Anisotropic SC gap: cannot converge near Tc, and different gap values for same T

[tyj]

Dear developers,

I am using EPW 7.3.1 and encountering two problems with anisotropic gap calculations. My material Tc is around 6-7K.
The problem occurs for all muc, here i just take muc=0.1 as an example. I'm wondering what's the correct way to obtain correct aniso gap value.
Input and output files are attached, with details in the README.

Issue 1: Cannot converge near Tc

For muc = 0.10, the extrapolated anisotropic Tc is ~7.2 K, but I can only converge up to 6.2 K. Above that, the Broyden
solver drifts monotonically toward zero gap and never satisfies conv_thr_iaxis (already lowerd from 1E-03 to 3E-03).
I have tried broyden_beta = 0.1, 0.3, 0.7 and nsiter up to 500, but none of these help.

Issue 2: Cold start and warm start give different converged gap values at the same temperature

In practice, due to wall time limits on the cluster, I cannot always run all temperatures in a single job. I observe that
the convergence behavior and converged gap value depend on how the calculation is started. When temperature T is part of
a chain (e.g. temps = 5.5 6.0 6.5), EPW uses the converged solution from the previous temperature as the initial guess
(warm start). I find that imag_read = .true. gives the same result as the in-chain warm start. However, starting from the
the temperature alone (cold start, e.g. temps = 6.5) gives a different result. As a result, the
gap curve is not smooth and does not follow the expected (Tc - T)^(1/2) trend near Tc. Is the warm start the correct
approach?

More details and all input/output files are in the README.

Best,
Yujia