonon excitations give raise to complex phenomena, such as high thermal conductivities, that are otherwise unexplained. As another example, collective excitations, at variance with conventional diffusive transport, can induce wave-like heat propagation, or second sound. This had been found only in a few exotic materials at cryogenic temperatures, but is present instead routinely in 2D materials at room temperature. The correlated-phonon description of heat transfer can be rationalised by introducing a new collective excitation, called 'relaxon', which is defined as the eigenstate of the collision operator. Whereas only oversimplifying assumptions endow phonons with well defined relaxation times (the average interval of time between collisions), relaxons have always well defined relaxation times and permit an exact description of thermal transport. The complex dynamic of heat transport in 2D is thus greatly simplified and a kinetic gas theory of thermal transport still applies, provided that the gas is not constituted by phonons, but by relaxons. Our work on thermal transport is part of a larger effort, aiming at the creation of a database of numerically computed properties of materials. The high-throughput production of simulated properties is a challenging task, since it necessitates the understanding of a physical model, but it also needs to face a myriad of technicalities and problems that hinder the execution of a large number of calculations. In order to allow the creation of computational materials databases, we developed AiiDA, an open-source automated interactive infrastructure and database for computational science. This platform tackles the problems of creation, management, analysis and sharing of data and simulations, summarized in the pillars of Automation, Data, Environment and Sharing. Automation is achieved by management of remote computational resources and the encoding of workflows, that allows the execution of complex sequences of calculations. The tight coupling between automation and data storage, handled by the platform, enables full reproducibility of the results and a suitable database design allows for efficient data analysis tools. Sharing of scientific knowledge is addressed by providing tools for distribution of data and of the underlying workflows that generated them, creating an ecosystem for computational materials science

Anomalous thermoelectric transport phenomena from interband electron-phonon scattering

The Seebeck coefficient and electrical conductivity are two critical quantities to optimize simultaneously in designing thermoelectric materials, and they are determined by the dynamics of carrier scattering. We uncover a new regime where the co-existence at the Fermi level of multiple bands with different effective masses leads to strongly energy-dependent carrier lifetimes due to intrinsic electron-phonon scattering. In this anomalous regime, electrical conductivity decreases with carrier concentration, Seebeck coefficient reverses sign even at high doping, and power factor exhibits an unusual second peak. We discuss the origin and magnitude of this effect using first-principles Boltzmann transport calculations and simplified models. We also identify general design rules for using this paradigm to engineer enhanced performance in thermoelectric materials.Comment: 11 pages, 7 figure

A posteriori metadata from automated provenance tracking: Integration of AiiDA and TCOD

In order to make results of computational scientific research findable, accessible, interoperable and re-usable, it is necessary to decorate them with standardised metadata. However, there are a number of technical and practical challenges that make this process difficult to achieve in practice. Here the implementation of a protocol is presented to tag crystal structures with their computed properties, without the need of human intervention to curate the data. This protocol leverages the capabilities of AiiDA, an open-source platform to manage and automate scientific computational workflows, and TCOD, an open-access database storing computed materials properties using a well-defined and exhaustive ontology. Based on these, the complete procedure to deposit computed data in the TCOD database is automated. All relevant metadata are extracted from the full provenance information that AiiDA tracks and stores automatically while managing the calculations. Such a protocol also enables reproducibility of scientific data in the field of computational materials science. As a proof of concept, the AiiDA-TCOD interface is used to deposit 170 theoretical structures together with their computed properties and their full provenance graphs, consisting in over 4600 AiiDA nodes

Optomechanical measurement of thermal transport in two-dimensional MoSe2 lattices

Nanomechanical resonators have emerged as sensors with exceptional sensitivities. These sensing capabilities open new possibilities in the studies of the thermodynamic properties in condensed matter. Here, we use mechanical sensing as a novel approach to measure the thermal properties of low-dimensional materials. We measure the temperature dependence of both the thermal conductivity and the specific heat capacity of a transition metal dichalcogenide (TMD) monolayer down to cryogenic temperature, something that has not been achieved thus far with a single nanoscale object. These measurements show how heat is transported by phonons in two-dimensional systems. Both the thermal conductivity and the specific heat capacity measurements are consistent with predictions based on first-principles

Thermal Transport in Crystals as a Kinetic Theory of Relaxons

Thermal conductivity in dielectric crystals is the result of the relaxation of lattice vibrations described by the phonon Boltzmann transport equation. Remarkably, an exact microscopic definition of the heat carriers and their relaxation times is still missing: Phonons, typically regarded as the relevant excitations for thermal transport, cannot be identified as the heat carriers when most scattering events conserve momentum and do not dissipate heat flux. This is the case for two-dimensional or layered materials at room temperature, or three-dimensional crystals at cryogenic temperatures. In this work, we show that the eigenvectors of the scattering matrix in the Boltzmann equation define collective phonon excitations, which are termed here "relaxons". These excitations have well-defined relaxation times, directly related to heat-flux dissipation, and they provide an exact description of thermal transport as a kinetic theory of the relaxon gas. We show why Matthiessen's rule is violated, and we construct a procedure for obtaining the mean free paths and relaxation times of the relaxons. These considerations are general and would also apply to other semiclassical transport models, such as the electronic Boltzmann equation. For heat transport, they remain relevant even in conventional crystals like silicon, but they are of the utmost importance in the case of two-dimensional materials, where they can revise, by several orders of magnitude, the relevant time and length scales for thermal transport in the hydrodynamic regime