Thermal Hall effect (THE) is to describe the phenomenon where heat carriers
are deflected by an external magnetic field applied perpendicular to the heat flow, and thus
the carriers gain transverse velocity, leading to a finite temperature gradient on the two sides
orthogonal to the heat flow and field. THE is predicted to occur in systems with nontrivial
Berry curvatures and thus can reveal topological properties, similar to the electrical Hall effect.
However, THE is not limited to charge excitations as in the electrical Hall effect, but rather, to
all kinds of excitations that are able to conduct heat, making it possible to explore the exotic
properties in strongly correlated electronic systems, which are typically insulators. Therefore,
THE is more universal than the electrical form and has become a powerful probe in detecting
charge-neutral excitations, such as phonons and magnons. Moreover, there are some sources
such as chiral phonons, which are beyond a simple nontrivial-Berry-curvature scenario, that
can also give rise to THE; examining THE wherein will shed light on the complex microscopic
mechanism hidden in materials. Despite these, heat signals are much weaker than electrical
ones. Especially for measurements of the thermal Hall conductivity, it is often needed to collect
weak signals on top of a large background. This makes measuring the THE challenging—but
thanks to the sustained efforts of the community, this field is developing rapidly in recent
years, with many interesting results on the measurements of the thermal Hall conductivity.
In this review article, we try to summarize some of these exciting accomplishments, point out
remaining outstanding issues, and suggest possible future directions.
