The properties of cuprate high-temperature superconductors are largely shaped by competing phases whose nature is often a mystery. Chiefly among them is the pseudogap phase, which sets in at a doping p* that is material-dependent. What determines p* is currently an open question. Here we show that the pseudogap cannot open on an electron-like Fermi surface, and can only exist below the doping p FS at which the large Fermi surface goes from hole-like to electron-like, so that p* ≤ p FS. We derive this result from high-magnetic-field transport measurements in La1.6−xNd0.4SrxCuO4 under pressure, which reveal a large and unexpected shift of p* with pressure, driven by a corresponding shift in p FS. This necessary condition for pseudogap formation, imposed by details of the Fermi surface, is a strong constraint for theories of the pseudogap phase. Our finding that p* can be tuned with a modest pressure opens a new route for experimental studies of the pseudogap.
The nature of the pseudogap phase of cuprates remains a major puzzle 1,2 . One ofnew signatures is a large negative thermal Hall conductivity κ xy , which appears for dopings p below the pseudogap critical doping p*, but whose origin is as yet unknown 3 . Because this large κ xy is observed even in the undoped Mott insulator La 2 CuO 4 , it cannot come from charge carriers, these being localized at p = 0. Here we show that the thermal Hall conductivity of La 2 CuO 4 is roughly isotropic, being nearly the same for heat transport parallel and normal to the CuO 2 planes, i.e. κ zy (T) ≈ κ xy (T). This shows that the Hall response must come from phonons, these being the only heat carriers able to move as easily normal and parallel to the planes 4 . At p > p*, in both La 1.6-x Nd 0.4 Sr x CuO 4 and La 1.8-x Eu 0.2 Sr x CuO 4 with
The thermal conductivity κ of the cuprate superconductor La1.6−xNd0.4SrxCuO4 was measured down to 50 mK in seven crystals with doping from p = 0.12 to p = 0.24, both in the superconducting state and in the magnetic field-induced normal state. We obtain the electronic residual linear term κ0/T as T → 0 across the pseudogap critical point p = 0.23. In the normal state, we observe an abrupt drop in κ0/T upon crossing below p , consistent with a drop in carrier density n from 1+p to p, the signature of the pseudogap phase inferred from the Hall coefficient. A similar drop in κ0/T is observed at H = 0, showing that the pseudogap critical point and its signatures are unaffected by the magnetic field. In the normal state, the Wiedemann-Franz law, κ0/T = L0/ρ(0), is obeyed at all dopings, including at the critical point where the electrical resistivity ρ(T ) is T -linear down to T → 0. We conclude that the non-superconducting ground state of the pseudogap phase at T = 0 is a metal whose fermionic excitations carry heat and charge as conventional electrons do.
Five transport coefficients of the cuprate superconductor Bi 2 Sr 2−x La x CuO 6+δ were measured in the normal state down to low temperature, reached by applying a magnetic field (up to 66 T) large enough to suppress superconductivity. The electrical resistivity, Hall coefficient, thermal conductivity, Seebeck coefficient, and thermal Hall conductivity were measured in two overdoped single crystals, with La concentration x = 0.2 (T c = 18 K) and x = 0.0 (T c = 10 K). The samples have dopings p very close to the critical doping p where the pseudogap phase ends. The resistivity displays a linear dependence on temperature whose slope is consistent with Planckian dissipation. The Hall number n H decreases with reduced p, consistent with a drop in carrier density from n = 1 + p above p to n = p below p . This drop in n H is concomitant with a sharp drop in the density of states inferred from prior NMR Knight shift measurements. The thermal conductivity satisfies the Wiedemann-Franz law, showing that the pseudogap phase at T = 0 is a metal whose fermionic excitations carry heat and charge as do conventional electrons. The Seebeck coefficient diverges logarithmically at low temperature, a signature of quantum criticality. The thermal Hall conductivity becomes negative at low temperature, showing that phonons are chiral in the pseudogap phase. Given the observation of these same properties in other, very different cuprates, our study provides strong evidence for the universality of these five signatures of the pseudogap phase and its critical point.
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