Giant Viscoelasticity near Mott Criticality in ${\mathrm{PbCrO}}_3$ with Large Lattice Anomalies

Coupling of charge and lattice degrees of freedom in materials can produce intriguing electronic phenomena, such as conventional superconductivity where the electrons are mediated by lattice for creating supercurrent. The Mott transition, which is a source for many fascinating emergent behaviors, is originally thought to be driven solely by correlated electrons with an Ising criticality. Recent studies on the known Mott systems have shown that the lattice degree of freedom is also at play, giving rise to either Landau or unconventional criticality. However, the underlying coupling mechanism of charge and lattice degrees of freedom around the Mott critical end point remains elusive, leading to difficulties in understanding the associated Mott physics. Here, we report a study of Mott transition in cubic ${\mathrm{PbCrO}}_3$ by measuring the lattice parameter, using high-pressure x-ray diffraction techniques. The Mott criticality in this material is revealed with large lattice anomalies, which is governed by giant viscoelasticity that presumably results from a combination of lattice elasticity and electron viscosity. Because of the viscoelastic effect, the lattice of this material behaves peculiarly near the critical end point, inconsistent with any existing university classes. We argue that the viscoelasticity may play as a hidden degree of freedom behind the Mott criticality.

Figure 1

Isothermal high-$P$ XRD patterns and $P\text{−}V$ data for ${\mathrm{PbCrO}}_3$. (a),(b) Contour plots of high-$P$ XRD patterns collected upon both compression and decompression (“$D$”) at 150 and 430 K, respectively. Inset is the unit cell. The incident x-ray wavelength is $\lambda =0.4246\AA$. (c)–(k) Isothermal $P\text{−}V$ data. In each panel, the cyan, dark yellow, and yellow shaded regions correspond to the phase-transition hysteresis loss, viscoelastic dissipation, and recoverable elastic energy, respectively. The error bars are too small to show.

Figure 2

Lattice Mott criticality near the end point $(P_c,T_c)$ and phase diagram of ${\mathrm{PbCrO}}_3$. (a) $P\text{−}V$ data at $T_c=430\mathrm{K}$. Compression $P\text{−}V$ line of $\beta$ can be divided into three different regions of I, II, and III, as highlighted in cyan, blue, and green, respectively. (b) $P\text{−}T$ phase diagram. The two spinodal lines are defined by the forward and reverse $\alpha \text{−}\beta$ thresholds. The delocalized electrons in $\beta \text{−}{\mathrm{PbCrO}}_3$ have three different states of “liquid,” “gas,” and viscoelastic state. Paramagnetic (PM)-to-antiferromagnetic (AFM) transition line ($T_N$) determined by high-$P$ neutron diffraction will be published elsewhere.

Figure 3

Mott critical behaviors, energy dissipation, and viscoelastic stiffness. (a) Lattice density vs pressure. (b) Lattice density vs temperature for metallic phase on the border of coexistence region. (c) Comparison of critical exponents of ${\mathrm{PbCrO}}_3$ with those of universality (e.g., mean-field, 2D-Ising, and 3D models [9]). Critical exponents of ${({\mathrm{V}}_{1-x}{\mathrm{Cr}}_x)}_2{\mathrm{O}}_3$ and $\kappa \text{−}\mathrm{Cl}$ are added [6, 9]. (d) Total elastic energy storage in $\beta \text{−}{\mathrm{PbCrO}}_3$, viscoelastic and hysteresis dissipations, and the ratio of viscoelastic loss to the stored elastic energy vs temperature derived from integrations of the $P\text{−}V$ data [Figs. 1 and Fig. S12]. The total elastic energy is the sum of viscoelastic and recoverable elastic energies. (e) Isothermal $P\text{−}V$ data for $\beta \text{−}{\mathrm{PbCrO}}_3$ collected during decompression. The inset is an enlarged portion of the cases at 390 and 430 K. Each blue line represents a fit of the associated isothermal $P\text{−}V$ data to a second-order Birch-Murnaghan EOS. (f) Isothermal bulk moduli for both α- and $\beta \text{−}{\mathrm{PbCrO}}_3$.