Muhammad Hilal
Advisor: Prof. Dr. Oğuz Gülseren
Title: Implications of the Anisotropic Mexican-Hat Band Structure in 2D Materials
on their Thermoelectric Properties: An Analytical and Computational Investigation
Abstract: The electronic band structures of two-dimensional (2D) materials often exhibit non-parabolic, highly anisotropic features near the valence band edge. A particularly intriguing case is the Mexican-hat-like dispersion, characterized by a ring-shaped energy extremum in momentum space. This topology gives rise to a van Hove singularity in the 2D density of states (DOS) and a sharp onset in the electronic transmission spectrum, both of which can significantly enhance thermoelectric performance. However, realistic materials frequently exhibit angular anisotropy in these dispersions, shifting the DOS singularity and degrading transport efficiency. In this thesis, we investigate the interplay between anisotropy in Mexican-hat-like band structures and thermoelectric properties across a family of 2D materials.
Using first-principles density functional theory (DFT) and density functional perturbation theory (DFPT), we systematically study seven monolayer compounds, including PbBrF, PbClF, PbIF, BaHI, BiOCl, CaHBr, and SrHI. For each material, we perform structural optimization, electronic band structure analysis, and phonon stability checks. Thermoelectric transport coefficients are computed using the semi-classical Boltzmann transport equation via BoltzTraP, incorporating spin-orbit coupling (SOC) for the PbXF compounds. Phonon-limited lattice thermal conductivity is evaluated through third-order force constants obtained from thirdorder.py and ShengBTE. To analytically interpret the Mexican-hat features, we develop a tight-binding model parameterized by the ratio of next-nearest to nearest-neighbor hopping amplitudes ($\xi = t_2/t_1$) and an angular anisotropy term $\beta$. We demonstrate how $\xi$ and $\beta$ jointly control the curvature and shape of the band edge, thus tuning the thermoelectric response.
Across the PbXF series, SOC suppresses the valence-edge singularity and tends to lower the $p$-type performance while modestly enhancing the $n$-type response by sharpening conduction edges. Phonon calculations (second- and third-order force constants; ShengBTE) reveal intrinsically low lattice thermal conductivities due to soft optical modes and strong three-phonon scattering.
As a case study in band-structure engineering, we apply \emph{biaxial tensile} strain ($0$–$6%$) to SrHI and show that strain reduces the Mexican-hat anisotropy, slightly decreases the hat height and ring radius, and sharpens the DOS onset. Consistent with the Mott relation, $p$-type $S$ and the power factor improve (with a mild trade-off in conductivity). In contrast, the lattice thermal conductivity decreases as strain softens modes and enlarges anharmonic phase space. Taken together, the results establish clear descriptors and knobs—$\xi$, $\beta$, hat height, and strain—for designing high-performance 2D thermoelectrics.
Date: September 12, Friday
Time: 10:00
Place: SA-240 Seminar Room