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The field of thermoelectric materials has undergone a revolutionary transformation over the last couple of decades as a result of the ability to nanostructure and synthesize myriads of materials and their alloys. The ZT figure of merit, which quantifies the performance of a thermoelectric material has more than doubled after decades of inactivity, reaching values larger than two, consistently across materials and temperatures. Central to this ZT improvement is the drastic reduction in the material thermal conductivity due to the scattering of phonons on the numerous interfaces, boundaries, dislocations, point defects, phases, etc., which are purposely included. In these new generation of nanostructured materials, phonon scattering centers of different sizes and geometrical configurations (atomic, nano- and macro-scale) are formed, which are able to scatter phonons of mean-free-paths across the spectrum. Beyond thermal conductivity reductions, ideas are beginning to emerge on how to use similar hierarchical nanostructuring to achieve power factor improvements. Ways that relax the adverse interdependence of the electrical conductivity and Seebeck coefficient are targeted, which allows power factor improvements. For this, elegant designs are required, that utilize for instance non-uniformities in the underlying nanostructured geometry, non-uniformities in the dopant distribution, or potential barriers that form at boundaries between materials. A few recent reports, both theoretical and experimental, indicate that extremely high power factor values can be achieved, even for the same geometries that also provide ultra-low thermal conductivities. Despite the experimental complications that can arise in having the required control in nanostructure realization, in this colloquium, we aim to demonstrate, mostly theoretically, that it is a very promising path worth exploring. We review the most promising recent developments for nanostructures that target power factor improvements and present a series of design ‘ingredients’ necessary to reach high power factors. Finally, we emphasize the importance of theory and transport simulations for materialoptimization, and elaborate on the insight one can obtain from computational tools routinely used in the electronic device communities. Graphical abstract

While studying magnetism of d-and f-electron systems has been consistently an active research area in physics, chemistry, and biology, there is an increasing interest in the novel magnetism of p-electron systems, especially in graphene and graphene-derived nanostructures. Bulk graphite is diamagnetic in nature, however, graphene is known to exhibit either a paramagnetic response or weak ferromagnetic ordering. Although many groups have attributed this magnetism in graphene to defects or unintentional magnetic impurities, there is a lack of compelling evidence to pinpoint its origin. To resolve this issue, we systematically studied the influence of entropically necessary intrinsic defects (e.g., vacancies, edges) and extrinsic dopants (e.g., S-dopants) on the magnetic properties of graphene. We found that the saturation magnetization of graphene decreased upon sulfur doping suggesting that S-dopants demagnetize vacancies and edges. Our density functional theory calculations provide evidence for: i) intrinsic defect demagnetization by the formation of covalent bonds between S-dopant and edges/vacancies concurring with the experimental results, and ii) a net magnetization from only zigzag edges, suggesting that the possible contradictory results on graphene magnetism in the literature could stem from different defect-types. Interestingly, we observed peculiar local maxima in the temperature dependent magnetizations that suggest the coexistence of different magnetic phases within the same graphene samples.

The Green-Kubo method is a commonly used approach for predicting transport properties in a system from equilibrium molecular dynamics simulations. The approach is founded on the fluctuation dissipation theorem and relates the property of interest to the lifetime of fluctuations in its thermodynamic driving potential. For heat transport, the lattice thermal conductivity is related to the integral of the autocorrelation of the instantaneous heat flux. A principal source of error in these calculations is that the autocorrelation function requires a long averaging time to reduce remnant noise. Integrating the noise in the tail of the autocorrelation function becomes conflated with physically important slow relaxation processes. In this paper we present a method to quantify the uncertainty on transport properties computed using the Green-Kubo formulation based on recognizing that the integrated noise is a random walk, with a growing envelope of uncertainty. By characterizing the noise we can choose integration conditions to best trade off systematic truncation error with unbiased integration noise, to minimize uncertainty for a given allocation of computational resources.