Dissipationless anomalous transport properties and Mott relation in Ga$_{1-x}$Mn$_{x}$As

We have found an anomalously large Nernst effect (ANE) accompanying the anomalous Hall effect (AHE) in~a series of Ga$_{1-x}$Mn$_{x}$As (x=0.04-0.07) ferromagnetic semiconductor samples with perpendicular anisotropy. Without applying a magnetic field, none-zero ANE and AHE are observed, and both effects are very well scaled with the sample magnetization. We have developed a method, which dose not depend on the accuracy of magnetization measurement, to study the anomalous transport effects. By measuring AHE and ANE under zero magnetic field and over a wide range of temperatures, we have demonstrated the dissipationless origin of the anomalous electrical and thermoelectric transport properties in these samples.~ Furthermore, we have successfully verified the Mott relation for the off-diagonal transport coefficients in the regime of dissipationless transport that may not depend on scattering.