Rational design of large anomalous Nernst effect in Dirac semimetals

Abstract Anomalous Nernst effect generates a transverse voltage perpendicular to the temperature gradient. It has several advantages compared with the longitudinal thermoelectricity for energy conversion, such as decoupling of electronic and thermal transports, higher flexibility, and simpler lateral structure. However, a design principle beyond specific materials systems for obtaining a large anomalous Nernst conductivity (ANC) is still absent. In this work, we theoretically demonstrate that a pair of Dirac nodes under a Zeeman field manifests an odd-distributed, double-peak anomalous Hall conductivity curve with respect to the chemical potential and a compensated carrier feature, leading to an enhanced ANC compared with that of a simple Weyl semimetal with two Weyl nodes. Based on first-principles calculations, we then provide two Dirac semimetal candidates, i.e., Na₃Bi and NaTeAu, and show that under a Zeeman field, they exhibit a sizable ANC value of 0.4 $${\rm{A}}{{\rm{m}}}^-1{{\rm{K}}}^-1$$ and 1.3 $${\rm{A}}{{\rm{m}}}^-1{{\rm{K}}}^-1$$, respectively, near the Fermi level. Such an approach is also applicable to ferromagnetic materials with intrinsic Zeeman splitting, as exemplified by a hypothetical alloy NaFeTe₂Au₂, exhibiting an ANC as high as 3.7 $${\rm{A}}{{\rm{m}}}^-1{{\rm{K}}}^-1$$ at the Fermi level. Our work provides a design principle with a prototype band structure for enhanced ANC pinning at the Fermi level, shedding light on the inverse design of other specific functional materials based on electronic structure.