  Topological Weyl semimetals (WSM), a new state of quantum matter with gapless
nodal bulk spectrum and open Fermi arc surface states, have recently sparked
enormous interest in condensed matter physics. Based on the symmetry and
fermiology, it has been proposed that WSMs can be broadly classified into two
types, type-I and type-II Weyl semimetals. While the undoped, conventional,
type-I WSMs have point like Fermi surface and vanishing density of states (DOS)
at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry
explicitly and have tilted conical spectra with electron and hole pockets
producing finite DOS at the Fermi level. The tilted conical spectrum and finite
DOS at Fermi level in type-II WSMs have recently been shown to produce
interesting effects such as a chiral anomaly induced longitudinal
magnetoresistance that is strongly anisotropic in direction and a novel
anomalous Hall effect. In this work, we consider the anomalous Nernst effect in
type-II WSMs in the absence of an external magnetic field using the framework
of semi-classical Boltzmann theory. Based on both a linearized model of
time-reversal breaking WSM with a higher energy cut-off and a more realistic
lattice model, we show that the anomalous Nernst response in these systems is
strongly anisotropic in space, and can serve as a reliable signature of type-II
Weyl semimetals in a host of magnetic systems with spontaneously broken time
reversal symmetry.
