Truncated mass divergence in a Mott metal

Abstract

The Mott metal-insulator transition represents one of the most fundamental phenomena in condensed matter physics. Yet, basic tenets of the canonical Brinkman-Rice picture of Mott localization remain to be tested experimentally by quantum oscillation measurements that directly probe the quasiparticle Fermi surface and effective mass. By extending this technique to high pressure, we have examined the metallic state on the threshold of Mott localization in clean, undoped crystals of NiS₂. We find that i) on approaching Mott localization, the quasiparticle mass is strongly enhanced, whereas the Fermi surface remains essentially unchanged; ii) the quasiparticle mass closely follows the divergent form predicted theoretically, establishing charge carrier slowdown as the driver for the metal-insulator transition; iii) this mass divergence is truncated by the metal-insulator transition, placing the Mott critical point inside the insulating section of the phase diagram. The inaccessibility of the Mott critical point in NiS₂ parallels findings at the threshold of ferromagnetism in clean metallic systems, in which criticality at low temperature is almost universally interrupted by first-order transitions or novel emergent phases such as incommensurate magnetic order or unconventional superconductivity.

Keywords: Mott localization; high-pressure techniques; quantum oscillations.

Fig. 1.

Mott metal–insulator transition in NiS₂, which is metallic at high pressure (large effective bandwidth $W$ and therefore small ratio $U/W$) and insulating at low pressure. Magnetic order sets in below a transition temperature $T_N$ [blue line, following experimental data (19, 20)]. The Mott transition line [purple, from resistivity data (21)] ends in a critical point at high temperature. Its first-order nature implies the possibility of metastable states (dotted region) surrounding the thermodynamic transition line. At low temperature, the transition line in DMFT calculations curves away toward higher $U/W$ (dashed purple line), ending in a zero-temperature critical point (–18) (thick red arrow). The inverse carrier mass extracted in this study (red circles with errorbars) extrapolates to zero deep inside the region of the phase diagram where transport measurements show insulating behavior.

Fig. 2.

Quantum oscillations in NiS₂. (A) Quantum oscillations are clearly resolved well above the metallization pressure, down to fields as low as $<$8T (Inset). The power spectrum shows a single peak at 6.17 kT (Lower axis). (B and C) The QO amplitude (B) follows the Lifshitz–Kosevich form as a function of temperature (solid line, see SI Appendix for the relevant details), with effective mass $m^{\ast }\simeq 4.3m_e$, and a rotation study (C) at a nearby pressure produces an angle dependence of the QO frequency that closely matches expectations (solid line) for a cube-shaped FS pocket (inset). (D) Key elements of the experimental setup.

Fig. 3.

Pressure evolution of the electronic structure of NiS₂. (A) Quantum oscillations in NiS₂ at selected pressures (scaled and off-set for clarity), with corresponding power spectra to the right. (B–D) Pressure dependences of the quantum oscillation frequency (B), the effective quasiparticle mass (C) and the residual resistivity ${\rho }_0$ (d). The blue line in panel (B) is a linear least-squares fit to the frequency coming from the cubic Fermi surface (the highest frequency at each pressure). The red line in panel (C) is a least-squares fit consistent with the one shown in Fig. 1 (see text). Although the effective mass grows by more than a factor of three over the investigated pressure range, the frequency and thereby the Fermi surface cross-section changes only slightly, at a rate which is broadly consistent with the change of the unit cell volume. Panel (D) compares ${\rho }_0$ determined in high-pressure transport measurements (21) (red markers) to ${\rho }_0$ expected from the electronic mean free paths determined from the quantum oscillation analysis (blue markers, the analysis is explained in the SI Appendix). Although the quantum-oscillation-derived mean free path and the resulting ${\rho }_0$ are pressure independent (blue shaded region), direct transport measurements show a strong increase of ${\rho }_0$ on approaching the metal–insulator threshold from high pressures. This discrepancy suggests a significant and increasing volume fraction of insulating regions close to the metal–insulator threshold, which we model within 3D effective medium theory (solid red line, explained in the SI Appendix). We ascribe the saturation of the transport-derived ${\rho }_0$ below 30 kbar to surface conduction (42).