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Physical Review B

Elastically driven polaron patterns: Stripes and glass phases

Panagiotis Maniadis, Turab Lookman, A. R. Bishop

Published Jul 18, 2011• 3 citations
Publisher

Abstract

We investigate a model of elasticity-driven polaron pattern formation on a two-dimensional lattice at finite temperatures. We show that, at high densities, polaron stripes (glass-like) form when the gas is cooled. These stripes melt to a polaron gas upon heating. We attribute the emergent behavior to the role of the long-range, directional elastic interactions that favor a minimum in energy for polaron stripe formation.

DOI
10.1103/physrevb.84.024304

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We investigate a model of elasticity-driven polaron pattern formation on a two-dimensional lattice at finite temperatures. We show that, at high densities, polaron stripes (glass-like) form when the gas is cooled. These stripes melt to a polaron gas upon heating. We attribute the emergent behavior to the role of the long-range, directional elastic interactions that favor a minimum in energy for polaron stripe formation.
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We predict a stable density-wave-type supersolid phase of a dilute gas of tilted dipolar bosons in a two-dimensional (2D) geometry. This many-body phase is manifested by the formation of the stripe pattern and elasticity coexisting together with the Bose-Einstein condensation and superfluidity at zero temperature. With the increasing of the tilting angle the type of the gas-supersolid transition changes from the first order to the second-order one despite the 2D character of the system, whereas the anisotropy and many-body stabilizing interactions play crucial roles. Our approach is based on the numerical analysis of the phase diagram using the simulated annealing method for a free-energy functional. The predicted supersolid effect can be realized in a variety of experimental setups ranging from excitons in heterostructures to cold atoms and polar molecules in optical potentials.
Motivated by the stripes of the high-Tc{T}_{c}Tc​ cuprates the problem was introduced recently of a system of free elastic quantum strings interacting via a hard-core condition embedded in 2+12+12+1 dimensions. At zero temperature this system is always a solid due to ``quantum-entropic'' (or ``kinetic'') interactions which dominate at long wavelengths. The high-temperature limit of this problem corresponds with thermally meandering elastic lines in two dimensions and this system is well known to be dominated by literal entropic interactions. Here we analyze in detail what happens in between zero and high temperature. We identify a ``renormalized classical'' intermediate regime where the on-string fluctuations have become predominantly quantum mechanical. Surprisingly, the entropic interactions keep their high-temperature nature in this regime. At a low, but finite temperature the quantum-mechanical kinetic interactions take over rather suddenly. Despite their origin in long-wavelength quantum fluctuations these are not affected by thermal fluctuations when temperature is low enough.
We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.
The influence of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of ${t}^{\ensuremath{'}}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest-neighbor intersite bipolaron. The role of ${t}^{\ensuremath{'}},$ electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.
Fluctuations typically destroy long-range order in two-dimensional (2D) systems, posing a fundamental challenge to the existence of exotic states like supersolids, which paradoxically combine solid-like structure with frictionless superfluid flow. While long-predicted, the definitive observation of a 2D supersolid has remained an outstanding experimental goal. Here, we report the observation of a supersolid stripe phase in a strongly dipolar quantum gas of erbium atoms confined to 2D. We directly image the periodic density modulation, confirming its global phase coherence through matter-wave interference and demonstrating its phase rigidity relevant to the low-energy Goldstone mode, consistent with numerical calculations. Through collective excitation measurements, we demonstrate the hydrodynamic behavior of the supersolid. This work highlights a novel mechanism for supersolid formation in low dimensions, and opens the door for future research on the intricate interplay between temperature, supersolidity, and dimensionality.