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nesseril
nesseril
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I am interested in the relation between the following three phases of matter (in 2D):

  • chiral $p$-wave superconductor (spineless $p_x + i p_y$ pairing)
  • $\nu=5/2$ fractional quantum Hall state
  • A-phase of ${}^3$He

I have read that all of these are topological ordered having Ising anyons as elementary excitations. All of them are at mean-field level described by a BCS theory.

However, I notice the following important difference:

  • the condensate in the superconductor is charged whereas ${}^3$He is a superfluid (so only the former has a Higgs-mechanism)
  • in $\nu=5/2$ composite fermions condense

So my question is if these three states are really equivalent (which is not clear to me). In particular, I am interested in the following:

  • do all show a degeneracy of the ground state when put on the torus? (for the superconductor this is not clear as typically, we need a vortex to bind a zero energy state)
  • is there a superflow of pairs of composite fermions in $\nu=5/2$ and what this corresponds to physically?

I am looking forward to your insights. As I have browed the internet already for some time without any good explanation, I would be also grateful if you could simply post some reference where the differences are discussed.

I am interested in the relation between the following three phases of matter (in 2D):

  • chiral $p$-wave superconductor (spineless $p_x + i p_y$ pairing)
  • $\nu=5/2$ fractional quantum Hall state
  • A-phase of ${}^3$He

I have read that all of these are topological ordered having Ising anyons as elementary excitations. All of them are at mean-field level described by a BCS theory.

However, I notice the following important difference:

  • the condensate in the superconductor is charged whereas ${}^3$He is a superfluid (so the former has a Higgs-mechanism)
  • in $\nu=5/2$ composite fermions condense

So my question is if these three states are really equivalent (which is not clear to me). In particular, I am interested in the following:

  • do all show a degeneracy of the ground state when put on the torus? (for the superconductor this is not clear as typically, we need a vortex to bind a zero energy state)
  • is there a superflow of pairs of composite fermions in $\nu=5/2$ and what this corresponds to physically?

I am looking forward to your insights. As I have browed the internet already for some time without any good explanation, I would be also grateful if you could simply post some reference where the differences are discussed.

I am interested in the relation between the following three phases of matter (in 2D):

  • chiral $p$-wave superconductor (spineless $p_x + i p_y$ pairing)
  • $\nu=5/2$ fractional quantum Hall state
  • A-phase of ${}^3$He

I have read that all of these are topological ordered having Ising anyons as elementary excitations. All of them are at mean-field level described by a BCS theory.

However, I notice the following important difference:

  • the condensate in the superconductor is charged whereas ${}^3$He is a superfluid (so only the former has a Higgs-mechanism)
  • in $\nu=5/2$ composite fermions condense

So my question is if these three states are really equivalent (which is not clear to me). In particular, I am interested in the following:

  • do all show a degeneracy of the ground state when put on the torus? (for the superconductor this is not clear as typically, we need a vortex to bind a zero energy state)
  • is there a superflow of pairs of composite fermions in $\nu=5/2$ and what this corresponds to physically?

I am looking forward to your insights. As I have browed the internet already for some time without any good explanation, I would be also grateful if you could simply post some reference where the differences are discussed.

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nesseril
nesseril
  • 113
  • 5

Difference between $\nu=5/2$ quantum Hall state, chiral p-wave superconductor, He 3

I am interested in the relation between the following three phases of matter (in 2D):

  • chiral $p$-wave superconductor (spineless $p_x + i p_y$ pairing)
  • $\nu=5/2$ fractional quantum Hall state
  • A-phase of ${}^3$He

I have read that all of these are topological ordered having Ising anyons as elementary excitations. All of them are at mean-field level described by a BCS theory.

However, I notice the following important difference:

  • the condensate in the superconductor is charged whereas ${}^3$He is a superfluid (so the former has a Higgs-mechanism)
  • in $\nu=5/2$ composite fermions condense

So my question is if these three states are really equivalent (which is not clear to me). In particular, I am interested in the following:

  • do all show a degeneracy of the ground state when put on the torus? (for the superconductor this is not clear as typically, we need a vortex to bind a zero energy state)
  • is there a superflow of pairs of composite fermions in $\nu=5/2$ and what this corresponds to physically?

I am looking forward to your insights. As I have browed the internet already for some time without any good explanation, I would be also grateful if you could simply post some reference where the differences are discussed.