Reference manual¶

Features of the main program of Superconducting-Toolkit, sctk.x, is as follows:

Compute the Coulomb interaction matrix \(K^{el}_{n {\bf k} n' {\bf k}'}\) as a preprocess. This program uses Kohn-Sham orbitals generated by QE.
Solve the gap equation and obtain the superconducting gap function \(\Delta_{n {\bf k}}\).
Solve the gap equation and obtain the superconducting transition temperature with the bisection method.
Perform non-SCF calculation for generating files readable by FermiSurfer.
Perform non-SCF calculation for obtaining quasi particle density of states.
Perform non-SCF calculation for obtaining ultrasonic attenuation coefficient(experimental).

Also, there is a script twingrid.x to generate the \({\bf k}\)-point grid where Kohn-Sham orbitals for the calculation of the Coulomb interaction are computed.

Usage¶

mpiexec options PATH/sctk.x -in input_file

Input-file format¶

The format of the input file is as follows:

&CONTROL
  prefix =
  outdir =
  calculation =
/
&KEL
  start_q =
  last_q =
  nci =
  laddxc =
  ecutfock =
  nq1 =
  nq2 =
  nq3 =
  lsf
/
&SCDFT
  temp =
  fbee =
  lbee =
  xic =
  nmf =
  nx =
  ne =
  emin =
  emax =
  electron_maxstep =
  conv_thr =
  fildyn =
  spin_fluc =
/

These parameter can be written in random order. If a parameter is omitted, the default value is used.

Namelist CONTROL¶

Parameter	Type	Default value	Description
prefix	String	“pwscf”	It must be the same as `prefix` in the input of pw.x.
outdir	String	“./”	It must be the same as `outdir` in the input of pw.x.
calculation	String	“kel”	Type of calculation

Namelist KEL¶

Parameters used for calculation = "kel".

Parameter	Type	Default value	Description
start_q	Positive integer	1	First \({\bf q}\) for computing screened Coulomb interaction and spin fluctuation
last_q	Positive integer	Number of \({\bf q}\) in Irreducible BZ	Last \({\bf q}\) for computing screened Coulomb interaction
laddxc	0 or 1	0	Specify the approximation used in the calculation of screened Coulomb interaction. 0 : RPA, 1: Adiabatic LDA.
lsf	0 or 1	0	Whether the spin-fluctuation is computed (1) or not (0)
ecutfock	Real	Same as pw.x	Cutoff of plane waves for the polarization function. [Ry].
nq1, nq2, nq3	Positive integer	Same as \({\bf k}\) mesh of a2Fsave	The \({\bf k}\) mesh of the Kohn-Sham orbitals. It must be the same as the twingrid.x input.
nci	Positive integer	5	The number of Matsubara frequencies of screened Coulomb interactions.

Namelist SCDFT¶

Parameters used when calculation = "scdft".

Parameter	Type	Default value	Description
temp	Positive real number	0.1	Temperature(Kelvin).
fbee	Positive integer	1	The first band in the gap equation.
lbee	Positive integer	nbnd in pw.x	The last band in the gap equation.
xic	Real number	-1.0	Parameter for gap-function extrapolation method. Ry unit. When this is lower than `0.0`, gap function extrapolation is not used (in default this extrapolation is not used.)
nmf	Real number	10	The number of Matsubara frequencies in the calculation of the Coulomb kernel. When it is `0` static Coulomb kernel is used. When negative value is specified, Coulomb kernel becomes 0. (Only the phononic kernel is used).
nx	Positive integer	100	The number of auxiliary energy grid in the vicinity of the Fermi level.
ne	Positive integer	50	Used only in the calculation of quasi-particle DOS. The number of energy grid for quasi particle density of states.
emin	Positive real number	1.0e-7	Minimum energy scale parameter for auxiliary energy grid. Ry unit.
emax	Positive real number	5.0	Used only in the calculation of quasi-particle DOS. The maximum energy where QPDOS is computed. meV unit.
electron_maxstep	Positive integer	100	The maximum iteration number for solving gap equation.
conv_thr	Positive real number	1.0e-15	The convergence threshold for the gap equation. When the norm of the difference between the new- and the old- gap function becomes lower than it, the system is thought to be converged. Ry unit.
filedyn	String	“matdyn”	It must be the same as filedyn in ph.x.
spin_fluc	Logical	.False.	If .True., the spin-fluctuation [3] is included.
scdft_kernel	Positive integer	1	1: Lüders2005 [4], 2: Sanna2020 [5]
lz_coulomb	Logical	.False.	Coulomb renormalization [6]

Data files¶

The following files are read/written by sctk.x:

{prefix}.xml¶

It contains informations about lattice constant, etc. It is generated by pw.x.

{prefix}.a2Fsave¶

It contains the Kohn-Sham energy,information of \({\bf k}\) mesh, and symmetrical operations. It is generated by pw.x with la2f=.true.

{prefix}.save/wfc*.dat¶

It contains Kohn-Sham orbitals at each \({\bf k}\) point. * should be the index of \({\bf k}\) point. It is generated by pw.x.

vel*.dat¶

It contains coefficients of the Chebyshev interpolation of the screened Coulomb interaction at each \({\bf q}\) point. * should be the index of \({\bf q}\) point. It is generated by sctk.x with calculation=”kel”.

elph*.dat¶

It contains electron-phonon interactions and phonon frequencies at each \({\bf q}\) point. * should be the index of \({\bf q}\) point. It is generated by modified ph.x.

lambda.frmsf, mu.frmsf¶

Data files for FermiSurfer for displaying the mass-renormalization factor \(\lambda_{n {\bf k}}\) on the Fermi surface. It is generated by sctk.x with calculation=”lambda_mu_k”.

delta.dat¶

It contains the superconducting gap functions \(\Delta_{n {\bf k}}\), associated Kohn-Sham energy \(\xi_{n {\bf k}}\), integration weights, band indices, \({\bf k}\)-indices, and the renormalization \(Z_{n {\bf k}}\). It is generated by sctk.x with calculation=”scdft”.

qpdos.dat¶

First column: quasiparticle energy (meV unit), Second column: quasiparticle density of states (Ry\(^{-1}\) unit). It is generated by sctk.x with calculation=”qpdos”.

delta.frmsf, Z.frmsf¶

Data files for FermiSurfer for displaying the superconducting gaps \(\Delta_{n {\bf k}}\) and the renormalization \(Z_{n {\bf k}}\) on the Fermi surface. It is generated by sctk.x with calculation=”deltaf”.

Type of calculation¶

We can specify the type of calculation by inputting the following string into the parameter calculation.