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High-$T_{\rm{c}}$ cuprate superconductors host spin, charge and lattice instabilities. In particular, in the antiferromagnetic glass phase, over a large doping range, lanthanum based cuprates display a glass-like spin freezing with antiferromagnetic correlations. Previously, sound velocity anomalies in La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) for hole doping $p\geq 0.145$ were reported and interpreted as arising from a coupling of the lattice to the magnetic glass [Frachet, Vinograd et al., Nat. Phys. 16, 1064-1068 (2020)]. Here we report both sound velocity and attenuation in LSCO $p=0.12$, i.e. at a doping level for which the spin freezing temperature is the highest. Using high magnetic fields and comparing with nuclear magnetic resonance (NMR) measurements, we confirm that the anomalies in the low temperature ultrasound properties of LSCO are produced by a coupling between the lattice and the spin glass. Moreover, we show that both sound velocity and attenuation can be simultaneously accounted for by a simple phenomenological model originally developed for canonical spin glasses. Our results point towards a strong competition between superconductivity and spin freezing, tuned by the magnetic field. A comparison of different acoustic modes suggests that the slow spin fluctuations have a nematic character.

The nature of the pseudogap phase of hole-doped cuprate superconductors is still not understood fully. Several experiments have suggested that this phase ends at a critical hole doping level p*, but the nature of the ground state for lower doping is still debated. Here, we use local nuclear magnetic resonance and bulk ultrasound measurements to show that, once competing effects from superconductivity are removed by high magnetic fields, the spin-glass phase of La2−xSrxCuO4 survives up to a doping level consistent with p*. In this material, the antiferromagnetic-glass phase extends from the doped Mott insulator at p = 0.02 up to p* ≈ 0.19, which provides a connection between the pseudogap and the physics of the Mott insulator. Furthermore, the coincidence of the pseudogap boundary with a magnetic quantum phase transition in the non-superconducting ground state has implications for the interpretation of other experiments, particularly for transport and specific-heat measurements in high magnetic fields. NMR and ultrasound measurements show that the spin-glass phase exists in a cuprate all the way up to the doping that marks the end of the pseudogap phase. This highlights the possible connection between the pseudogap and Mott physics.

Lightly doped III-V semiconductor InAs is a dilute metal, which can be pushed beyond its extreme quantum limit upon the application of a modest magnetic field. In this regime, a Mott-Anderson metal-insulator transition, triggered by the magnetic field, leads to a depletion of carrier concentration by more than one order of magnitude. Here, we show that this transition is accompanied by a two-hundred-fold enhancement of the Seebeck coefficient which becomes as large as 11.3mV.K$^{-1}\approx 130\frac{k_B}{e}$ at T=8K and B=29T. We find that the magnitude of this signal depends on sample dimensions and conclude that it is caused by phonon drag, resulting from a large difference between the scattering time of phonons (which are almost ballistic) and electrons (which are almost localized in the insulating state). Our results reveal a path to distinguish between possible sources of large thermoelectric response in other low density systems pushed beyond the quantum limit., supplementary material on request