IsoME

IsoME is a state-of-the-art method to solve the isotropic Eliashberg equations. In addition to being one of the most accurate Eliashberg solvers currently available, it also supports high-throughput calculations through a fast implementation based on the constant density of states (DOS) and Morel-Anderson pseudopotential approximations.

In its simplest form, IsoME requires only the Eliashberg spectral function $\alpha^2 F$ as input to compute the superconducting critical temperature (Tc). For more advanced calculations, input files containing the DOS and the screened Coulomb interaction (W) are necessary.

The package is capable of solving the isotropic Eliashberg equations within any of the following approximations:

constant Dos with Morel-Anderson pseudopotential $\mu^*$
variable Dos with Morel-Anderson pseudopotential $\mu^*$
variable Dos with screened Coulomb interaction $W(\varepsilon,\varepsilon')$

Furthermore, results based on the Allen-Dynes and Allen-Dynes-McMillan formulas are provided. In principle, a fourth level of approximation that combines the static Coulomb interaction $W(\varepsilon,\varepsilon')$ with the constant DOS approximation exists. However, this variant is not recommended, as it requires the same input data as the vDOS+W approach while being less rigorous and offering no notable computational advantage. There is also an option to save the self-energy components $\Delta, Z, \chi, \phi$ at each temperature. An analytic continuation to the real frequency axis will be implemented in a future release.

Installation

In order to run the code you need to install julia 1.10 or higher. IsoME.jl is a registered package and it can be installed using the Julia package manager.

julia> using Pkg
julia> Pkg.add("IsoME")

Usage

After adding the package to your environment it can be loaded via

julia> using IsoME

To search for the Tc within the constant dos approximation using the Anderson-Pseuodopotential, only the path to the $\alpha^2F$-file has to be provided. We recommend to set also the path to the output directory, beacuse per default the results will be written into the current working directory. The inputs are handed over by creating an instance of the custom data type arguments().

julia> inp = arguments(
                a2f_file="Path to a2f-file", 
                outdir="Path to output directory"
                )

All other input values are optional and are contained within arguments(). The inputs can be viewed using the dot notation, e.g.

julia> inp.omega_c
7000.0

gives the cutoff of the Matsubara summation in meV. Note that some of the values in inp will only be set during the execution. This is usually indicated by a -1 or "" for numeric and string values, respectively. E.g. if the $\alpha^2F$ contains several columns with different smearings and the smearing index (ind_smear) is set to -1, the middle column will be used per default. The code should automatically recognize the format of the input files and remove the header and footer lines. If this fails, there is the option to specify these parameters manually. Furthermore, the unit and in the case of a vDOS or W calculation the fermi energy will be extracted from the header. For a detailed description have a look at the Input page. Finally, the calculation can be started via

julia> EliashbergSolver(inp)

As output a log-file, a file summarizing the results and an overview of the inputs, as well as figures of the superconducting gap and the a2f-values are created. Saving the self-energy components has to be enabled explicitly by setting flag_writeSelfEnergy=1. Calculations within one of the other approximations can be started completely analog by specifying the paths to the dos/W-file and setting the corresponding flags.

julia> inp = arguments(
                a2f_file            = "Path to a2f-file", 
                outdir              = "Path to output directory",
                dos_file            = "Path to dos-file",
                Weep_file           = "Path to W-file",
                cDOS_flag           = 0,
                include_Weep        = 1
                )

If the energy grid is not containted within the Weep-file, it can be provided through an addional file: Wen_file = "Path to W energies-file"

Minimal example

A minimal example can be found at Example files. If you have installed the package you should be able to run the file examples.jl in any of the appoximations.

~ $ julia examples.jl

If you have installed IsoME into a separate project environment, specify the path to the environment via

~ $ julia --project=/path/to/environment/ examples.jl

For more information please refer to Best practices.