No twentieth-century physicist worked across so many fields. Landau left his name on a dozen pieces of physics — and his fingerprints on far more.
Cool liquid helium below 2.17 K — the “lambda point” — and something uncanny happens: it becomes helium-II, a fluid with exactly zero viscosity that climbs walls and flows through cracks too small for any normal liquid. In 1941 Landau explained it. The key was to stop thinking about individual atoms and instead describe the liquid’s collective quasiparticles — phonons (sound quanta) and rotons (higher-energy swirls). From their energy spectrum he derived a critical velocity below which flow is frictionless, and predicted a wholly new wave, “second sound,” later confirmed in the laboratory.
Landau’s 1937 theory describes a continuous phase transition through an order parameter η, which is non-zero in the ordered phase and falls smoothly to zero at the critical temperature. Drag the temperature across the λ-point (2.17 K) and watch helium pass from the ordered superfluid to the disordered normal state.
Landau’s framework for second-order phase transitions (1937) is one of the most influential ideas in modern physics. Near a continuous transition he characterised the change by an order parameter and expanded the system’s free energy as a power series in it, letting symmetry decide which terms may appear:
The free-energy expansion of Landau’s theory; symmetry forbids odd terms in a symmetric system.
Minimising this free energy describes magnets, superconductors, ferroelectrics and superfluids alike — and it became the language of spontaneous symmetry breaking at the centre of modern physics.
Landau’s deepest single idea may be the quasiparticle: that a fearsomely complex system of interacting particles can behave like a simple gas of new, “dressed” entities. His Fermi-liquid theory (1956–58) explained why the free-electron picture of metals works so well; his Landau levels (1930) quantise electrons in a magnetic field and underpin the quantum Hall effect; his phonons and rotons are quasiparticles of the superfluid.
Few names recur so often across physics. A partial list of what carries his name or bears his mark:
In 1932 he even argued that massive stars must collapse to nuclear densities — anticipating neutron stars in the same month the neutron itself was discovered.
With his student and collaborator Evgeny Lifshitz, Landau wrote the Course of Theoretical Physics — roughly ten volumes spanning mechanics, fields, quantum mechanics, statistical physics, fluids and more. Translated worldwide and still in daily use, it is among the most influential scientific textbook series ever written; the two shared the 1962 Lenin Prize for it.
To work with Landau a student first had to pass his “theoretical minimum”: a brutal sequence of about nine exams covering all of theoretical physics. Landau examined most of the candidates himself. Between 1934 and 1961, only forty-three people passed — and many became giants of physics in their own right, the famous Landau school.
Half in jest, Landau ranked physicists on a logarithmic scale of achievement, where each class meant a factor of ten and lower was better. Newton stood alone at 0, Einstein at 0.5, the founders of quantum mechanics at 1. Landau placed himself modestly at 2.5 — and, after the superfluidity work, allowed himself a promotion to 2.
Lower is better; each step is a factor of ten. The exact numbers vary between retellings — Ginzburg recalled Landau placing himself at 1.5 — so treat the scale as characteristic wit, not a ledger.