Condensed Matter Ep 12: Strange Metals and the Unsolved

A plot on a laboratory wall: resistivity against temperature for a copper-oxide superconductor above the temperature where it superconducts. The line is straight. It is straight down through a hundred kelvin, through ten, and as far down as anyone can push it with the superconductivity switched off by a magnet. That is the whole problem, and it has been on the wall for four decades. The third conversation in this series proved — not fitted, proved — that a metal's resistivity must rise as the *square* of temperature. Two Pauli squeezes on the available phase space, and no interaction strength anywhere in the argument, which is why it holds for copper and for the heavy-fermion compounds where electrons are a thousand times heavier than free ones. A straight line is not a small deviation from that. It is a different law. So this finale rebuilds the theorem on air and then asks which assumption dies. The answer is precise, and it is the episode's central takeaway: **the excitation is sharper than the energy it carries**. That is what makes a quasiparticle a thing at all — a bump narrow enough to have a name. In a strange metal the width equals the energy. There is no small parameter, no long-lived excitation, and therefore no Fermi surface to count seats around. The apparatus that explains every ordinary metal does not fail by a bit; it has nothing to describe. Also: why a Mott insulator is not a band insulator — a material every band calculation calls a metal that refuses to conduct, because the electrons jam each other rather than running out of states; the Zhang–Rice singlet; why doping one is so hard, since a moving hole drags a string of broken magnetic bonds behind it and pays for every link; the pseudogap and the Fermi arcs; quantum criticality; **Planckian dissipation**, the scattering rate at the fastest anything is allowed to relax; the Hall-number jump that says the carrier count changes from the doping to one-plus-the-doping across a particular concentration; and **quantum spin liquids** — order with no order parameter, the last callback to the broken-symmetry conversation. Then how the field is actually attacking it: **moiré materials** as designer strong correlation, where two graphene sheets twisted by about one degree produce a superconductor you can tune with a knob; and cold-atom and quantum-computer simulation of the Hubbard model, with a straight account of what those machines have and have not yet shown — including that the pure two-dimensional Hubbard model appears *not* to superconduct until one further hopping term is added. The series ends where it has to. Nothing is resolved; high-temperature superconductivity is unsolved after forty years. But the closing observation is the one all twelve conversations were built toward: every time this subject has understood something, it did so by finding a new object — a macroscopic phase, a dressed excitation, an order parameter, a diverging length, an integer belonging to a band — and never by working harder on the thing written in the Hamiltonian. The strange metal is not unsolved because the equations are difficult. The Hamiltonian is three lines long. It is unsolved because nobody has yet found the object. ——— Series: Physics - Tutorial · Grad level. Every equation spoken in full, no chalkboard required. Built by Fermi AI.