Numerical study of quantum vortex phase diagram in two-dimensional superconductors

Abstract

Vortex phase diagrams of weakly disordered two-dimensional ͑2D͒ superconductors under a magnetic field perpendicular to the plane are numerically studied based on a recent development on the corresponding issue in three-dimensional ͑3D͒ systems with a low density of columnar defects at high temperatures. By examining the field dependences of magnetic quantities and the glass correlation, two consecutive first-order transitions ͑FOTs͒ are found to occur in weakly disordered cases even at low but finite temperatures, and the lower FOT is identified with a remnant of the melting transition of Bragg-Bose glass at zero temperature. The resulting phase diagram is discussed in relation to a FOT-like behavior found in superconducting thin films.

Vortex lattice melting in two-dimensional superconductors in intermediate fields

“…In our simulations, the field dependence has been examined at the fixed number of field-induced vortices N s and by changing L j following our previous work in LLL [8], because numerical results become much clearer than those under fixed L j and a field-induced change of N s . We have performed three simulations with N s = 36 and six LLs (0 ≤ n ≤ 5), N s = 64 and the six LLs at only h = 0.1 and 0.3, and N s = 36 and seven LLs (0 ≤ n ≤ 6).…”

“…As a thermodynamic evidence of a first order transition, we focus on the hysteresis ∆E of the internal energy, which can be defined by [8]…”

“…In the warming process, the vortices is assumed to form the triangular lattice at a low enough temperature. This condition can be expressed as [5,8] c n,l = (−1) m(m+1)/2 πN…”

“…Our simulations have been performed by fixing [8] the number of vortices N s in the manner commensurate with the triangular lattice…”