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Physics of the Solid State

Charge order–superfluidity transition in a two-dimensional system of hard-core bosons and emerging domain structures

Alexander S. Moskvin, Yu. D. Panov, Filipp N. Rybakov, Aleksandr Borisovich Borisov

Published Nov 1, 2017• 0 citations
Publisher

Abstract

We have used high-performance parallel computations by NVIDIA graphics cards applying the method of nonlinear conjugate gradients and Monte Carlo method to observe directly the developing ground state configuration of a two-dimensional hard-core boson system with decrease in temperature, and its evolution with deviation from a half-filling. This has allowed us to explore unconventional features of a charge order—superfluidity phase transition, specifically, formation of an irregular domain structure, emergence of a filamentary superfluid structure that condenses within of the charge-ordered phase domain antiphase boundaries, and formation and evolution of various topological structures.

DOI
10.1134/s1063783417110233

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We have used high-performance parallel computations by NVIDIA graphics cards applying the method of nonlinear conjugate gradients and Monte Carlo method to observe directly the developing ground state configuration of a two-dimensional hard-core boson system with decrease in temperature, and its evolution with deviation from a half-filling. This has allowed us to explore unconventional features of a charge order—superfluidity phase transition, specifically, formation of an irregular domain structure, emergence of a filamentary superfluid structure that condenses within of the charge-ordered phase domain antiphase boundaries, and formation and evolution of various topological structures.
Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite-temperature Kosterlitz-Thouless transition. The relationship between low-temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
We suppose that the doping of the 2D hard-core boson system away from half-filling may result in the formation of a multicenter topological defect such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or a topological CO + BS phase separation , rather than a uniform mixed CO + BS supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to resemble that of granular superconductors, CDW materials, Wigner crystals, and multiskyrmion system akin in a quantum Hall ferromagnetic state of a 2D electron gas.
We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.
We suppose that the doping of the two-dimensional (2D) hard-core (hc) boson system away from half-filling may result in the formation of a multicenter topological inhomogeneity (defect), such as charge order (CO) bubble domain(s) with Bose superfluid (BS) and extra bosons both localized in domain wall(s), or else in a topological CO+BS\text{CO}+\text{BS}CO+BS phase separation rather than a uniform mixed CO+BS\text{CO}+\text{BS}CO+BS supersolid phase. Starting from the classical model, we predict the properties of the respective quantum system. The long-wavelength behavior of the system is believed to be reminiscent of that of granular superconductors, charge-density wave materials, Wigner crystals, and multi-Skyrmion systems akin to the quantum Hall ferromagnetic state of a 2D electron gas. To elucidate the role played by quantum effects and that of the lattice discreteness, we have addressed the simplest nanoscopic counterpart of the bubble domain in the checkerboard CO phase of a 2D hc Bose-Hubbard (BH) square lattice. It is shown that the relative magnitude and symmetry of a multicomponent order parameter are mainly determined by the sign of the nearest-neighbor and next-nearest-neighbor transfer integrals. In general, the topologically inhomogeneous phase of the hc-BH system away from the half-filling can exhibit the signatures of the sss, ddd, and ppp symmetries of the off-diagonal order.
We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. Away from half-filling, we show that the presence of next-nearest-neighbor hopping in the effective Hamiltonian leads to a superfluid-to-supersolid transition at intermediate boson-phonon (b-p) couplings, while at strong-couplings the system phase separates. However, at half-filling and at a critical b-p coupling (as in the xxz-model), the system undergoes a superfluid-to-charge-density-wave transition without any signature of supersolidity. Our analyses is based on extensive calculations of the structure factor, the superfluid fraction, the Bose-Einstein condensate fraction, and the system energy at various fillings. We present a phase diagram for this system and compare it to that of the xxz-model. We also demonstrate explicitly that the next-nearest-neighbor hopping (in the absence of nearest-neighbor hopping) in the effective Hamiltonian leads only to a single transition, i.e., a first-order superfluid-to-supersolid transition.