A class to process transport calculations on quantum dots. More...

Inheritance diagram for QuantumDot:

[legend]

Public Member Functions
function	CalcTunnelingRate (Energy, gateVoltage, varargin)
	closing the parallel pool More...

function	CalcTunnelingRates (gateVoltage)
	Determine the tunneling rates for all energy values in the energy array Evec for a given gateVoltage. More...

function	DensityCalc (varargin)
	Calculates the onsite desnity using the method in Nanotechnology 25 (2014), 465201. More...

function	DensityCalcSmall (num_occupied_states)
	determine the number of sites in the calculations to preallocate memory More...

function	DetermineCurrent (bias, gateVoltage, leadnum)
	Calculates the current (in units of e^2/hbar) through a lead leadnum at gate voltage gateVoltage and at bias bias. More...

function	DetermineCurrentOperator (bias, gateVoltage, leadnum)
	Determine the current operator (in units of $e^2/\hbar$ ) to calculate the current through a lead leadnum at gate voltage gateVoltage and at bias bias. More...

function	DetermineDensityOfStates (Emin, Emax, Edb)
	Calculates the DOS to deremine the one-electron occupation levels. More...

function	DetermineOccupationProbabilities ()
	Determines the non-equilibrium occupation probabilities P_N (see Eq (8) in Eur. More...

function	DetermineSelfEnergy (bias, gateVoltage)
	Determine the self-energy matrix elements describing the transition rates between the N occupated states of the QD. More...

function	DetermineThermalOccupationProbabilities (gateVoltage)
	Determines the equilibrium occupation probabilities PN (see Eq (8) in Eur. More...

function	diagInv (A)
	Calculates the diagonal part of the inverse of a sparse matrix. 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	display (message, nosilent)
	Displays output messages on the screen. More...

function	DOSCalc (Evec, varargin)
	Calculates the onsite desnity of states. More...

function	eig (A, B)
	Calculates the generalized eigenvalue problem based on the zggev and dggev LAPACK functions. 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	Fermi (E)
	A function of the Fermi-Dirac statistics. More...

function	getBandWidth ()
	creating site indexes corresponding to the elements of the density vector More...

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

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

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

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

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

function	Initialize ()
	Initializes class attributes. More...

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

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

function	IVcalc (varargin)
	Calculates the current-voltage relation as a function of the bias. More...

function	LocalDOSCalc (Energy, varargin)
	preallocate memory for Densitysurf More...

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

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

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

function	SetChemicalPotentials (doping_levels, gateVoltage)
	Manually sets the chemical potentials corresponding to the given single-electron doping levels. More...

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

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

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

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

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

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

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

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	BandWidth
	An instance of structure BandWidth. More...

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

Property	DOSdata

	DOSvec
	Array of the density of states values. More...

Property	Ec
	The charging energy. More...

	Evec
	Array of the enrgy points. More...

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

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

Protected Member Functions
function	complexDensity (junction_loc, JustScatter)
	Calculates the density at a complex energy. More...

function	complexSpectral (junction_loc, JustScatter)
	setting the current energy More...

function	create_Hamiltonians (varargin)
	Creates the Hamiltonians of the system. More...

function	create_scatter (varargin)
	cerating Hamiltonian of the scattering region More...

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

function	CreateEnergyArray (varargin)
	Creates the array of energy values for the integration. More...

function	currentcalc (differentialConductance, Evec, tuned_contact)
	Calculates the current by integrating the differential conductance in a bias window. More...

function	DifferentialConductanceT0 (Energy, junction)
	Calculates the zero temperature differential conductance for a given energy. More...

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

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

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

Property	bias_max
	The maximal bias to be used in the calculations. More...

Property	CurrentOp
	The calculated current operator between the QD and a chosen lead. (see method DetermineCurrentOperator) More...

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

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

Property	Edb
	The number of the energy points in the attribute Evec. More...

Property	Evec
	The energy array used in the calculations. More...

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

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

Property	MaxSize
	Maximal size of full matrixes to be handled. 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	mu
	The Chemical potential in the same unit as other energy scales in the Hamiltonians. More...

Property	mu_QD
	An array containing the chamical potentials corresponding to the occupation numbers of OccNumbers. More...

Property	OccNumbers
	Array containing the occupation numbers. More...

Property	OccupationProbabilities
	Occupation probabilities of the QD connected to the leads occupied by N-N0 excess charge. More...

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

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

Property	PartitionFunctionsOneElectron
	Array of partition functions of 1<N<StatesNum occupied one-electron states ( Z = sum_n(exp(-beta*En)) ) More...

Property	ProgramName
	Name of the package. More...

Property	ProgramName
	Name of the package. More...

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

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

Property	SelfEnergy
	The calculated transition rates between the individual N-occupations states of the QD. More...

Property	StatesNum
	Number of states utilized in the calculations. More...

Property	T
	The temperature in Kelvin. More...

Property	T
	The temperature in Kelvin. More...

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

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

Property	ThermalOccupationProbabilities
	Occupation probabilities of an isolated, the N-occupied QD in thermal equilibrium. More...

Property	TunnelingRates
	The calculated tunneling rates between the individual leads and the QD. More...

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

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

Detailed Description

A class to process transport calculations on quantum dots.

Based on the real-time diagrammatic method of PRB 50, 18439

Available

EQuUs v4.9 or later

Definition at line 26 of file QuantumDot.m.

Constructor & Destructor Documentation

◆ QuantumDot()

function QuantumDot::QuantumDot	(	Opt	,
		varargin
	)

Constructor of the class.

Parameters

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

Returns: An instance of the class

Member Function Documentation

◆ BadInputType() [1/2]

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.

◆ BadInputType() [2/2]

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() [1/2]

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.

◆ BadInputTypeNoDefault() [2/2]

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.

◆ CalcTunnelingRate()

function QuantumDot::CalcTunnelingRate	(	Energy	,
		gateVoltage	,
		varargin
	)

closing the parallel pool

Determine the tunneling rate for a given Energy and gateVoltage

Parameters

Energy	The current energy value in units of the energy unit used in the Hamiltonian parameters.
gateVoltage	The back gate voltage in units of the energy unit used in the Hamiltonian parameters.
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.

◆ CalcTunnelingRates()

function QuantumDot::CalcTunnelingRates ( gateVoltage )

Determine the tunneling rates for all energy values in the energy array Evec for a given gateVoltage.

Parameters

gateVoltage The back gate voltage in units of the energy unit used in the Hamiltonian parameters.

◆ checkMEXfile() [1/2]

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.

◆ checkMEXfile() [2/2]

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.

◆ complexDensity()

function Density::complexDensity	(	junction_loc	,
		JustScatter
	)

protectedinherited

Calculates the density at a complex energy.

Parameters

junction_loc	An instance of class NTerminal or its subclass describing the junction.
JustScatter	Logical value. True if only an isolated scattering center should be considered in the self-consistent calculations, false otherwise.

◆ complexSpectral()

function DOS::complexSpectral	(	junction_loc	,
		JustScatter
	)

protectedinherited

setting the current energy

creating the Hamiltonian of the scattering region evaluating the energy resolved density creating the data structure of the local density of states Calculates the spectral function at a complex energy

Parameters

junction_loc	An instance of class NTerminal or its subclass representing the junction.
JustScatter	logical value. True if only an isolated scattering center should be considered in the calculations, false otherwise.

Returns: spectral_function The calculted spectral function and a data structure containing geometry data of the junction.

◆ create_Hamiltonians()

function DOS::create_Hamiltonians ( varargin )

protectedinherited

Creates the Hamiltonians of the system.

Parameters

varargin Cell array of optional parameters:.

◆ create_scatter()

function DOS::create_scatter ( varargin )

protectedinherited

cerating Hamiltonian of the scattering region

creating the Lead Hamiltonians Creates the Hamiltonian of the scattering center

Parameters

varargin Cell array of optional parameters:.

◆ create_scatter_GreensFunction()

function IV::create_scatter_GreensFunction ( varargin )

protectedinherited

Calculates the surface Green operator of the scattering region.

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.

Returns: The inverse of the Green operator.

◆ CreateEnergyArray()

function IV::CreateEnergyArray ( varargin )

protectedinherited

Creates the array of energy values for the integration.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'tuned_contact'	String value. Identifies the tuned contact for the calculations. Possible values are: 'right', 'left', 'symmetric'.

◆ currentcalc()

function IV::currentcalc	(	differentialConductance	,
		Evec	,
		tuned_contact
	)

protectedinherited

Calculates the current by integrating the differential conductance in a bias window.

Parameters

differentialConductance	Array of differential conductance
Evec	Array of energy values
tuned_contact	String value. Identifies the tuned contact for the calculations. Possible values are: 'right', 'left', 'symmetric'.

Returns: Returns with the calculated current

◆ DensityCalc()

function Density::DensityCalc ( varargin )

inherited

Calculates the onsite desnity using the method in Nanotechnology 25 (2014), 465201.

Parameters

varargin	Cell array of optional parameters:
'Edb'	The number of the energy points over the contour integral.
'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'	The complex energy points in case of custom integration path. (Overrides all other optional parameters.)
'Emin'	The minimum of the energy array.
'JustScatter'	Logical value. True if only an isolated scattering center should be considered in the self-consistent calculations, false otherwise.

Returns: An array of the calculated density and a structure describing the geometry of the sites.

◆ DensityCalcSmall()

function Density::DensityCalcSmall ( num_occupied_states )

inherited

determine the number of sites in the calculations to preallocate memory

preallocate memory for Densitysurf creating function handles for parallel for setting the current energy creating the Hamiltonian of the scattering region evaluating the energy resolved density closing the parallel pool calculating the contour integrals Calculates the onsite desnity using the method in Nanotechnology 25 (2014), 465201. This method is usable for small isolated scattering centers for which an exact diagonalization can be performed

Parameters

num_occupied_states Number of occupied states

Returns: An array of the calculated density and a structure describing the geometry of the sites.

◆ DetermineCurrent()

function QuantumDot::DetermineCurrent	(	bias	,
		gateVoltage	,
		leadnum
	)

Calculates the current (in units of e^2/hbar) through a lead leadnum at gate voltage gateVoltage and at bias bias.

Parameters

bias	The bias voltage applied through the leads in units of the energy unit used in the Hamiltonian parameters.
gateVoltage	The back gate voltage in units of the energy unit used in the Hamiltonian parameters.
leadnum	Identification number of the lead. (see attribute CreateLeadHamiltonians.Hanyadik_Lead).

Returns: Returns with the calculated current in units of $e^2/\hbar$

◆ DetermineCurrentOperator()

function QuantumDot::DetermineCurrentOperator	(	bias	,
		gateVoltage	,
		leadnum
	)

Determine the current operator (in units of $e^2/\hbar$ ) to calculate the current through a lead leadnum at gate voltage gateVoltage and at bias bias.

Parameters

bias	The bias voltage applied through the leads in units of the energy unit used in the Hamiltonian parameters.
gateVoltage	The back gate voltage in units of the energy unit used in the Hamiltonian parameters.
leadnum	Identification number of the lead. (see attribute CreateLeadHamiltonians.Hanyadik_Lead).

◆ DetermineDensityOfStates()

function QuantumDot::DetermineDensityOfStates	(	Emin	,
		Emax	,
		Edb
	)

Calculates the DOS to deremine the one-electron occupation levels.

This must be done manually.

Parameters

Emin	The minimum of the energy array.
Emax	The maximum of the energy array.
Edb	The number of the energy points in the energy array.

◆ DetermineOccupationProbabilities()

function QuantumDot::DetermineOccupationProbabilities ( )

Determines the non-equilibrium occupation probabilities P_N (see Eq (8) in Eur.

Phys. J B 10, 119)

Returns: Returns with the calculated occupation probabilities

◆ DetermineSelfEnergy()

function QuantumDot::DetermineSelfEnergy	(	bias	,
		gateVoltage
	)

Determine the self-energy matrix elements describing the transition rates between the N occupated states of the QD.

(see the diagrammatic rules in PRB 50, 18439)

Parameters

bias	The bias voltage applied through the leads in units of the energy unit used in the Hamiltonian parameters.
gateVoltage	The back gate voltage in units of the energy unit used in the Hamiltonian parameters.

Returns: The calulated self-energy (transition rates between the N occupated states of the QD.)

◆ DetermineThermalOccupationProbabilities()

function QuantumDot::DetermineThermalOccupationProbabilities ( gateVoltage )

Determines the equilibrium occupation probabilities PN (see Eq (8) in Eur.

Phys. J B 10, 119)

Parameters

gateVoltage The back gate voltage in units of the energy unit used in the Hamiltonian parameters.

◆ diagInv() [1/2]

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

◆ diagInv() [2/2]

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

◆ DifferentialConductanceT0()

function IV::DifferentialConductanceT0	(	Energy	,
		junction
	)

protectedinherited

Calculates the zero temperature differential conductance for a given energy.

Parameters

Energy	The energy value (use the same units as in the Hamiltonian)
junction	An instance of class NTerminal or its subclass.

Returns: Returns with the calculated zero temperature differential conductance.

◆ display() [1/2]

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.

◆ display() [2/2]

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.

◆ DOSCalc()

function DOS::DOSCalc	(	Evec	,
		varargin
	)

inherited

Calculates the onsite desnity of states.

Parameters

Evec	One-dimensional array of the energy points.
varargin	Cell array of optional parameters:
'JustScatter'	Logical value. Set true to omit the contacts from the system

◆ eig() [1/2]

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.

◆ eig() [2/2]

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() [1/2]

static function Messages::ExceedIteration ( )

staticinherited

Throws an "iteration exceeded" warning.

◆ ExceedIteration() [2/2]

static function Messages::ExceedIteration ( )

staticinherited

Throws an "iteration exceeded" warning.

◆ Fermi() [1/2]

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).

◆ Fermi() [2/2]

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 Density::getBandWidth ( )

inherited

creating site indexes corresponding to the elements of the density vector

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

Returns: ret An instance of structure BandWidth containing the bandwidths.

◆ getOpt() [1/2]

function Messages::getOpt ( )

inherited

Retrives the structure containing the calculation parameters.

Returns: Return an instance of structure Opt.

◆ getOpt() [2/2]

function Messages::getOpt ( )

inherited

Retrives the structure containing the calculation parameters.

Returns: Return an instance of structure Opt.

◆ getProgramName() [1/2]

function CommonFunctions::getProgramName ( )

inherited

Gets the name of the package.

Returns: Returns the name of the package.

◆ getProgramName() [2/2]

function CommonFunctions::getProgramName ( )

inherited

Gets the name of the package.

Returns: Returns the name of the package.

◆ getProgramShortName() [1/2]

function CommonFunctions::getProgramShortName ( )

inherited

Gets the short name of the package.

Returns: Returns the short name of the package.

◆ getProgramShortName() [2/2]

function CommonFunctions::getProgramShortName ( )

inherited

Gets the short name of the package.

Returns: Returns the short name of the package.

◆ getVersion() [1/2]

function CommonFunctions::getVersion ( )

inherited

Gets the current version of the package.

Returns: Returns the current version of the package.

◆ getVersion() [2/2]

function CommonFunctions::getVersion ( )

inherited

Gets the current version of the package.

Returns: Returns the current version of the package.

◆ Initialize()

function QuantumDot::Initialize ( )

Initializes class attributes.

◆ InputParsing()

function QuantumDot::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 absolute temperature in Kelvins.
'silent'	Set true to suppress output messages.
'scatterPotential'	A function handle y=f( #coordinates coords ) or y=f( CreateHamiltonians CreateH, E ) of the potential across the junction.
'useSelfEnergy'	Logical value. Set true (default) to solve the Dyson equation with the self energies of the leads, or false to use the surface Green operators.
'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).
'junction'	An instance of a class NTerminal or its subclass describing the junction.
'bias_max'	The maximal bias to be used in the calculations
'Edb'	The number of the energy points in the attribute Evec
'Ec'	The charging energy in the same units as the Hamiltonians.

◆ inv_SVD() [1/2]

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.

◆ inv_SVD() [2/2]

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() [1/2]

function CommonFunctions::IsDeployedMKL ( )

inherited

Checks whether the MKL component is deployed.

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

◆ IsDeployedMKL() [2/2]

function CommonFunctions::IsDeployedMKL ( )

inherited

Checks whether the MKL component is deployed.

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

◆ isOctave() [1/2]

static function CommonFunctions::isOctave ( )

staticinherited

Checks whether the running environment is matlab or octave.

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

◆ isOctave() [2/2]

static function CommonFunctions::isOctave ( )

staticinherited

Checks whether the running environment is matlab or octave.

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

◆ IVcalc()

function IV::IVcalc ( varargin )

inherited

Calculates the current-voltage relation as a function of the bias.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'tuned_contact'	String value. Identifies the tuned contact for the calculations. Possible values are: 'right', 'left', 'symmetric'.

Returns: [1] The calculated current array.; [2] The calculated voltage bias array.; [3] The calculated differential conductance.

◆ LocalDOSCalc()

function DOS::LocalDOSCalc	(	Energy	,
		varargin
	)

inherited

preallocate memory for Densitysurf

creating function handles for parallel for setting the current energy creating the Hamiltonian of the scattering region evaluating the energy resolved density closing the parallel pool Calculates the local desnity of states for a given energy.

Parameters

Energy	The energy value in the units of the Hamiltonians
varargin	Cell array of optional parameters:
'JustScatter'	Logical value. Set true to omit the contacts from the system

Returns: Returns with the calculated local DOS. (An instance of structure LocalDOS)

◆ partialInv() [1/2]

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

◆ partialInv() [2/2]

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

◆ SetChemicalPotentials()

function QuantumDot::SetChemicalPotentials	(	doping_levels	,
		gateVoltage
	)

Manually sets the chemical potentials corresponding to the given single-electron doping levels.

Parameters

doping_levels	The user defined single-electron doping levels obatined from the calculated density of states.
gateVoltage	The back gate voltage in units of the energy unit used in the Hamiltonian parameters.

◆ SetEnergy() [1/2]

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.

◆ SetEnergy() [2/2]

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() [1/2]

function FermiDirac::setTemperature ( T )

inherited

Sets the temperature for the calculations.

Parameters

T	The temperature in Kelvin (scalar or an array)

◆ setTemperature() [2/2]

function FermiDirac::setTemperature ( T )

inherited

Sets the temperature for the calculations.

Parameters

T	The temperature in Kelvin (scalar or an array)

◆ SimphsonInt() [1/2]

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.

◆ SimphsonInt() [2/2]

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() [1/2]

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.)

◆ xmlread() [2/2]

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() [1/2]

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.)

◆ xmlwrite() [2/2]

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

◆ BandWidth [1/2]

Property UtilsBase::BandWidth

inherited

An instance of structure BandWidth.

Definition at line 36 of file UtilsBase.m.

◆ BandWidth [2/2]

Property UtilsBase::BandWidth

inherited

An instance of structure BandWidth.

Definition at line 36 of file UtilsBase.m.

◆ beta [1/2]

Property FermiDirac::beta

protectedinherited

$\beta = 1/(k_BT)$

Definition at line 38 of file FermiDirac.m.

◆ beta [2/2]

Property FermiDirac::beta

protectedinherited

$\beta = 1/(k_BT)$

Definition at line 38 of file FermiDirac.m.

◆ bias_max

Property IV::bias_max

protectedinherited

The maximal bias to be used in the calculations.

Definition at line 37 of file IV.m.

◆ CurrentOp

Property QuantumDot::CurrentOp

protected

The calculated current operator between the QD and a chosen lead. (see method DetermineCurrentOperator)

Definition at line 55 of file QuantumDot.m.

◆ DeployedMKL [1/2]

Property CommonFunctions::DeployedMKL

protectedinherited

True if MKL component is built, false otherwise.

Definition at line 32 of file CommonFunctions.m.

◆ DeployedMKL [2/2]

Property CommonFunctions::DeployedMKL

protectedinherited

True if MKL component is built, false otherwise.

Definition at line 32 of file CommonFunctions.m.

◆ DOSdata

Property DOS::DOSdata

inherited

Definition at line 34 of file DOS.m.

◆ DOSvec

DOS::DOSvec

inherited

Array of the density of states values.

Definition at line 198 of file structures.m.

◆ Ec

Property QuantumDot::Ec

The charging energy.

Definition at line 33 of file QuantumDot.m.

◆ Edb

Property IV::Edb

protectedinherited

The number of the energy points in the attribute Evec.

Definition at line 40 of file IV.m.

◆ Evec [1/2]

Property IV::Evec

protectedinherited

The energy array used in the calculations.

Definition at line 34 of file IV.m.

◆ Evec [2/2]

DOS::Evec

inherited

Array of the enrgy points.

Definition at line 200 of file structures.m.

◆ gfininvfromHamiltonian [1/2]

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.

◆ gfininvfromHamiltonian [2/2]

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 [1/2]

Property UtilsBase::junction

inherited

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

Definition at line 33 of file UtilsBase.m.

◆ junction [2/2]

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 [1/2]

Property FermiDirac::k_B

protectedinherited

Boltzmann constant in eV/K.

Definition at line 32 of file FermiDirac.m.

◆ k_B [2/2]

Property FermiDirac::k_B

protectedinherited

Boltzmann constant in eV/K.

Definition at line 32 of file FermiDirac.m.

◆ MaxSize [1/2]

Property CommonFunctions::MaxSize

protectedinherited

Maximal size of full matrixes to be handled.

Definition at line 44 of file CommonFunctions.m.

◆ MaxSize [2/2]

Property CommonFunctions::MaxSize

protectedinherited

Maximal size of full matrixes to be handled.

Definition at line 44 of file CommonFunctions.m.

◆ mu [1/2]

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.

◆ mu [2/2]

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.

◆ mu_QD

Property QuantumDot::mu_QD

protected

An array containing the chamical potentials corresponding to the occupation numbers of OccNumbers.

Definition at line 61 of file QuantumDot.m.

◆ OccNumbers

Property QuantumDot::OccNumbers

protected

Array containing the occupation numbers.

Definition at line 58 of file QuantumDot.m.

◆ OccupationProbabilities

Property QuantumDot::OccupationProbabilities

protected

Occupation probabilities of the QD connected to the leads occupied by N-N0 excess charge.

Definition at line 46 of file QuantumDot.m.

◆ Opt [1/2]

Property Messages::Opt

protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

◆ Opt [2/2]

Property Messages::Opt

protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

◆ PartitionFunctionsOneElectron

Property QuantumDot::PartitionFunctionsOneElectron

protected

Array of partition functions of 1<N<StatesNum occupied one-electron states ( Z = sum_n(exp(-beta*En)) )

Definition at line 40 of file QuantumDot.m.

◆ ProgramName [1/2]

Property CommonFunctions::ProgramName

protectedinherited

Name of the package.

Definition at line 38 of file CommonFunctions.m.

◆ ProgramName [2/2]

Property CommonFunctions::ProgramName

protectedinherited

Name of the package.

Definition at line 38 of file CommonFunctions.m.

◆ ProgramShortName [1/2]

Property CommonFunctions::ProgramShortName

protectedinherited

Short name of the package.

Definition at line 41 of file CommonFunctions.m.

◆ ProgramShortName [2/2]

Property CommonFunctions::ProgramShortName

protectedinherited

Short name of the package.

Definition at line 41 of file CommonFunctions.m.

◆ scatterPotential [1/2]

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.

◆ scatterPotential [2/2]

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.

◆ SelfEnergy

Property QuantumDot::SelfEnergy

protected

The calculated transition rates between the individual N-occupations states of the QD.

Definition at line 49 of file QuantumDot.m.

◆ StatesNum

Property QuantumDot::StatesNum

protected

Number of states utilized in the calculations.

Definition at line 64 of file QuantumDot.m.

◆ T [1/2]

Property FermiDirac::T

protectedinherited

The temperature in Kelvin.

Definition at line 35 of file FermiDirac.m.

◆ T [2/2]

Property FermiDirac::T

protectedinherited

The temperature in Kelvin.

Definition at line 35 of file FermiDirac.m.

◆ T_treshold [1/2]

Property FermiDirac::T_treshold

protectedinherited

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

Definition at line 41 of file FermiDirac.m.

◆ T_treshold [2/2]

Property FermiDirac::T_treshold

protectedinherited

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

Definition at line 41 of file FermiDirac.m.

◆ ThermalOccupationProbabilities

Property QuantumDot::ThermalOccupationProbabilities

protected

Occupation probabilities of an isolated, the N-occupied QD in thermal equilibrium.

Definition at line 43 of file QuantumDot.m.

◆ TunnelingRates

Property QuantumDot::TunnelingRates

protected

The calculated tunneling rates between the individual leads and the QD.

Definition at line 52 of file QuantumDot.m.

◆ useSelfEnergy [1/2]

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.

◆ useSelfEnergy [2/2]

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 [1/2]

Property UtilsBase::varargin

inherited

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

Definition at line 48 of file UtilsBase.m.

◆ varargin [2/2]

Property UtilsBase::varargin

inherited

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

Definition at line 48 of file UtilsBase.m.

◆ version [1/2]

Property CommonFunctions::version

protectedinherited

The current version of the package.

Definition at line 35 of file CommonFunctions.m.

◆ version [2/2]

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:

QuantumDot.m

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Available

Constructor & Destructor Documentation

◆ QuantumDot()

Member Function Documentation

◆ BadInputType() [1/2]

◆ BadInputType() [2/2]

◆ BadInputTypeNoDefault() [1/2]

◆ BadInputTypeNoDefault() [2/2]

◆ CalcTunnelingRate()

◆ CalcTunnelingRates()

◆ checkMEXfile() [1/2]

◆ checkMEXfile() [2/2]

◆ complexDensity()

◆ complexSpectral()

◆ create_Hamiltonians()

◆ create_scatter()

◆ create_scatter_GreensFunction()

◆ CreateEnergyArray()

◆ currentcalc()

◆ DensityCalc()

◆ DensityCalcSmall()

◆ DetermineCurrent()

◆ DetermineCurrentOperator()

◆ DetermineDensityOfStates()

◆ DetermineOccupationProbabilities()

◆ DetermineSelfEnergy()

◆ DetermineThermalOccupationProbabilities()

◆ diagInv() [1/2]

◆ diagInv() [2/2]

◆ DifferentialConductanceT0()

◆ display() [1/2]

◆ display() [2/2]

◆ DOSCalc()

◆ eig() [1/2]

◆ eig() [2/2]

◆ ExceedIteration() [1/2]

◆ ExceedIteration() [2/2]

◆ Fermi() [1/2]

◆ Fermi() [2/2]

◆ getBandWidth()

◆ getOpt() [1/2]

◆ getOpt() [2/2]

◆ getProgramName() [1/2]

◆ getProgramName() [2/2]

◆ getProgramShortName() [1/2]

◆ getProgramShortName() [2/2]

◆ getVersion() [1/2]

◆ getVersion() [2/2]

◆ Initialize()

◆ InputParsing()

◆ inv_SVD() [1/2]

◆ inv_SVD() [2/2]

◆ IsDeployedMKL() [1/2]

◆ IsDeployedMKL() [2/2]

◆ isOctave() [1/2]

◆ isOctave() [2/2]

◆ IVcalc()

◆ LocalDOSCalc()

◆ partialInv() [1/2]

◆ partialInv() [2/2]

◆ SetChemicalPotentials()

◆ SetEnergy() [1/2]

◆ SetEnergy() [2/2]

◆ setTemperature() [1/2]

◆ setTemperature() [2/2]

◆ SimphsonInt() [1/2]

◆ SimphsonInt() [2/2]

◆ xmlread() [1/2]

◆ xmlread() [2/2]

◆ xmlwrite() [1/2]

◆ xmlwrite() [2/2]

Member Data Documentation

◆ BandWidth [1/2]

◆ BandWidth [2/2]