  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 a double-peak anomalous Hall conductivity curve with respect to the
chemical potential and a compensated carriers feature, leading to an enhanced
ANC pinning at the Fermi level 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 A/(m*K) and 1.3 A/(m*K),
respectively, near the Fermi level. Our work provides a design principle with a
prototype band structure for enhanced ANC pinning at Fermi level, shedding
light on the inverse design of other specific functional materials base on
electronic structure.
