---
abstract: 'Motivated by recent interest in spin-triplet superconductors, we investigate the vortex lattice structures for this class of unconventional superconductors. We discuss how the order parameter symmetry can give rise to U(1)$\times$U(1) symmetry in the same sense as in spinor condensates, making half-quantum vortices (HQVs) topologically stable.We then calculate the vortex lattice structure of HQVs, with particular attention on the roles of the crystalline lattice, the Zeeman coupling and Meissner screening, all absent in spinor condensates. Finally, we consider how spin.orbit coupling leads to a breakdown of the U(1)$\times$U(1) symmetry in free energy and whether the HQV lattice survives this symmetry breaking. As examples, we examine simpler spin-triplet models proposed in the context of Na$_x$CoO$_2 \cdot y$H$_2$O and Bechgaard salts, as well as the better known and more complex model for Sr$_2$RuO$_4$.'
author:
- 'Suk Bum Chung$^1$, Daniel F. Agterberg$^2$, and Eun-Ah Kim$^3$'
title: Fractional vortex lattice structures in spin triplet superconductors
---

Introduction
============

A half quantum vortices (HQV) with vorticity $h/4e$, which is half that of usual Abrikosov vortex with vorticity $\Phi_0\equiv h/2e$, presents an exciting example of fractionalized topological defects. Quantization of collective topological defects provides clear cut access to the nature of the ground state. 