Bound states of edge dislocations: The quantum dipole problem in two dimensions

Details Bound states of edge dislocations: The quantum dipole problem in two dimensions Bound states of edge dislocations: The quantum dipole problem in two dimensions

2009-12-18

arxiv.org/abs/0912.3760v1

Phys. Rev. B 81, 064516 (2010)

Physics

Condensed Matter

Other Condensed Matter

6 pages, 3 figures, submitted to PRB

Scientific paper

10.1103/PhysRevB.81.064516

We investigate bound state solutions of the 2D Schr\"odinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. The knowledge of these states could be useful for understanding a wide variety of physical systems, including superfluid behavior along dislocations in solid $^4$He. We present a review of the results obtained by previous workers together with an improved variational estimate of the ground state energy. We then numerically solve the eigenvalue problem and calculate the energy spectrum. In our dimensionless units, we find a ground state energy of -0.139, which is lower than any previous estimate. We also make successful contact with the behavior of the energy spectrum as derived from semiclassical considerations.

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