# Topology of Helium 3A and 3B

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The question concerns the topology and dimensions of Helium 3A and 3B

A. The Helium 3A phase shows the same low energy excitations as those of a 2 spatial dimensional chiral p-wave superconductor --- with the half-quantum vortex in a chiral p-wave superconductor of spinful fermions (as the order parameter of A phase of 3He). The chiral p-wave superconductor is a gapped long range entangled state with topological order.

B. The Helium 3B phase shows the nature of 3 spatial dimensional topological superconductor (TSC) with time reversal symmetry $$T^2=(-1)^f$$. The TSC is a gapped short range entangled state protected by the time reversal symmetry known as symmetry protected order.

## questions

• (Why) are Helium 3A and 3B are realized in different dimensions? 2 spatial vs. 3 spatial dimensions? Should they live in the same phase diagram with the same dimensions?

• Why are Helium 3A and 3B have realized different long vs short range entanglement?

This post imported from StackExchange Physics at 2020-12-15 17:03 (UTC), posted by SE-user annie marie heart
asked Nov 13, 2020

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