A class to calculate the DC Josephson current. More...

Inheritance diagram for SNSJosephson:

[legend]

Public Member Functions
function	createCurrentOperator (varargin)
	Calculates the charge current operator from the inverse of the Greens function of the scattering region. More...

function	CurrentCalc_continuum (DeltaPhi_vec, varargin)
	Calculates the Josephson current of the continous scattering states. More...

function	CurrentCalc_discrete (DeltaPhi_vec, varargin)
	Calculates the Josephson current using the method in PRB 93, 224510 (2016) More...

function	diagInv (A)
	Calculates the diagonal part of the inverse of a sparse matrix. More...

function	display (message, nosilent)
	Displays output messages on the screen. More...

function	eig (A, B)
	Calculates the generalized eigenvalue problem based on the zggev and dggev LAPACK functions. More...

function	Fermi (E)
	A function of the Fermi-Dirac statistics. More...

function	getBandWidth ()
	Determines the band width of the leads and of the scattering region. More...

function	getOpt ()
	Retrives the structure containing the calculation parameters. More...

function	getProgramName ()
	Gets the name of the package. More...

function	getProgramShortName ()
	Gets the short name of the package. More...

function	getVersion ()
	Gets the current version of the package. More...

function	IsDeployedMKL ()
	Checks whether the MKL component is deployed. More...

function	partialInv (A, sizeInv)
	Calculates a partial inverse of a sparse matrix. More...

function	SetEnergy (newE, varargin)
	Sets the energy for the calculations. More...

function	setTemperature (T)
	Sets the temperature for the calculations. More...

function	SNSJosephson (Opt, varargin)
	Constructor of the class. More...

function	xmlread (filename)
	Function to load XML files (based on xerces libraries), providing octave compatibility. More...

function	xmlwrite (filename, DOM)
	Function to export XML files (based on xerces libraries), providing octave compatibility. More...

Static Public Member Functions
static function	BadInputType (variable, type)
	Throws a "bad input type" warning, with using the default value. More...

static function	BadInputTypeNoDefault (variable, type)
	Throws a "bad input type" warning without setting it to default. More...

static function	checkMEXfile (fncname)
	Checks the presence of a given MEX file. More...

static function	ExceedIteration ()
	Throws an "iteration exceeded" warning. More...

static function	inv_SVD (A)
	Inverts badly conditioned matrix A with SVD regularization. More...

static function	isOctave ()
	Checks whether the running environment is matlab or octave. More...

static function	SimphsonInt (y, h)
	Simphson integral: y is a vector of function values at equal distant points: y_i = f(x_i), x_i-x_{i-1}=h. More...

Public Attributes
Property	B
	The magnetic field in Tesla (OBSOLETE) More...

Property	BandWidth
	An instance of structure BandWidth. More...

Property	gfininvfromHamiltonian
	logical value. Set true for calculate the Greens function of the scattering region from Hamiltonian, or false (default) otherwise. More...

Property	junction
	An instance of class NTerminal (or its subclass) representing the junction. More...

Property	scatterPotential
	Function handle pot = f(#coordinates) for the additional potential to be applied in the scattering region. More...

Property	useSelfEnergy
	logical value. Set true (default) for solve the Dyson equation with the self energies, or false otherwise. More...

Property	varargin
	cell array of optional parameters. (For details see InputParsing) More...

Protected Member Functions
function	create_scatter_GreensFunction (varargin)
	Calculates the surface Green operator of the scattering region. More...

function	increasePhaseDifference (delta_phi, junction_loc)
	Increase the phase difference between the Leads by delta_phi (apply gauge transformation on the second lead) More...

function	InputParsing (varargin)
	Parses the optional parameters for the class constructor. More...

function	ResetPhase (varargin)
	Resets the phase difference to the initial value. More...

Protected Attributes
Property	beta
	$\beta = 1/(k_BT)$ More...

Property	DeployedMKL
	True if MKL component is built, false otherwise. More...

Property	k_B
	Boltzmann constant in eV/K. More...

Property	MaxSize
	Maximal size of full matrixes to be handled. More...

Property	mu
	The Chemical potential in the same unit as other energy scales in the Hamiltonians. More...

Property	Opt
	An instance of structure Opt. More...

Property	ProgramName
	Name of the package. More...

Property	ProgramShortName
	Short name of the package. More...

Property	T
	The temperature in Kelvin. More...

Property	T_treshold
	treshold temperature (makes difference between T=0 and T>0) More...

Property	version
	The current version of the package. More...

Detailed Description

A class to calculate the DC Josephson current.

Definition at line 24 of file SNSJosephson.m.

Constructor & Destructor Documentation

◆ SNSJosephson()

function SNSJosephson::SNSJosephson	(	Opt	,
		varargin
	)

Constructor of the class.

Parameters

Opt	An instance of the structure Opt.
varargin	Cell array of optional parameters. For details see InputParsing.

Returns: An instance of the class

Member Function Documentation

◆ BadInputType()

static function Messages::BadInputType	(	variable	,
		type
	)

staticinherited

Throws a "bad input type" warning, with using the default value.

Parameters

variable	A string conatining the name of the variable.
type	A string describing the desired type.

◆ BadInputTypeNoDefault()

static function Messages::BadInputTypeNoDefault	(	variable	,
		type
	)

staticinherited

Throws a "bad input type" warning without setting it to default.

Parameters

variable	A string conatining the name of the variable.
type	A string describing the desired type.

◆ checkMEXfile()

static function CommonFunctions::checkMEXfile ( fncname )

staticinherited

Checks the presence of a given MEX file.

Parameters

fncname The name of the function.

Returns: Returns true if the MEX file is present, false otherwise.

◆ create_scatter_GreensFunction()

function SNSJosephson::create_scatter_GreensFunction ( varargin )

protected

Calculates the surface Green operator of the scattering region.

The calculated Green operator is stored within the objec junction (or in the object junction given as an optional parameter)

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'gauge_trans'	Logical value. Set true (default) to perform gauge transformation on the Green's function and on the Hamiltonians, or false otherwise.
'junction'	An instance of class NTerminal (or its subclass) describing the junction.

◆ createCurrentOperator()

function SNSJosephson::createCurrentOperator ( varargin )

Calculates the charge current operator from the inverse of the Greens function of the scattering region.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'junction'	An instance of class NTerminal (or its subclass) describing the junction.

Returns: [1] The matrix operator of the current operator.

◆ CurrentCalc_continuum()

function SNSJosephson::CurrentCalc_continuum	(	DeltaPhi_vec	,
		varargin
	)

Calculates the Josephson current of the continous scattering states.

Parameters

DeltaPhi_vec	Array of phase diffrencies between the superconducting contacts.
varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'Edb'	The number of the energy points over the contour integral. (default value is 511)

Returns: [1] An array of the calculated current corresponding to the phase differencies DeltaPhi_vec; [2] Energy resolved Josephson current.

◆ CurrentCalc_discrete()

function SNSJosephson::CurrentCalc_discrete	(	DeltaPhi_vec	,
		varargin
	)

Calculates the Josephson current using the method in PRB 93, 224510 (2016)

Parameters

DeltaPhi_vec	Array of phase diffrencies between the superconducting contacts.
varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'range'	String. Set 'ABS' (default) for the Andreev bound states, 'NBS' for the normal bound states, 'CONT' for the scattering states, or 'ALL' for calculating all ranges at once.
'Edb'	The number of the energy points over the contour integral. (default value is 511)
'DeltaPhi'	A parameter to control the incident angle of the integration contour near the real axis. (Default value is $\Delta\Phi=0.5\pi$ ).
'Evec'	An array containing the complex energy points in case of custom integration path.
'Emin'	A minimum of the energy array on the real axis.
'Emax'	A maximum of the energy array on the real axis.
'ProximityOn'	Logical value. Set true to recalculate the Green operator of the scattering center for every phase difference. Useful for self-consistent modelling of the proximity effect.

Returns: An array of the calculated current corresponding to the phase differencies DeltaPhi_vec

◆ diagInv()

function CommonFunctions::diagInv ( A )

inherited

Calculates the diagonal part of the inverse of a sparse matrix.

If MKL component is advised to build.

Parameters

A	A sparse matrix to be inverted

Returns: Returns the diagonal elements of the inverse

◆ display()

function Messages::display	(	message	,
		nosilent
	)

inherited

Displays output messages on the screen.

Parameters

message	String containing the message to be displayed
nosilent	Set true to override the silent option given in Opt.Silent.

◆ eig()

function CommonFunctions::eig	(	A	,
		B
	)

inherited

Calculates the generalized eigenvalue problem based on the zggev and dggev LAPACK functions.

Parameters

A	A square matrix on the left side.
B	A square matrix on the right side.

Returns: Returns the calculated generalized eigenvalues and the right and left sided eigenvectors.

◆ ExceedIteration()

static function Messages::ExceedIteration ( )

staticinherited

Throws an "iteration exceeded" warning.

◆ Fermi()

function FermiDirac::Fermi ( E )

inherited

A function of the Fermi-Dirac statistics.

Parameters

E	The energy value in eV (scalar or an array of energy values).

Returns: Returns with the occupation number (numbers).

◆ getBandWidth()

function SNSJosephson::getBandWidth ( )

Determines the band width of the leads and of the scattering region.

Returns: An instance of structure BandWidth containing the bandwidths.

◆ getOpt()

function Messages::getOpt ( )

inherited

Retrives the structure containing the calculation parameters.

Returns: Return an instance of structure Opt.

◆ getProgramName()

function CommonFunctions::getProgramName ( )

inherited

Gets the name of the package.

Returns: Returns the name of the package.

◆ getProgramShortName()

function CommonFunctions::getProgramShortName ( )

inherited

Gets the short name of the package.

Returns: Returns the short name of the package.

◆ getVersion()

function CommonFunctions::getVersion ( )

inherited

Gets the current version of the package.

Returns: Returns the current version of the package.

◆ increasePhaseDifference()

function SNSJosephson::increasePhaseDifference	(	delta_phi	,
		junction_loc
	)

protected

Increase the phase difference between the Leads by delta_phi (apply gauge transformation on the second lead)

Parameters

delta_phi	The phase difference increment between the leads.
ribbon_loc	An instance of class NTerminal (or its subclass) describing the junction.

◆ InputParsing()

function SNSJosephson::InputParsing ( varargin )

protected

Parses the optional parameters for the class constructor.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'T'	The temperature in Kelvin (scalar or an array)
'mu'	The Chemical potential in the same unit as other energy scales in the Hamiltonians.
'scatterPotential'	A function handle pot=f( #coordinates ) or pot=f( CreateHamiltonians, Energy) for the potential to be applied in the Hamiltonian (used when FiniteGreensFunctionFromHamiltonian=true).
'gfininvfromHamiltonian'	Logical value. Set true calculate the surface Greens function of the scattering region from the Hamiltonaian of the scattering region, or false (default) to calculate it by the fast way (see Phys. Rev. B 90, 125428 (2014) for details).
'useSelfEnergy'	Logical value. Set true to use the self energies of the leads in the Dyson equation, or false (default) to use the surface Green function instead.
'junction'	An instance of class NTerminal (or its derived class) representing the junction.

◆ inv_SVD()

static function CommonFunctions::inv_SVD ( A )

staticinherited

Inverts badly conditioned matrix A with SVD regularization.

Parameters

A	A square matrix to be inverted.

Returns: Returns the calculated inverse.

◆ IsDeployedMKL()

function CommonFunctions::IsDeployedMKL ( )

inherited

Checks whether the MKL component is deployed.

Returns: Returns with true if MKL component is deployed, false otherwise.

◆ isOctave()

static function CommonFunctions::isOctave ( )

staticinherited

Checks whether the running environment is matlab or octave.

Returns: Returns true if running environment is octave, false otherwise.

◆ partialInv()

function CommonFunctions::partialInv	(	A	,
		sizeInv
	)

inherited

Calculates a partial inverse of a sparse matrix.

If MKL component is not developed, the backslash operator is used insted.

Parameters

A	A sparse matrix to be inverted
sizeInv	The size of partial inverse to be calculated.

Returns: Returns the calculated partial inverse

◆ ResetPhase()

function SNSJosephson::ResetPhase ( varargin )

protected

Resets the phase difference to the initial value.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'junction'	An instance of class NTerminal (or its subclass) describing the junction.

◆ SetEnergy()

function UtilsBase::SetEnergy	(	newE	,
		varargin
	)

inherited

Sets the energy for the calculations.

Parameters

newE	The value of the energy in the same units as the Hamiltonian.
varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'junction'	An instance of class NTerminal (or its derived class) representing the junction.

◆ setTemperature()

function FermiDirac::setTemperature ( T )

inherited

Sets the temperature for the calculations.

Parameters

T	The temperature in Kelvin (scalar or an array)

◆ SimphsonInt()

static function CommonFunctions::SimphsonInt	(	y	,
		h
	)

staticinherited

Simphson integral: y is a vector of function values at equal distant points: y_i = f(x_i), x_i-x_{i-1}=h.

Parameters

y	Function values to be integrated
h	Increment between the x_i points.

◆ xmlread()

function CommonFunctions::xmlread ( filename )

inherited

Function to load XML files (based on xerces libraries), providing octave compatibility.

Parameters

filename Absolute path to the file to be opened. (In matlab relative path is sufficient)

Returns: The loaded document object model (see http://www.mathworks.com/help/matlab/ref/xmlread.html#outputarg_DOMnode for details.)

◆ xmlwrite()

function CommonFunctions::xmlwrite	(	filename	,
		DOM
	)

inherited

Function to export XML files (based on xerces libraries), providing octave compatibility.

Parameters

filename	Absolute path to the file to be opened. (In matlab relative path is sufficient)
DOM	The loaded document object model (see http://www.mathworks.com/help/matlab/ref/xmlread.html#outputarg_DOMnode for details.)

Member Data Documentation

◆ B

Property SNSJosephson::B

The magnetic field in Tesla (OBSOLETE)

Definition at line 31 of file SNSJosephson.m.

◆ BandWidth

Property UtilsBase::BandWidth

inherited

An instance of structure BandWidth.

Definition at line 36 of file UtilsBase.m.

◆ beta

Property FermiDirac::beta

protectedinherited

$\beta = 1/(k_BT)$

Definition at line 38 of file FermiDirac.m.

◆ DeployedMKL

Property CommonFunctions::DeployedMKL

protectedinherited

True if MKL component is built, false otherwise.

Definition at line 32 of file CommonFunctions.m.

◆ gfininvfromHamiltonian

Property UtilsBase::gfininvfromHamiltonian

inherited

logical value. Set true for calculate the Greens function of the scattering region from Hamiltonian, or false (default) otherwise.

Definition at line 45 of file UtilsBase.m.

◆ junction

Property UtilsBase::junction

inherited

An instance of class NTerminal (or its subclass) representing the junction.

Definition at line 33 of file UtilsBase.m.

◆ k_B

Property FermiDirac::k_B

protectedinherited

Boltzmann constant in eV/K.

Definition at line 32 of file FermiDirac.m.

◆ MaxSize

Property CommonFunctions::MaxSize

protectedinherited

Maximal size of full matrixes to be handled.

Definition at line 44 of file CommonFunctions.m.

◆ mu

Property FermiDirac::mu

protectedinherited

The Chemical potential in the same unit as other energy scales in the Hamiltonians.

Definition at line 44 of file FermiDirac.m.

◆ Opt

Property Messages::Opt

protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

◆ ProgramName

Property CommonFunctions::ProgramName

protectedinherited

Name of the package.

Definition at line 38 of file CommonFunctions.m.

◆ ProgramShortName

Property CommonFunctions::ProgramShortName

protectedinherited

Short name of the package.

Definition at line 41 of file CommonFunctions.m.

◆ scatterPotential

Property UtilsBase::scatterPotential

inherited

Function handle pot = f(#coordinates) for the additional potential to be applied in the scattering region.

Definition at line 42 of file UtilsBase.m.

◆ T

Property FermiDirac::T

protectedinherited

The temperature in Kelvin.

Definition at line 35 of file FermiDirac.m.

◆ T_treshold

Property FermiDirac::T_treshold

protectedinherited

treshold temperature (makes difference between T=0 and T>0)

Definition at line 41 of file FermiDirac.m.

◆ useSelfEnergy

Property UtilsBase::useSelfEnergy

inherited

logical value. Set true (default) for solve the Dyson equation with the self energies, or false otherwise.

Definition at line 39 of file UtilsBase.m.

◆ varargin

Property UtilsBase::varargin

inherited

cell array of optional parameters. (For details see InputParsing)

Definition at line 48 of file UtilsBase.m.

◆ version

Property CommonFunctions::version

protectedinherited

The current version of the package.

Definition at line 35 of file CommonFunctions.m.

The documentation for this class was generated from the following file:

SNSJosephson.m

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SNSJosephson()

Member Function Documentation

◆ BadInputType()

◆ BadInputTypeNoDefault()

◆ checkMEXfile()

◆ create_scatter_GreensFunction()

◆ createCurrentOperator()

◆ CurrentCalc_continuum()

◆ CurrentCalc_discrete()

◆ diagInv()

◆ display()

◆ eig()

◆ ExceedIteration()

◆ Fermi()

◆ getBandWidth()

◆ getOpt()

◆ getProgramName()

◆ getProgramShortName()

◆ getVersion()

◆ increasePhaseDifference()

◆ InputParsing()

◆ inv_SVD()

◆ IsDeployedMKL()

◆ isOctave()

◆ partialInv()

◆ ResetPhase()

◆ SetEnergy()

◆ setTemperature()

◆ SimphsonInt()

◆ xmlread()

◆ xmlwrite()

Member Data Documentation

◆ B

◆ BandWidth

◆ beta

◆ DeployedMKL

◆ gfininvfromHamiltonian

◆ junction

◆ k_B

◆ MaxSize

◆ mu

◆ Opt

◆ ProgramName

◆ ProgramShortName

◆ scatterPotential

◆ T

◆ T_treshold

◆ useSelfEnergy

◆ varargin

◆ version