Unzipping of vortex lines from extended defects in superconductors with point disorder Anatoli Polkovnikov Yariv Kafri, David Nelson Department of Physics, Harvard University.
Plan of the talk 1.Unzipping a single vortex from a columnar pin. 2.Unzipping from higher-dimensional defects. Relation to anomalous diffusion. 3.Unzipping from a two-dimensional Luttinger liquid. Revealing the Luttinger liquid parameter.
Unzipping experiment x Our goal is to find
Elastic energy Partition function: Formal analogy with quantum mechanics: identify with the imaginary time of a quantum particle,. MFM Tip f x
No disorder, unzipping from a columnar pin energy of the unbound piece energy of the localized piece N. Hatano, D. Nelson (1997)
Add point disorder on the pin D.K. Lubensky and D.R. Nelson, 2000
Problem with averaging over disorder in the denominator Edwards-Anderson: replica trick Disorder averaging is trivial for integer positive m!
Analytic expression for unzipping from a columnar pin: is the disorder strength, =1 Replica trick gives exact result!
Unzipping from a twin plane Anomalous diffusion in the presence of point disorder.
x is the anomalous diffusion exponent. Relation between energy fluctuations and anomalous diffusion D. Huse, C. Henley (1985)
In general Columnar pin: d=1, d =1/2 Twin plane: d=2, d =1/3 Twin plane: Measuring critical properties of the unzipping transition one can extract anomalous diffusion exponent.
Numerical verification Use finite size scaling LL G is the scaling function.
Results of numerical simulations. / L (f c -f) L 2/3
What if disorder is both on the defect and in the bulk? At long distances disorder on the defect always dominates and determines universal properties of the unzipping transition.
Unbinding from a columnar pin into 2D bulk with disorder in the bulk. Extracted best scaling exponent from comparison of L x and L x /2. b =0.03 disorder strength in the bulk c =0 (main graph) disorder strength on the defect
Unzipping from a 2D defect containing many flux lines. Flux lines are interacting. Use elastic description: u is the coarse- grained phonon displacement field Luttinger liquid parameter
Method of images: energy of a dislocation distance from the boundary is equal to a half of energy of a dislocation pair of opposite signs. Schulz, Halperin, Henley (1982) Compute boson-boson correlation function using Luttinger liquid formalism. I. Affleck, W. Hofstetter, D.R. Nelson, U. Schollwöck (2004)
Interactions renormalize the prefactor but do not change the power. Interactions renormalize the power. Unzipping transition becomes discontinuous.
Conclusions 1.Unzipping transition of a single flux line from an extended defect is universal. 2.The critical exponent depends only on the dimensionality of the defect. It is directly related to the anomalous wondering exponent in 2D defects. 3.Critical properties of the unzipping transition from a twin plane containing other flux lines depend on a single (Luttinger) parameter, which is proportional to the ratio of temperature and the geometric mean of the elastic moduli.