Generalized Anisotropic Scaling Theory and the Transverse Meissner Transition

Abstract

We consider a depinning transition in vortex systems with columnar disorder and tilted applied magnetic fields. From scaling arguments and Monte Carlo simulations, we find that this transverse Meissner transition is governed by a fixed point which is anisotropic in all three directions. This generalization of conventional anisotropic scaling means that the correlation length in different directions diverges with different rates, and we derive exact results for the anisotropy exponents. We make predictions which can be tested in experiments on superconductors with columnar disorder.

A vortex solid-to-liquid transition with fully anisotropic scaling

“…Another view is to neglect the vortex segment in between the columns and only consider the depinning of vortex segments along the columns. On a short length scale, this is then identical to the situation of a transverse Meissner phase, which was studied theoretically in [2]. As indicated above, such an assumption leads to the same relative order between the exponents and can qualitatively explain our results.…”

“…This can be directly related to a general assumption based on different critical exponents for the glass correlation lengths associated with the three spatial directions. More specifically, assuming correlation lengths ξ x = ξ χ , ξ y = ξ and ξ z = ξ ζ where ξ ∼ |T − T c | ν and ν is the static critical exponent and a correlation time for critical scaling down τ ∼ ξ z , one obtains [2,3]. Within this assumption, the only way to obtain three different values of s i is to have different critical scaling exponents of the correlation lengths (1 = χ = ζ = 1), i.e.…”

“…For a magnetic field tilted away from the columnar defects at a sufficiently small angle, the vortices will stay on the columns leading to a transverse Meissner effect. In this case, the transverse component of the magnetic field makes the three directions non-equivalent, which should give different critical exponents in all directions [2]. In a recent study on untwinned YBa 2 Cu 3 O 7−δ (YBCO) single crystals with columnar defects and an inclined magnetic field, we Figure 1.…”

Fully anisotropic superconducting transition in ion-irradiatedYBa2Cu3O7−δwith a tilt

“…The transverse component of the magnetic field then makes all three directions nonequivalent and opens for the possibility of fully anisotropic scaling, i.e., with different critical exponents in all directions. 10 Furthermore, the problem of vortex depinning from columnar defects is formally equivalent to the Boseglass transition of bosons in a random potential. 3 In this analogy, the tilted magnetic field corresponds to an imaginary vector potential, resulting in a non-Hermitian localization problem.…”

“…As the tilt angle or the temperature is increased the vortices will eventually depin and enter the vortex liquid phase. The transverse component of the magnetic field then makes all three directions nonequivalent and opens for the possibility of fully anisotropic scaling, i.e., with different critical exponents in all directions [10]. Furthermore, the problem of vortex depinning from columnar defects is formally equivalent to the Boseglass transition of bosons in a random potential [3].…”