Linked Questions

12
votes
3answers
1k views

Validity of mean-field approximation

In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where $...
0
votes
0answers
46 views

How does phase gets aligned in a superconductor?

I am trying to make an analogy between the spontaneous symmetry breaking occurring in magnetism and that of superconducvity, but I am struggling to make it precise. In magnetism, we know that ...
35
votes
2answers
16k views

What is a $p_x + i p_y$ superconductor? Relation to topological superconductors

I often read about s-wave and p-wave superconductors. In particular a $p_x + i p_y$ superconductor - often mentioned in combination with topological superconductors. I understand that the overall ...
2
votes
1answer
299 views

Symmetry breaking and Superfluid - Mott Insulator transition

I know my question is similar to what mentioned in this post: Symmetry breaking in Bose-Hubbard model. Yet, I don't find it clear. I've in mind a 1D Bose-Hubbard Hamiltonian. Moving from the Mott ...
11
votes
1answer
5k views

Superconductor symmetry breaking

When water freezes continuous translational symmetry is broken. When a metal becomes superconducting, what is the symmetry that gets broken?
3
votes
1answer
376 views

Ginzburg criterion and superconductivity

The Ginzburg criterion tells us quantitatively when mean field theory is valid. If $\phi$ is the order parameter of the system, then mean field theory requires that the fluctuations in the order ...
6
votes
2answers
420 views

Topology and Superconductor Symmetry Breaking

I read an article today on stack exchange titled "Superconductor Symmetry Breaking". The 2016 Nobel Prize was awarded for research on topological phase transitions in the study of superconductors and ...
6
votes
1answer
627 views

BCS state with well-defined particle number - interpretation?

It's common knowledge (and has been discussed in other questions on this site) that the standard BCS ground state $ \left|\Psi_{BCS}\right\rangle = \prod_k \left( u_k + v_k c_{k\uparrow}^{\dagger} c_{-...
14
votes
2answers
3k views

Why is the Fermi surface stable?

As a condensed matter physicist, I take it for granted that a Fermi surface is stable. But it is stable with respect to what? For instance, Cooper pairing is known as an instability of the Fermi ...
13
votes
2answers
2k views

What does “particle number conservation” mean in condensed matter physics?

What exactly does it imply about a condensed matter system to have particle number conserved or not conserved? For example, why does the superconducting phase break particle number conservation while ...