Class to create and store Hamiltonian of the translational invariant leads. More...

Inheritance diagram for CreateLeadHamiltonians:

[legend]

Public Member Functions
function	AddPotential (V)
	Adds on-site potential to the Hamiltonian H0. More...

function	ApplyOverlapMatrices (E)
	Applies the overlap matrices to the Hamiltonians: K = H-ES. More...

function	CalcSpektrum (varargin)
	Calculates the band structure of the lead. More...

function	Clear (MemberName)
	Clears the value of an attribute in the interface. More...

function	CreateClone (varargin)
	Creates a clone of the present class. More...

function	CreateHamiltonians (varargin)
	Creates the Hamiltonians H_0 and H_1 of the lead. More...

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

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

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

function	isSuperconducting ()
	Test, whether the lead is in the superconducting phase or not. More...

function	MomentumDependentHamiltonian (k, q)
	Construct a momentum dependent (Fourier-transformed) Hamiltonian. More...

function	Read (MemberName)
	Query for the value of an attribute in the interface. More...

function	Reset ()
	Resets all elements in the object. More...

function	saveLeads ()
	Save Lead Hamiltonians into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'. More...

function	ShiftCoordinates (shift)
	Shifts the coordinates of the sites by an integer multiple of the lattice vector Coordinates.a. More...

function	ShiftLead (Energy)
	Shifts the on-site energies in the leads by a given energy. More...

function	Transform2BdG ()
	Transforms the Hamiltonians and the overlap matrices into the BdG model in the Nambu space representation according to New Journal of Physics 9 (2007) 278. More...

function	Transform2Spin ()
	Transforms the Hamiltonians and the overlap matrices to include electron spin. More...

function	Write (MemberName, input)
	Sets the value of an attribute in the interface. 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	ExceedIteration ()
	Throws an "iteration exceeded" warning. More...

Protected Member Functions
function	Initialize ()
	Initializes object properties. More...

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

function	setM ()
	Updates the number of sites in the cross section. More...

Protected Attributes
Property	coordinates
	An instance of the structure coordinates. More...

Property	fazis_mtx_H0
	The matrix of the Peierls phases in the unit cell. More...

Property	fazis_mtx_H1
	The matrix of the Peierls phases in the coupling matrix between the unit cells. More...

Property	fazis_mtx_H1t
	The matrix of the Peierls phases in the transverse coupling matrix between the unit cells. More...

Property	GaugeTransformationApplied
	A logical value. True if a gauge transformation was incorporated into the Hamiltonians or false otherwise. More...

Property	H0
	The Hamiltonian of a unit cell. More...

Property	H00
	Obsolete. More...

Property	H1
	The coupling Hamiltonian between the unit cells. More...

Property	H1_skew_left
	The skew coupling (in the positive direction) between Hamiltonians H0 for transverse calculations. More...

Property	H1_skew_right
	The skew upward (in the negative direction) coupling between Hamiltonians H0 for transverse calculations. More...

Property	H1_transverse
	The transverse coupling between the slabs for transverse calculations. More...

Property	H1adj
	The coupling Hamiltonian between the unit cells in the opposite direction as H1. (For complex energies they differ from each other.) More...

Property	HamiltoniansCreated
	A logical value. True if the Hamiltonians were created, false otherwise. More...

Property	HamiltoniansDecimated
	A logical value. True if the Hamiltonians were decimated, false otherwise. More...

Property	Hanyadik_Lead
	The id number of the current lead. More...

Property	K0
	K0=H0-E*S0, see Eq (4) of PRB 78, 035407. More...

Property	K1
	K1=H1-E*S1, see Eq (4) of PRB 78, 035407. More...

Property	K1_transverse
	K1_transverse=H1_transverse-E*S1_transverse. More...

Property	K1adj
	K1adj=H1adj-E*S1', see Eq (4) of PRB 78, 035407. More...

Property	kulso_szabfokok
	List of sites in the unit cell that should be kept after decimation. More...

Property	Lead_Orientation
	The orientation of the lead. Set +1 is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise. More...

Property	M
	The number of the sites in the cross section. More...

Property	MagneticFieldApplied
	A logical value. True if magnetic field was applied in the Hamiltonians, false otherwise. More...

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

Property	OverlapApplied
	A logical value. True if the overlap integrals were applied, false otherwise. More...

Property	param
	An instance of the structure param. More...

Property	params
	An instance of the structure lead_param. More...

Property	q
	The tranverse momentum for transverse computations. More...

Property	S0
	The overlap integrals of a unit cell. More...

Property	S1
	The overlap integrals between the unit cells. More...

Property	S1_transverse
	The overlap integrals between the slabs for transverse calculations. More...

Property	S1adj
	The adjungate of the overlap integrals between the unit cells. More...

Property	varargin
	list of optional parameters (see http://www.mathworks.com/help/matlab/ref/varargin.html for details) More...

Detailed Description

Class to create and store Hamiltonian of the translational invariant leads.

The notations and the structure of the Hamiltonian is defined accroding to the following image:

Available

EQuUs v4.8 or later

Definition at line 29 of file CreateLeadHamiltonians.m.

Constructor & Destructor Documentation

◆ CreateLeadHamiltonians()

function CreateLeadHamiltonians::CreateLeadHamiltonians	(	Opt	,
		param	,
		varargin
	)

Constructor of the class.

Parameters

Opt	An instance of the structure Opt.
param	An instance of structure param.
varargin	Cell array of optional parameters. See InputParsing for details.

Returns: An instance of the class

Member Function Documentation

◆ AddPotential()

function CreateLeadHamiltonians::AddPotential ( V )

Adds on-site potential to the Hamiltonian H0.

Parameters

V	The potential calculated on the sites.

◆ ApplyOverlapMatrices()

function CreateLeadHamiltonians::ApplyOverlapMatrices ( E )

Applies the overlap matrices to the Hamiltonians: K = H-ES.

Parameters

E	The energy value.

◆ 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.

◆ CalcSpektrum()

function CreateLeadHamiltonians::CalcSpektrum ( varargin )

Calculates the band structure of the lead.

Parameters

varargin	Cell array of optional parameters:
'toPlot'	Set 1 in order to plot the calculated spectrum, 0 (default) otherwise
'ka_min'	The lower bound of the wave numbers. (Default is -pi.)
'ka_max'	The upper bound of the wave numbers. (Default is pi.)
'ka_num'	The number of wave number points involved in the calculations. (Default is 300.)
'ka_vec'	One dimensional array of the k-pints. (Overrides previous attributes related to the k-vector array.)
'center'	The calculated energy eigenvalues are centered around this value. (Default is 0.001.)
'db'	The number of the calculated eigenvalues.
'offset'	Offset value to shift the spectrum along the energy axis.
'calcWaveFnc'	Logical value. Set true to calculate also the wave functions, or false (default) otherwise.

Returns: [1] ka_num x 2 array of the calculated spactrum. In the first column are the k-points, whil ein the second columns are the calculated energy points.; [2] The calculated wave functions stored in a structure WaveFnc.

◆ Clear()

function CreateLeadHamiltonians::Clear ( MemberName )

Clears the value of an attribute in the interface.

Parameters

MemberName The name of the attribute to be cleared.

◆ CreateClone()

function CreateLeadHamiltonians::CreateClone ( varargin )

Creates a clone of the present class.

Returns: Returns with the cloned object.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'empty'	Set true to create an empty clone, or false (default) to clone all atributes.

◆ CreateHamiltonians()

function CreateLeadHamiltonians::CreateHamiltonians ( varargin )

Creates the Hamiltonians H_0 and H_1 of the lead.

The created Hamiltonians are stored by within the object.

Parameters

varargin	Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
'toSave'	Logical value. If true, the created Hamiltonians are saved into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'.
'CustomHamiltonian'	An instance of class Custom_Hamiltonians describing external source of Hamiltonians.

◆ 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.

◆ ExceedIteration()

static function Messages::ExceedIteration ( )

staticinherited

Throws an "iteration exceeded" warning.

◆ getOpt()

function Messages::getOpt ( )

inherited

Retrives the structure containing the calculation parameters.

Returns: Return an instance of structure Opt.

◆ Initialize()

function CreateLeadHamiltonians::Initialize ( )

protected

Initializes object properties.

◆ InputParsing()

function CreateLeadHamiltonians::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):
'Hanyadik_Lead'	The ID number of the current lead. Set to empty (default) for using parameters of the scatter region.
'Lead_Orientation'	Orientation of the lead. Set +1 (default) is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise.
'q'	The transverse momentum. Set to empty (default) for computations without transverse momentums.

◆ isSuperconducting()

function CreateLeadHamiltonians::isSuperconducting ( )

Test, whether the lead is in the superconducting phase or not.

Returns: True if the lead is superconducting, false otherwise.

◆ MomentumDependentHamiltonian()

function CreateLeadHamiltonians::MomentumDependentHamiltonian	(	k	,
		q
	)

Construct a momentum dependent (Fourier-transformed) Hamiltonian.

Parameters

k	The longitudinal momentum times the lattice constant.
q	The transverse momentum times the lattice constant.

Returns: Return with the momentum dependent Hamiltonian.

◆ Read()

function CreateLeadHamiltonians::Read ( MemberName )

Query for the value of an attribute in the interface.

Parameters

MemberName The name of the attribute to be set.

Returns: Returns with the value of the attribute.

◆ Reset()

function CreateLeadHamiltonians::Reset ( )

Resets all elements in the object.

◆ saveLeads()

function CreateLeadHamiltonians::saveLeads ( )

Save Lead Hamiltonians into a file 'Hamiltoni_Lead_' + num2str(Hanyadik_Lead) + '.mat'.

◆ setM()

function CreateLeadHamiltonians::setM ( )

protected

Updates the number of sites in the cross section.

◆ ShiftCoordinates()

function CreateLeadHamiltonians::ShiftCoordinates ( shift )

Shifts the coordinates of the sites by an integer multiple of the lattice vector Coordinates.a.

Parameters

shift Integer by which the coordinates are shifted.

◆ ShiftLead()

function CreateLeadHamiltonians::ShiftLead ( Energy )

Shifts the on-site energies in the leads by a given energy.

Parameters

Energy The enrgy value.

◆ Transform2BdG()

function CreateLeadHamiltonians::Transform2BdG ( )

Transforms the Hamiltonians and the overlap matrices into the BdG model in the Nambu space representation according to New Journal of Physics 9 (2007) 278.

It is assumed, that the Hamiltonian is already transfromed to the grand canonical operator: $\hat{H} \rightarrow \hat{H} - E_F\hat{N}$

◆ Transform2Spin()

function CreateLeadHamiltonians::Transform2Spin ( )

Transforms the Hamiltonians and the overlap matrices to include electron spin.

◆ Write()

function CreateLeadHamiltonians::Write	(	MemberName	,
		input
	)

Sets the value of an attribute in the interface.

Parameters

MemberName	The name of the attribute to be set.
input	The value to be set.

Member Data Documentation

◆ coordinates

Property CreateLeadHamiltonians::coordinates

protected

An instance of the structure coordinates.

Definition at line 58 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H0

Property CreateLeadHamiltonians::fazis_mtx_H0

protected

The matrix of the Peierls phases in the unit cell.

Definition at line 106 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H1

Property CreateLeadHamiltonians::fazis_mtx_H1

protected

The matrix of the Peierls phases in the coupling matrix between the unit cells.

Definition at line 109 of file CreateLeadHamiltonians.m.

◆ fazis_mtx_H1t

Property CreateLeadHamiltonians::fazis_mtx_H1t

protected

The matrix of the Peierls phases in the transverse coupling matrix between the unit cells.

Definition at line 112 of file CreateLeadHamiltonians.m.

◆ GaugeTransformationApplied

Property CreateLeadHamiltonians::GaugeTransformationApplied

protected

A logical value. True if a gauge transformation was incorporated into the Hamiltonians or false otherwise.

Definition at line 127 of file CreateLeadHamiltonians.m.

◆ H0

Property CreateLeadHamiltonians::H0

protected

The Hamiltonian of a unit cell.

Definition at line 73 of file CreateLeadHamiltonians.m.

◆ H00

Property CreateLeadHamiltonians::H00

protected

Obsolete.

Definition at line 82 of file CreateLeadHamiltonians.m.

◆ H1

Property CreateLeadHamiltonians::H1

protected

The coupling Hamiltonian between the unit cells.

Definition at line 76 of file CreateLeadHamiltonians.m.

◆ H1_skew_left

Property CreateLeadHamiltonians::H1_skew_left

protected

The skew coupling (in the positive direction) between Hamiltonians H0 for transverse calculations.

Definition at line 91 of file CreateLeadHamiltonians.m.

◆ H1_skew_right

Property CreateLeadHamiltonians::H1_skew_right

protected

The skew upward (in the negative direction) coupling between Hamiltonians H0 for transverse calculations.

Definition at line 88 of file CreateLeadHamiltonians.m.

◆ H1_transverse

Property CreateLeadHamiltonians::H1_transverse

protected

The transverse coupling between the slabs for transverse calculations.

Definition at line 85 of file CreateLeadHamiltonians.m.

◆ H1adj

Property CreateLeadHamiltonians::H1adj

protected

The coupling Hamiltonian between the unit cells in the opposite direction as H1. (For complex energies they differ from each other.)

Definition at line 79 of file CreateLeadHamiltonians.m.

◆ HamiltoniansCreated

Property CreateLeadHamiltonians::HamiltoniansCreated

protected

A logical value. True if the Hamiltonians were created, false otherwise.

Definition at line 115 of file CreateLeadHamiltonians.m.

◆ HamiltoniansDecimated

Property CreateLeadHamiltonians::HamiltoniansDecimated

protected

A logical value. True if the Hamiltonians were decimated, false otherwise.

Definition at line 118 of file CreateLeadHamiltonians.m.

◆ Hanyadik_Lead

Property CreateLeadHamiltonians::Hanyadik_Lead

protected

The id number of the current lead.

Definition at line 43 of file CreateLeadHamiltonians.m.

◆ K0

Property CreateLeadHamiltonians::K0

protected

K0=H0-E*S0, see Eq (4) of PRB 78, 035407.

Definition at line 61 of file CreateLeadHamiltonians.m.

◆ K1

Property CreateLeadHamiltonians::K1

protected

K1=H1-E*S1, see Eq (4) of PRB 78, 035407.

Definition at line 64 of file CreateLeadHamiltonians.m.

◆ K1_transverse

Property CreateLeadHamiltonians::K1_transverse

protected

K1_transverse=H1_transverse-E*S1_transverse.

Definition at line 70 of file CreateLeadHamiltonians.m.

◆ K1adj

Property CreateLeadHamiltonians::K1adj

protected

K1adj=H1adj-E*S1', see Eq (4) of PRB 78, 035407.

Definition at line 67 of file CreateLeadHamiltonians.m.

◆ kulso_szabfokok

Property CreateLeadHamiltonians::kulso_szabfokok

protected

List of sites in the unit cell that should be kept after decimation.

Definition at line 55 of file CreateLeadHamiltonians.m.

◆ Lead_Orientation

Property CreateLeadHamiltonians::Lead_Orientation

protected

The orientation of the lead. Set +1 is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise.

Definition at line 40 of file CreateLeadHamiltonians.m.

◆ M

Property CreateLeadHamiltonians::M

protected

The number of the sites in the cross section.

Definition at line 46 of file CreateLeadHamiltonians.m.

◆ MagneticFieldApplied

Property CreateLeadHamiltonians::MagneticFieldApplied

protected

A logical value. True if magnetic field was applied in the Hamiltonians, false otherwise.

Definition at line 124 of file CreateLeadHamiltonians.m.

◆ Opt

Property Messages::Opt

protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

◆ OverlapApplied

Property CreateLeadHamiltonians::OverlapApplied

protected

A logical value. True if the overlap integrals were applied, false otherwise.

Definition at line 121 of file CreateLeadHamiltonians.m.

◆ param

Property CreateLeadHamiltonians::param

protected

An instance of the structure param.

Definition at line 37 of file CreateLeadHamiltonians.m.

◆ params

Property CreateLeadHamiltonians::params

protected

An instance of the structure lead_param.

Definition at line 49 of file CreateLeadHamiltonians.m.

◆ q

Property CreateLeadHamiltonians::q

protected

The tranverse momentum for transverse computations.

Definition at line 52 of file CreateLeadHamiltonians.m.

◆ S0

Property CreateLeadHamiltonians::S0

protected

The overlap integrals of a unit cell.

Definition at line 94 of file CreateLeadHamiltonians.m.

◆ S1

Property CreateLeadHamiltonians::S1

protected

The overlap integrals between the unit cells.

Definition at line 97 of file CreateLeadHamiltonians.m.

◆ S1_transverse

Property CreateLeadHamiltonians::S1_transverse

protected

The overlap integrals between the slabs for transverse calculations.

Definition at line 103 of file CreateLeadHamiltonians.m.

◆ S1adj

Property CreateLeadHamiltonians::S1adj

protected

The adjungate of the overlap integrals between the unit cells.

Definition at line 100 of file CreateLeadHamiltonians.m.

◆ varargin

Property CreateLeadHamiltonians::varargin

protected

list of optional parameters (see http://www.mathworks.com/help/matlab/ref/varargin.html for details)

Definition at line 130 of file CreateLeadHamiltonians.m.

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

CreateLeadHamiltonians.m

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Available

Constructor & Destructor Documentation

◆ CreateLeadHamiltonians()

Member Function Documentation

◆ AddPotential()

◆ ApplyOverlapMatrices()

◆ BadInputType()

◆ BadInputTypeNoDefault()

◆ CalcSpektrum()

◆ Clear()

◆ CreateClone()

◆ CreateHamiltonians()

◆ display()

◆ ExceedIteration()

◆ getOpt()

◆ Initialize()

◆ InputParsing()

◆ isSuperconducting()

◆ MomentumDependentHamiltonian()

◆ Read()

◆ Reset()

◆ saveLeads()

◆ setM()

◆ ShiftCoordinates()

◆ ShiftLead()

◆ Transform2BdG()

◆ Transform2Spin()

◆ Write()

Member Data Documentation

◆ coordinates

◆ fazis_mtx_H0

◆ fazis_mtx_H1

◆ fazis_mtx_H1t

◆ GaugeTransformationApplied

◆ H0

◆ H00

◆ H1

◆ H1_skew_left

◆ H1_skew_right

◆ H1_transverse

◆ H1adj

◆ HamiltoniansCreated

◆ HamiltoniansDecimated

◆ Hanyadik_Lead

◆ K0

◆ K1

◆ K1_transverse

◆ K1adj

◆ kulso_szabfokok

◆ Lead_Orientation

◆ M

◆ MagneticFieldApplied

◆ Opt

◆ OverlapApplied

◆ param

◆ params

◆ q

◆ S0

◆ S1

◆ S1_transverse

◆ S1adj

◆ varargin