# What is the source of Chirality in Chiral superconductivity?

1. Chiral super conductors, have a gap function that rotates in cw or ccw direction as wave vector rotates on fermi surface. E.g. $\Delta_{k}=k_{x}\pm ik_{y}$ or $\Delta_{k}\propto exp(il\phi)$ where $\phi$ is angle between $k_{x}$ and $k_{y}$.

2. we can write orde parameter in more generl form but not the most general form as $\Delta=(d_{0,p}+\mathbf{\mathbf{d_{p}\cdot\mathbf{\mathbf{\tau}}}})i\tau_{2}$, where $\tau$ is pauli matrices in spin basis. And if our order parameter is symmetric matrix we have singlet pairing case, and if we have anti symmetric matrix we have triplet case.

3. i am not at all sure about this part. But as far as i understand the order paramater is a consequence of interaction, i.e. it depends to the two body attractive potential between electrons. And we can write this potential in terms of angular momentum components i.e. $V_{k-k'}=\sum(2l+1)V_{l}(k,k')P_{l}(\mathbf{\hat{k}\cdot\mathbf{\hat{k}'}})$ where P is legendre polynomials and we sum on l index. But we have some dominant channel where only for some particular $l$ we have dominant contributions. and that $l$ is actually our orbital angular momentum number. and if we have even $l$ then we have singlet case in 2, and if we odd $l$ we an have triplet case. hence we can indeed have a chiral superconductor even in singlet case.

Now my first question is on terminology, when we talk about s wave and p wave superconductors, we talk about $l$ is whether 0 or 1. but when we talk about singlet and triplet pairing we talk about evenness of $l$ and symmetry of $\Delta$. is it true? but for example in d wave pairing we can have chiral spin singlet solution.

And my actual question is, the chirality actually comes from nothing but the interaction potential. In scattering theory as far as i remember we have s wave scattering, p wave scattering ect. When we write Schrodinger equation for scattering we have angular momentum part in the equation, which produces centrifugal barrier for low energy. that's why we have s wave scaterring at low energy.

so when we have chiral super conductors does it mean that we have some scatering channel for non zero $l$? in other words, when we talk about the orbital angular momentum of cooper pairs is it the $l$ at 15.4?

• Please see an answer of mine : physics.stackexchange.com/a/62364/16689 which might help you understanding the difference between the s- and p-wave pairings. Then about chiral superconductor: a review can be find there : arxiv.org/abs/1512.01151 Chirality may come from either the interaction potential or the proximity to spin textures. Actually, the microscopic origin is under study in bulk systems. – FraSchelle Nov 22 '16 at 10:12
• what do you mean by ''Proximity to spin textures''? – physshyp Nov 22 '16 at 14:17
• Proximity to spin texture = Proximity effect + spin texture. Proximity effect : en.wikipedia.org/wiki/Proximity_effect_(superconductivity). Spin texture : Basically something with spin-orbit interaction, or a magnetic domain. Anything which gives a texture to the spin = a spatial or momentum variation of the spin interaction. See also this answer of mine, with related content : physics.stackexchange.com/a/294133/16689 – FraSchelle Nov 23 '16 at 9:36