Quantum Monte Carlo study of a magnetic-field-driven two-dimensional superconductor-insulator transition

2008/10/29 by Kwangmoo Kim, D. Stroud, David Stroud · 1 citation
Mathematics · Physics and Astronomy · #Classical XY model #Condensed matter physics #Coupling (piping) #Coupling constant #Josephson effect #Magnetic field #Magnetic flux quantum #Mathematical physics #Mathematics #Monte Carlo method #Order (exchange) #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Quantum phase transition #Superconductivity #Theoretical and Computational Physics #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevb.78.174517

17 pages, 23 figures, accepted for publication in Phys. Rev. B

arxiv created 2008/10/29 · openalex publication_date 2008/11/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We numerically study the superconductor-insulator phase transition in a model disordered two-dimensional (2D) superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the (2+1)D XY model in the presence of both disorder and magnetic field. The XY coupling is assumed to have the form \ensuremath-J cos(\ensuremathθ_i\ensuremath-\ensuremathθ_j\ensuremath-A_ij), where A_ij has a mean of zero and a standard deviation \ensuremathΔA_ij. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The different values \ensuremathΔA_ij then correspond to an applied field such that the average number of flux quanta per plaquette has various integer values N: larger N corresponds to larger \ensuremathΔA_ij. For any value of \ensuremathΔA_ij, there appears to be a critical coupling constant K_c(\ensuremathΔA_ij)=√[J/(2U)]_c, where U is the charging energy, below which the system is a Mott insulator; there is also a corresponding critical conductivity \ensuremathσ^\ensuremath∗(\ensuremathΔA_ij) at the transition. For \ensuremathΔA_ij=\ensuremath∞, the order parameter of the transition is a renormalized coupling constant g. Using a numerical technique appropriate for disordered systems, we show that the transition at this value of \ensuremathΔA_ij takes place from an insulating (I) phase to a Bose glass (BG) phase, and that the dynamical critical exponent characterizing this transition is z\ensuremath∼1.3. By contrast, z=1 for this model at \ensuremathΔA_ij=0. We suggest that the superconductor-to-insulator transition is actually of this I to BG class at all nonzero \ensuremathΔA_ij's, and we support this interpretation by both numerical evidence and an analytical argument based on the Harris criterion [A. B. Harris, J. Phys. C 7, 1671 (1974)]. K_c is found to be a monotonically increasing function of \ensuremathΔA_ij. For certain values of K, a disordered Josephson array may undergo a transition from an ordered, Bose glass phase to an insulator with increasing \ensuremathΔA_ij.

Citations

• Quantum phase transitions in the two-dimensional hardcore boson model
• Continuous Quantum Phase Transitions
• Thickness-Magnetic Field Phase Diagram at the Superconductor-Insulator Transition in 2D
• Superfluid-insulator transition of the Josephson-junction array model with commensurate frustration
• Phase Diagram of a Disordered Boson Hubbard Model in Two Dimensions
• Suppression of 2D superconductivity by the magnetic field: Quantum corrections vs. The superconductor-insulator transition
• Effect of random defects on the critical behaviour of Ising models
• Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition

Cited by

• Disorder influences the quantum critical transport at a superconductor-to-insulator transition