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In the last two or three years, significant advances in the study of hydrogen and its compounds under extreme conditions (ultrahigh pressures over a wide temperature range) have notably changed the hydrogen phase diagram, provided a break-through in understanding hydrides' behavior under pressure (as exemplified by the discovery of high-temperature superconductivity in hydrogen sulfide), and, finally, enabled achieving cold metallization of hydrogen. The situation prior to the 2010s is reviewed in brief and more recent work is examined in detail. While the primary focus is on experimental research, mention is also made of the theoretical and numerical work it stimulates.

This brief paper supplements the review by A F Barabanov et al. (Physics–Uspekhi 58 446 (2015)) concerning the Hall and Righi–Leduc effects. Both effects are diagonal in the sense that the initial current perpendicular to the magnetic field and the transverse response (perpendicular to both the magnetic field and the initial current) are of the same nature (the electric current in the Hall effect and the heat current in the Righi–Leduc effect). We here take a similar perspective in discussing the nondiagonal Ettingshausen and Nernst effects, in which the transverse current is different in nature from the initial longitudinal one. A summary of transverse effects in a magnetic field is also given.

We draw attention to a similarity between mutually related kinetic material phenomena that are odd in the magnetic field and produce an electric current or heat flow perpendicular (1) to the magnetic field, (2) to the electric field strength or to the temperature gradient. These phenomena include the Hall effect, the Righi–Leduc effect in nonmagnetic metals, the anomalous Hall effect in magnets, the odd Senftleben–Beenakker effect in molecular gases, and the phonon Hall effect in dielectrics. While these phenomena have much in common in terms of geometry, their formation mechanisms — dynamic and dissipative — are different. However, in all cases, the flow perpendicular to the magnetic field arises from the spin-orbit interaction of carriers with magnetic moments.