# Gapless excitations of axially symmetric vortices in systems with tensorial order parameter

## Abstract

We extend the results of previous work on vortices in systems with tensorial order parameters. Specifically, we focus our attention on systems with a Ginzburg–Landau free energy with a global U(1){sub P}×SO(3){sub S}×SO(3){sub L} symmetry in the phase, spin and orbital degrees of freedom. We consider axially symmetric vortices appearing on the spin–orbit locked SO(3){sub S+L} vacuum. We determine the conditions required on the Ginzburg–Landau parameters to allow for an axially symmetric vortex with off diagonal elements in the order parameter to appear. The collective coordinates of the axial symmetric vortices are determined. These collective coordinates are then quantized using the time dependent Ginzburg–Landau free energy to determine the number of gapless modes propagating along the vortex.

- Authors:

- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22403380

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 348; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AXIAL SYMMETRY; COLLECTIVE EXCITATIONS; DEGREES OF FREEDOM; FIELD THEORIES; FREE ENERGY; GINZBURG-LANDAU THEORY; L-S COUPLING; ORDER PARAMETERS; SO-3 GROUPS; TIME DEPENDENCE; VORTICES

### Citation Formats

```
Peterson, Adam J., E-mail: pete5997@umn.edu, Shifman, Mikhail, E-mail: shifman@umn.edu, and Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455.
```*Gapless excitations of axially symmetric vortices in systems with tensorial order parameter*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.05.010.

```
Peterson, Adam J., E-mail: pete5997@umn.edu, Shifman, Mikhail, E-mail: shifman@umn.edu, & Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455.
```*Gapless excitations of axially symmetric vortices in systems with tensorial order parameter*. United States. doi:10.1016/J.AOP.2014.05.010.

```
Peterson, Adam J., E-mail: pete5997@umn.edu, Shifman, Mikhail, E-mail: shifman@umn.edu, and Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455. Mon .
"Gapless excitations of axially symmetric vortices in systems with tensorial order parameter". United States. doi:10.1016/J.AOP.2014.05.010.
```

```
@article{osti_22403380,
```

title = {Gapless excitations of axially symmetric vortices in systems with tensorial order parameter},

author = {Peterson, Adam J., E-mail: pete5997@umn.edu and Shifman, Mikhail, E-mail: shifman@umn.edu and Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455},

abstractNote = {We extend the results of previous work on vortices in systems with tensorial order parameters. Specifically, we focus our attention on systems with a Ginzburg–Landau free energy with a global U(1){sub P}×SO(3){sub S}×SO(3){sub L} symmetry in the phase, spin and orbital degrees of freedom. We consider axially symmetric vortices appearing on the spin–orbit locked SO(3){sub S+L} vacuum. We determine the conditions required on the Ginzburg–Landau parameters to allow for an axially symmetric vortex with off diagonal elements in the order parameter to appear. The collective coordinates of the axial symmetric vortices are determined. These collective coordinates are then quantized using the time dependent Ginzburg–Landau free energy to determine the number of gapless modes propagating along the vortex.},

doi = {10.1016/J.AOP.2014.05.010},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = ,

volume = 348,

place = {United States},

year = {2014},

month = {9}

}