The anomalous Nernst effect (ANE), generating a transverse voltage perpendicular to a temperature gradient without an external magnetic field, is promising for energy harvesting. Unlike the ordinary Nernst effect driven by Lorentz force, ANE arises from intrinsic (Berry curvature) and extrinsic contributions (magnon drag, skew scattering, side jump). Topological semimetals, with their band crossing points (Weyl points or nodal lines), are attractive candidates due to their high Berry curvature. While several materials exhibit sizable ANC (0.1–10 Am⁻¹K⁻¹), a design principle for achieving large, Fermi-level-pinned ANC remains elusive. The Mott relation connects anomalous Hall conductivity (AHC) and ANC, suggesting that a band structure with opposite AHC peaks around the Fermi level can enhance ANC. Carrier compensation further boosts the effect, but most materials with high ANC require Fermi level tuning. This study aims to establish an electronic structure design principle for enhanced, Fermi-level-pinned ANC.

Previous research has focused on identifying materials with large ANE in topological semimetals such as Co₂MnGa, Co₃Sn₂S₂, Mn₃X (X = Sn, Ge), and Heusler compounds. These studies have demonstrated the potential of these materials for energy harvesting applications. However, the reported ANC values are still relatively small compared to the potential of magneto-thermoelectricity. The Mott relation has been utilized to understand the connection between AHC and ANC, and suggests strategies for enhancing ANC by engineering the band structure. However, a general design principle for obtaining large, Fermi-level-pinned ANC has been lacking.

The study employs a multi-pronged approach. First, a model Hamiltonian of a Dirac semimetal under a Zeeman field is analyzed. This model demonstrates the emergence of a double-peak AHC curve (oddly distributed with respect to the chemical potential), a feature linked to enhanced Fermi-level-pinned ANC. The authors then use first-principles calculations based on density functional theory (DFT) to investigate two realistic Dirac semimetals, Na₃Bi and NaTeAu. These calculations utilize the Vienna ab initio simulation package (VASP) with the generalized gradient approximation (GGA) and projector augmented wave (PAW) method. Spin-orbit coupling (SOC) is included. Tight-binding Hamiltonians are constructed using Wannier orbitals via Wannier90, and a modified version of WannierTools is used to calculate AHC and ANC, replacing the Fermi-Dirac distribution function with a Gaussian-like function for ANC calculations. The Berry curvature, crucial for understanding ANE, is evaluated via the Kubo formula. Finally, a hypothetical ferromagnetic alloy, NaFeTe₂Au₂, is designed to further demonstrate the design principle. The authors carefully analyze the effect of different parameters (Fermi velocity, effective mass, distance of Dirac nodes, Zeeman field strength) on the ANC values.

The key findings are threefold: (1) A theoretical model demonstrates that a Dirac semimetal under a Zeeman field exhibits a double-peak AHC curve, leading to a significantly enhanced ANC (approximately 300% increase compared to a simple Weyl semimetal) pinned at the Fermi level. (2) DFT calculations on Na₃Bi show a sizable ANC of approximately 0.38 Am⁻¹K⁻¹ near the Fermi level, resulting from the symmetric band splitting under the Zeeman field. The calculation of NaTeAu shows a more pronounced double-peak feature in AHC, resulting in an even higher ANC value of approximately 1.3 Am⁻¹K⁻¹ near the Fermi level due to the symmetric band splitting. (3) A hypothetical ferromagnetic alloy, NaFeTe₂Au₂, designed to exhibit the double-peak AHC feature, demonstrates an exceptionally high ANC value of 3.7 Am⁻¹K⁻¹ at the Fermi level. This emphasizes the potential for manipulating the electronic structure to achieve large ANC values. The analysis of parameter dependence shows the optimum conditions for maximizing ANC in the Dirac semimetal model.

This study successfully demonstrates that enhancing the anomalous Nernst conductivity can be achieved through a rational design of the electronic band structure. The double-peak AHC feature, arising from the specific arrangement of Weyl points in Dirac semimetals under a Zeeman field, is identified as crucial for achieving high ANC values at the Fermi level. This eliminates the need for Fermi level tuning, simplifying material synthesis and device fabrication. The findings provide a crucial bridge between theoretical understanding and material design, opening avenues for targeted exploration of new materials with enhanced ANE for energy harvesting applications. The successful application of the design principle to both model systems and realistic materials, including a hypothetical ferromagnetic topological material, underscores the robustness and generalizability of the approach.

This work presents a design principle for achieving large, Fermi-level-pinned anomalous Nernst conductivity based on the double-peak AHC feature in Dirac semimetals under a Zeeman field. The theoretical model and DFT calculations on Na₃Bi and NaTeAu, along with the design of NaFeTe₂Au₂, validate this principle. This provides a valuable guideline for future materials discovery and inverse design efforts focused on enhancing ANE for energy applications. Future work could explore other material systems exhibiting similar band structures and investigate strategies to further enhance ANC through material engineering and external field control.

The study focuses primarily on theoretical modeling and DFT calculations. Experimental verification of the predicted ANC values in the proposed materials is necessary to fully validate the design principle. The hypothetical ferromagnetic material NaFeTe₂Au₂ remains to be synthesized and characterized. Further exploration of the influence of various factors, including temperature effects, defects, and impurities, on ANC is also warranted.