Matter in strong magnetic fields

The properties of matter are drastically modified by strong magnetic fields, $B\gg m_e^2{e}^{3}c/{ħ}^3=2.35\mathrm{}\times {10}^9\mathrm{G}$ $\left(1\mathrm{}\mathrm{G}{=10\mathrm{}}^{-4}\mathrm{T}\right),$ as are typically found on the surfaces of neutron stars. In such strong magnetic fields, the Coulomb force on an electron acts as a small perturbation compared to the magnetic force. The strong-field condition can also be mimicked in laboratory semiconductors. Because of the strong magnetic confinement of electrons perpendicular to the field, atoms attain a much greater binding energy compared to the zero-field case, and various other bound states become possible, including molecular chains and three-dimensional condensed matter. This article reviews the electronic structure of atoms, molecules, and bulk matter, as well as the thermodynamic properties of dense plasma, in strong magnetic fields, ${10}^9\mathrm{G}\ll B\lesssim {10}^{16}\mathrm{G}.$ The focus is on the basic physical pictures and approximate scaling relations, although various theoretical approaches and numerical results are also discussed. For a neutron star surface composed of light elements such as hydrogen or helium, the outermost layer constitutes a nondegenerate, partially ionized Coulomb plasma if $B\lesssim {10}^{15}$ G (at temperature $T\gtrsim {10}^6$ K), and may be in the form of a condensed liquid if the magnetic field is stronger (and T $\gtrsim {10}^6\mathrm{K}).\mathrm{}$ For an iron surface, the outermost layer of the neutron star can be in a gaseous or a condensed phase, depending on the cohesive property of the iron condensate.