Kane fermions are characterized by a linear Dirac cone intersecting with a flat band, resembling a pseudo-spin-1 Dirac semimetal. Similar to relativistic Dirac fermions, Kane fermions satisfy a linear energy-momentum relation and can be classified as being pseudorelativistic. Unlike Dirac fermions, they are not protected by symmetry or by topology, but respect time-reversal symmetry, and can emerge by suitable band engineering, for example, in mercury-telluride compounds. Here we discuss the reminiscences of Berry-phase physics in Kane fermions that emerge in the presence of broken time-reversal symmetry. We discuss anomalous transport in Kane fermions and show its similarity to transport in a Dirac semimetal. Furthermore, we study anisotropy in their response that can be probed in current experiments.

Science and Engineering Research Board http://dx.doi.org/10.13039/501100001843

Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659

National Science Foundation http://dx.doi.org/10.13039/100000001