Quantum criticality at cryogenic melting of polar bubble lattices

Abstract

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr_0.4Ti_0.6)O₃ (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Fig. 1. Topological patterns for different Trotter Numbers.

(a) P = 1, (b) P = 2, (c) P = 4, (d), P = 8, (e) P = 16 and (f) P = 32 for PZT films under zero electric field. The $u_z$ represents local modes.

Fig. 2. Phase diagram of PZT films as a function of electric fields.

a Phase diagram of PZT films as a function of electric field from CMC calculations (P = 1). a1-a5 Selected topological patterns from the last configuration of CMC simulations for Phases I, II, III, IV and V in the middle (001) layer of a 26 × 26 × 5 supercell. (b) Same as panel (a) but from PI-QMC calculations (P = 32). b1-b8 Selected topological patterns from PI-QMC simulations for Phases I, II, I’, III, IV, IV’, IV” and V in the middle (001) layer of a 26 × 26 × 5 supercell. The yellow (blue) color indicates dipoles that are aligned along the [001] $\left(\left[00\overline{1}\right]\right)$ pseudo-cubic direction.

Fig. 3. The zeroth Betti number (β₀) as a function of electric fields.

a CMC (P = 1) simulations. b PI-QMC (P = 32) simulations.

Fig. 4. Piezoelectricity from CMC and PI-QMC.

The ${\eta }_3$ strain as a function of electric field for CMC (P = 1) (a) and PI-QMC (P = 32) (b) simulations. The resulting piezoelectric coefficient ($d_{33}$) as a function of electric field for CMC (c) and PI-QMC (d) computations. The red region in (d) represents the quantum critical fluctuations region.