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arXiv:cond-mat/9911473

Dissipation-Driven Breakdown of Universality in Two-Dimensional Superconductors

Klaus Voelker

Published Nov 30, 1999• 0 citations
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Abstract

The influence of gapless dissipative degrees of freedom on the superconductor-insulator transition in two dimensions is investigated. We develop a series expansion for the free energy of a (2+1)-dimensional XY model coupled to a bosonic heat bath that can be approximately summed to all orders. The calculation explicitly conserves topological excitations. We derive the zero temperature phase diagram and the free energy critical exponent, and find a transition from universal to non-universal scaling behavior as the coupling to the dissipative environment is increased, implying the existence of a new universality class.

DOI
10.48550/arxiv.cond-mat/9911473

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The influence of gapless dissipative degrees of freedom on the superconductor-insulator transition in two dimensions is investigated. We develop a series expansion for the free energy of a (2+1)-dimensional XY model coupled to a bosonic heat bath that can be approximately summed to all orders. The calculation explicitly conserves topological excitations. We derive the zero temperature phase diagram and the free energy critical exponent, and find a transition from universal to non-universal scaling behavior as the coupling to the dissipative environment is increased, implying the existence of a new universality class.
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We use quantum Monte Carlo simulations to calculate the phase diagram and the correlation functions for the quantum phase transitions in the two-dimensional dissipative quantum XY model with and without fourfold anisotropy. Without anisotropy, the model describes the superconductor-to-insulator transition in two-dimensional dirty superconductors. With anisotropy, the model represents the loop-current order observed in the underdoped cuprates and its fluctuations, as well as the fluctuations near the ordering vector in simple models of two-dimensional itinerant ferromagnets and itinerant antiferromagnets. These calculations test an analytic solution of the model which reexpressed it in terms of topological excitations: the vortices with interactions only in space but none in time, and warps with leading interactions only in time but none in space, as well as subleading interactions which are both space and time dependent. For parameters where the proliferation of warps dominates the phase transition, the critical fluctuations as functions of the deviation of the dissipation parameter $\ensuremath{\alpha}$ on the disordered side from its critical value ${\ensuremath{\alpha}}_{c}$ are scale invariant in imaginary time $\ensuremath{\tau}$ as the correlation length in time ${\ensuremath{\xi}}_{\ensuremath{\tau}}={\ensuremath{\tau}}_{c}{e}^{{[{\ensuremath{\alpha}}_{c}/({\ensuremath{\alpha}}_{c}\ensuremath{-}\ensuremath{\alpha})]}^{1/2}}$ diverges, where ${\ensuremath{\tau}}_{c}$ is a short-time cutoff. On the other hand, the spatial correlations develop with a correlation length ${\ensuremath{\xi}}_{x}\ensuremath{\approx}{\ensuremath{\xi}}_{0}ln({\ensuremath{\xi}}_{\ensuremath{\tau}})$, with ${\ensuremath{\xi}}_{0}$ of the order of a lattice constant. The dynamic correlation exponent zzz is therefore $\ensuremath{\infty}$. The Monte Carlo calculations also directly show warps and vortices. Their densities and correlations across the various transitions in the model are calculated and related to those of the order-parameter correlations in the dissipative quantum XY model.
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The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical XY model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of the magnetic field is characterized by the frustration f. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent z, the correlation length exponent \ensuremath{\nu}, and the universal conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z\ensuremath{\approxeq}1, 1/\ensuremath{\nu}\ensuremath{\approxeq}1.5, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.52\ifmmode\pm\else\textpm\fi{}0.03, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.83\ifmmode\pm\else\textpm\fi{}0.06. The value of ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.27\ifmmode\pm\else\textpm\fi{}0.04 for the case f=0, and z=1.14\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.49\ifmmode\pm\else\textpm\fi{}0.04 for the case f=1/2.