ABSTRACT - DRUM - University of Maryland

0.015
T/t
0.01
Normal
p x + ip y
0.005
0
4 2 0 2 4
µ/t
Figure 2.1:
The phase diagram for fermions on a square lattice with nearestneighbor
hoppings and attraction (g/t=1). The phase boundary separates a normal
metal and a topological (p x + ip y )-wave SC. The insets display FSs for µ < 0 (left)
and µ > 0 (right).
To see how this happens in the specific model, we define two independent order
parameters on horizontal and vertical links: ∆ n = g〈ĉ r ĉ r+en 〉, where n = x or y
and e n is the corresponding lattice vector (we use units where the lattice constant,
a = 1). These real-space order parameters are related to the momentum-space
definition (2.2) via ∆ k = 2i ∑
−g ∑
α=x,y
α=x,y
∆ α φ α (k), with the BCS interaction being ˜f k,k ′ =
φ α (k)φ α (k ′ ). Here we defined two eigenfunctions of the above-mentioned
2D representation of D 4 : φ x,y (k) = sin (k · e x,y ). It is straightforward to calculate
the BCS free energy given by Eqs. (2.4) and (2.5) for all possible order parameters
encompassed by the linear combinations ∆ k = g [λ x φ x (k) + λ y φ y (k)], with arbitrary
λ x,y ∈ C. We find that a p x +ip y -superconducting state with λ x = ±iλ y is selected at
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