Large Fermi Surface of Heavy Electrons at the Border of Mott Insulating State in NiS2

Abstract

One early triumph of quantum physics is the explanation why some materials are metallic whereas others are insulating. While a treatment based on single electron states is correct for most materials this approach can fail spectacularly, when the electrostatic repulsion between electrons causes strong correlations. Not only can these favor new and subtle forms of matter, such as magnetism or superconductivity, they can even cause the electrons in a half-filled energy band to lock into position, producing a correlated, or Mott insulator. The transition into the Mott insulating state raises important fundamental questions. Foremost among these is the fate of the electronic Fermi surface and the associated charge carrier mass, as the Mott transition is approached. We report the first direct observation of the Fermi surface on the metallic side of a Mott insulating transition by high pressure quantum oscillatory measurements in NiS2. Our results point at a large Fermi surface consistent with Luttinger's theorem and a strongly enhanced quasiparticle effective mass. These two findings are in line with central tenets of the Brinkman-Rice picture of the correlated metal near the Mott insulating state and rule out alternative scenarios in which the carrier concentration vanishes continuously at the metal-insulator transition.

Figure 1. Resistivity of NiS₂ under pressure.

For pressures larger than 2.6 GPa, a rapid drop in the resistivity is observed at a temperature T_MIT, defined from the steepest slope. (Inset) Schematic representation of the formation of upper and lower Hubbard bands for large Coulomb interaction U, and of the emergence of a coherent quasiparticle peak at the chemical potential, when the bandwidth W is increased, for instance by tuning the lattice density under pressure.

Figure 2. High-pressure phase diagram of NiS₂.

Solid circles and triangles represent the transition temperatures of the MIT and ferromagnetic order (cf. Supplementary information II) as extracted from resistivity, respectively. Open squares and triangles reflect the magnetic transition temperatures in the metallic and insulating state from Refs ,, respectively. Left inset shows the pyrite structure of NiS₂ with the sulphur dimers indicated. Right inset shows the evolution of room-temperature (red triangles) and low-temperature (blue triangles) resistivity.

Figure 3. Quantum oscillations in the metallic phase of NiS₂.

(A) We analyze the derivative dF/dH of the TDO frequency F with respect to field H. Numerical differentiation used locally fitted polynomials. A smooth background has been subtracted. Plotting against inverse magnetic field reveals the characteristic periodicity in 1/H of quantum oscillations. Data obtained from several sweeps with different sweep rates are averaged thus ruling out parasitic signals as a source of 1/H periodicity. (B) Power spectra of the Fourier transformed signal were obtained at several temperatures. The magnetic field was oriented along the crystallographic (100) direction within the cubic unit cell notation.

Figure 4. Determination of the effective mass.

The temperature dependence of the quantum oscillation amplitude (solid circles) is fitted with the Lifshitz-Kosevich form for two subsequent runs (solid red line). Vertical lines reflect standard errors estimated from background in the Fourier spectrum close to 6 kT (cf. Fig. 3).

Figure 5. Calculated Fermi surface.

The Fermi surface was determined from band structure calculations using the lattice parameters and atomic positions as determined by our x-ray diffraction (see Supplementary information I). Besides the major sheets depicted here we find two small pockets in the Brillouin-zone corners. The solid red line on the first sheet represents its belly orbit.