Eötvös Quantum Utilities  v4.9.146
Providing the Horsepowers in the Quantum Realm
List of all members | Public Member Functions | Static Public Member Functions | Protected Member Functions | Protected Attributes | Private Member Functions
EigenProblemLead Class Reference

Class to solve the eigenproblem of a translational invariant leads and calculate the group velocities. More...

Inheritance diagram for EigenProblemLead:
Inheritance graph
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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 Calc_Effective_Hamiltonians (E)
 Calculates the effective Hamiltonians according to Eq (48) of of PRB 78, 035407. More...
 
function CalcSpektrum (varargin)
 Calculates the band structure of the lead. More...
 
function Clear (MemberName)
 Clears the value of an attribute in the class. More...
 
function CreateClone (varargin)
 Creates a clone of the present object. More...
 
function CreateClone ()
 Creates a clone of the present object. More...
 
function CreateHamiltonians (varargin)
 Creates the Hamiltonians H_0 and H_1 of the lead. More...
 
function Decimate_Hamiltonians ()
 Decimates the Hamiltonians (if the singular sites are predefined). More...
 
function Determine_Open_Channels ()
 Determines the open channels in the lead. The data are storen within the attribute open_channels. More...
 
function display (message, nosilent)
 Displays output messages on the screen. More...
 
function EigenProblemLead (Opt, param, varargin)
 Constructor of the class. More...
 
function Get_Effective_Coordinates ()
 Gets the coordinates of the sites of the effective Hamiltonians. More...
 
function Get_Effective_Hamiltonians ()
 Gets the effective Hamiltonians K0_eff, K1_eff, K1adj_eff according to Eq (48) of of PRB 78, 035407. More...
 
function Get_Effective_Overlaps ()
 Gets the effective Hamiltonians S0_eff, S1_eff, S1adj_eff according to Eq (48) of of PRB 78, 035407. More...
 
function Get_Neff ()
 Gets the effective number of sites after the elimination of the singular values. More...
 
function Get_V ()
 Gets the total transformation U related to the SVD transformation. More...
 
function getOpt ()
 Retrives the structure containing the calculation parameters. More...
 
function Group_Velocity ()
 Calculates the group velocities corresponding to the propagating states. The calculated group velocities are stored within the class. More...
 
function is_SVD_needed ()
 Decides whether SVD regularization is needed or not. 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 class. 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 SVD_transform ()
 Regularize the Hamiltonians of the lead by SVD regularization. More...
 
function SVDdecompozition ()
 Calculates the SVD decomposition of the matrix H1. More...
 
function szetvalaszto (tolerance)
 Sorts the left and right propagating (decaying) modes. 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 TrukkosSajatertekek (E)
 Calculates the wave numbers corresponding to the propagating states at given energy. More...
 
function Unitary_Transform (Umtx)
 Transforms the effective Hamiltonians by a unitary transformation. More...
 
function Write (MemberName, input)
 Sets the value of an attribute in the class. 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 Extend_Wavefnc (wavefnc_reduced, expk)
 Extend a reduced wave function to the original basis before the SVD regularization (Eq (45) in PRB 78 035407. More...
 
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 csoportseb
 The unsorted group velocities. More...
 
Property d_modusmtx_m
 The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the negative direction. More...
 
Property d_modusmtx_p
 The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the positive direction. More...
 
Property degenerate_k_subspaces
 Logical matrix containing the degenerate k subspaces. More...
 
Property E
 The energy value for which the TrukkosSajatertekek eigenvalue problem was solved. More...
 
Property expk
 The unsorted wave numbers in form exp(1i*k). More...
 
Property expk_m
 The wave numbers of the eigenstates in form exp(1i*k), that propagates or decays in the negative direction. More...
 
Property expk_p
 The wave numbers of the eigenstates, that propagates or decays in the positive direction. 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 is_SVD_transformed
 true if the Hamiltonians were SVD transformed, false otherwise 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 modusmtx
 The unsorted right-sided eigenstates. More...
 
Property modusmtx_left
 The unsorted left-sided eigenstates. More...
 
Property modusmtx_m
 The right-sided wave functions of the eigenstates, that propagates or decays in the negative direction. More...
 
Property modusmtx_m_left
 The left-sided wave functions of the eigenstates, that propagates or decays in the negative direction. More...
 
Property modusmtx_p
 The right sided wave functions of the eigenstates, that propagates or decays in the positive direction. More...
 
Property modusmtx_p_left
 The left-sided wave numbers of the eigenstates, that propagates or decays in the positive direction. More...
 
Property Neff
 Effective number of sites after the elimination of the singular values. More...
 
Property next_SVD_cycle
 Somethimes it is needed to perform another SVD cycle to regularize the H1 matrix. More...
 
Property open_channels
 A structure open_channels containing info on the open channels. 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 retarted
 true for calculating the retarded Green function, or false for the advanced Green function. More...
 
Property S
 S matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407. 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 sort_tolerance
 A real number corresponding to the tolerance used to sort the left and right moving (decaying) modes. More...
 
Property tolerance
 SVD tolerance to identify singular values. More...
 
Property U
 U matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407. More...
 
Property V
 V matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407. More...
 
Property varargin
 list of optional parameters (see http://www.mathworks.com/help/matlab/ref/varargin.html for details) More...
 
Property vcsop_m
 The group velocities of the eigenstates, that propagates or decays in the negative direction. More...
 
Property vcsop_p
 The group velocities of the eigenstates in form exp(1i*k), that propagates or decays in the positive direction. More...
 

Private Member Functions

function Determine_Degenerate_k_subspaces ()
 Determine the degenerate k subspaces for which the current operator needs to be diagonalized. More...
 
function Extend_Wavefncs ()
 Extend the reduced wave functions to the original basis before the SVD regularization (Eq (45) in PRB 78 035407) This function is in a development stage. More...
 
function NormalizeModes ()
 Renormalizes the wave functions with the overlap integrals (Eq (9) in PRB 78 035407. More...
 

Detailed Description

Class to solve the eigenproblem of a translational invariant leads and calculate the group velocities.

Available

EQuUs v4.8 or later

Definition at line 26 of file EigenProblemLead.m.

Constructor & Destructor Documentation

◆ EigenProblemLead()

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

Constructor of the class.

Parameters
OptAn instance of the structure Opt.
paramAn instance of structure param.
vararginCell array of optional parameters identical to SVDregularizationLead.SVDregularizationLead.
Returns
An instance of the class

Member Function Documentation

◆ AddPotential()

function EigenProblemLead::AddPotential ( V  )

Adds on-site potential to the Hamiltonian H0.

Parameters
VThe potential calculated on the sites.

◆ ApplyOverlapMatrices()

function CreateLeadHamiltonians::ApplyOverlapMatrices ( )
inherited

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

Parameters
EThe energy value.

◆ BadInputType()

static function Messages::BadInputType ( variable  ,
type   
)
staticinherited

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

Parameters
variableA string conatining the name of the variable.
typeA 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
variableA string conatining the name of the variable.
typeA string describing the desired type.

◆ Calc_Effective_Hamiltonians()

function SVDregularizationLead::Calc_Effective_Hamiltonians ( )
inherited

Calculates the effective Hamiltonians according to Eq (48) of of PRB 78, 035407.

Parameters
EThe energy value

◆ CalcSpektrum()

function CreateLeadHamiltonians::CalcSpektrum ( varargin  )
inherited

Calculates the band structure of the lead.

Parameters
vararginCell 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 EigenProblemLead::Clear ( MemberName  )

Clears the value of an attribute in the class.

Parameters
MemberNameThe name of the attribute to be cleared.

◆ CreateClone() [1/2]

function SVDregularizationLead::CreateClone ( varargin  )
inherited

Creates a clone of the present object.

Returns
Returns with the cloned object.
Parameters
vararginCell array of optional parameters:.

◆ CreateClone() [2/2]

function EigenProblemLead::CreateClone ( )

Creates a clone of the present object.

Returns
Returns with the cloned class.
Parameters
vararginCell array of optional parameters:
'empty'Set true to create an empty class, or false (default) to copy all the attributes.
Returns
Returns with an instance of the cloned class.

◆ CreateHamiltonians()

function CreateLeadHamiltonians::CreateHamiltonians ( varargin  )
inherited

Creates the Hamiltonians H_0 and H_1 of the lead.

The created Hamiltonians are stored by within the object.

Parameters
vararginCell 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.

◆ Decimate_Hamiltonians()

function SVDregularizationLead::Decimate_Hamiltonians ( )
inherited

Decimates the Hamiltonians (if the singular sites are predefined).

◆ Determine_Degenerate_k_subspaces()

function EigenProblemLead::Determine_Degenerate_k_subspaces ( )
private

Determine the degenerate k subspaces for which the current operator needs to be diagonalized.

◆ Determine_Open_Channels()

function EigenProblemLead::Determine_Open_Channels ( )

Determines the open channels in the lead. The data are storen within the attribute open_channels.

◆ display()

function Messages::display ( message  ,
nosilent   
)
inherited

Displays output messages on the screen.

Parameters
messageString containing the message to be displayed
nosilentSet true to override the silent option given in Opt.Silent.

◆ ExceedIteration()

static function Messages::ExceedIteration ( )
staticinherited

Throws an "iteration exceeded" warning.

◆ Extend_Wavefnc()

function SVDregularizationLead::Extend_Wavefnc ( wavefnc_reduced  ,
expk   
)
protectedinherited

Extend a reduced wave function to the original basis before the SVD regularization (Eq (45) in PRB 78 035407.

Parameters
wavefnc_reducedThe reduced wavefunction of the effective system
expke^(i*k)
Returns
A matrix conatining the extended wave functions.

◆ Extend_Wavefncs()

function EigenProblemLead::Extend_Wavefncs ( )
private

Extend the reduced wave functions to the original basis before the SVD regularization (Eq (45) in PRB 78 035407) This function is in a development stage.

◆ Get_Effective_Coordinates()

function SVDregularizationLead::Get_Effective_Coordinates ( )
inherited

Gets the coordinates of the sites of the effective Hamiltonians.

(Has sense if the singular sites were given directly)

Returns
[1] A class Coordinates containing the coordinates of the sites of the effective Hamiltonian

◆ Get_Effective_Hamiltonians()

function SVDregularizationLead::Get_Effective_Hamiltonians ( )
inherited

Gets the effective Hamiltonians K0_eff, K1_eff, K1adj_eff according to Eq (48) of of PRB 78, 035407.

Returns
[1] The effective Hamiltonian of one unit cell
[2] The effective coupling between unit cells K1_eff
[3] The adjungate of the effective coupling between unit cells K1adj_eff

◆ Get_Effective_Overlaps()

function SVDregularizationLead::Get_Effective_Overlaps ( )
inherited

Gets the effective Hamiltonians S0_eff, S1_eff, S1adj_eff according to Eq (48) of of PRB 78, 035407.

Returns
[1] The effective overlap matrix of one unit cell S0_eff
[2] The effective overlap matrix between unit cells S1_eff
[3] The adjungate of the effective overlap matrix between unit cells S1adj_eff

◆ Get_Neff()

function SVDregularizationLead::Get_Neff ( )
inherited

Gets the effective number of sites after the elimination of the singular values.

Returns
Returns with the effective number of sites

◆ Get_V()

function SVDregularizationLead::Get_V ( )
inherited

Gets the total transformation U related to the SVD transformation.

Returns
Returns with the total transformation U

◆ getOpt()

function Messages::getOpt ( )
inherited

Retrives the structure containing the calculation parameters.

Returns
Return an instance of structure Opt.

◆ Group_Velocity()

function EigenProblemLead::Group_Velocity ( )

Calculates the group velocities corresponding to the propagating states. The calculated group velocities are stored within the class.

◆ Initialize()

function EigenProblemLead::Initialize ( )
protected

Initializes object properties.

◆ InputParsing()

function CreateLeadHamiltonians::InputParsing ( varargin  )
protectedinherited

Parses the optional parameters for the class constructor.

Parameters
vararginCell 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.

◆ is_SVD_needed()

function SVDregularizationLead::is_SVD_needed ( )
inherited

Decides whether SVD regularization is needed or not.

Returns
Returns with true if SVD regularization is needed, false otherwise

◆ isSuperconducting()

function CreateLeadHamiltonians::isSuperconducting ( )
inherited

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

Returns
True if the lead is superconducting, false otherwise.

◆ MomentumDependentHamiltonian()

function CreateLeadHamiltonians::MomentumDependentHamiltonian ( ,
q   
)
inherited

Construct a momentum dependent (Fourier-transformed) Hamiltonian.

Parameters
kThe longitudinal momentum times the lattice constant.
qThe transverse momentum times the lattice constant.
Returns
Return with the momentum dependent Hamiltonian.

◆ NormalizeModes()

function EigenProblemLead::NormalizeModes ( )
private

Renormalizes the wave functions with the overlap integrals (Eq (9) in PRB 78 035407.

◆ Read()

function EigenProblemLead::Read ( MemberName  )

Query for the value of an attribute in the class.

Parameters
MemberNameThe name of the attribute to be set.
Returns
Returns with the value of the attribute.

◆ Reset()

function EigenProblemLead::Reset ( )

Resets all elements in the object.

◆ saveLeads()

function CreateLeadHamiltonians::saveLeads ( )
inherited

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

◆ setM()

function CreateLeadHamiltonians::setM ( )
protectedinherited

Updates the number of sites in the cross section.

◆ ShiftCoordinates()

function CreateLeadHamiltonians::ShiftCoordinates ( shift  )
inherited

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

Parameters
shiftInteger by which the coordinates are shifted.

◆ ShiftLead()

function CreateLeadHamiltonians::ShiftLead ( Energy  )
inherited

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

Parameters
EnergyThe enrgy value.

◆ SVD_transform()

function SVDregularizationLead::SVD_transform ( )
inherited

Regularize the Hamiltonians of the lead by SVD regularization.

◆ SVDdecompozition()

function SVDregularizationLead::SVDdecompozition ( )
inherited

Calculates the SVD decomposition of the matrix H1.

◆ szetvalaszto()

function EigenProblemLead::szetvalaszto ( tolerance  )

Sorts the left and right propagating (decaying) modes.

Parameters
toleranceThe tolerance to be used during the sort.

◆ Transform2BdG()

function CreateLeadHamiltonians::Transform2BdG ( )
inherited

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 ( )
inherited

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

◆ TrukkosSajatertekek()

function EigenProblemLead::TrukkosSajatertekek ( E  )

Calculates the wave numbers corresponding to the propagating states at given energy.

The calculated wave numbers are stored by attribute expk.

Parameters
EThe energy value used in the calculations.

◆ Unitary_Transform()

function EigenProblemLead::Unitary_Transform ( Umtx  )

Transforms the effective Hamiltonians by a unitary transformation.

Parameters
UmtxThe matrix of the unitary transformation.

◆ Write()

function EigenProblemLead::Write ( MemberName  ,
input   
)

Sets the value of an attribute in the class.

Parameters
MemberNameThe name of the attribute to be set.
inputThe value to be set.

Member Data Documentation

◆ coordinates

Property CreateLeadHamiltonians::coordinates
protectedinherited

An instance of the structure coordinates.

Definition at line 58 of file CreateLeadHamiltonians.m.

◆ csoportseb

Property EigenProblemLead::csoportseb
protected

The unsorted group velocities.

Definition at line 46 of file EigenProblemLead.m.

◆ d_modusmtx_m

Property EigenProblemLead::d_modusmtx_m
protected

The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the negative direction.

Definition at line 76 of file EigenProblemLead.m.

◆ d_modusmtx_p

Property EigenProblemLead::d_modusmtx_p
protected

The dual basis of the right-sided wave functions of the eigenstates, that propagates or decays in the positive direction.

Definition at line 73 of file EigenProblemLead.m.

◆ degenerate_k_subspaces

Property EigenProblemLead::degenerate_k_subspaces
protected

Logical matrix containing the degenerate k subspaces.

Definition at line 85 of file EigenProblemLead.m.

◆ E

Property EigenProblemLead::E
protected

The energy value for which the TrukkosSajatertekek eigenvalue problem was solved.

Definition at line 88 of file EigenProblemLead.m.

◆ expk

Property EigenProblemLead::expk
protected

The unsorted wave numbers in form exp(1i*k).

Definition at line 43 of file EigenProblemLead.m.

◆ expk_m

Property EigenProblemLead::expk_m
protected

The wave numbers of the eigenstates in form exp(1i*k), that propagates or decays in the negative direction.

Definition at line 52 of file EigenProblemLead.m.

◆ expk_p

Property EigenProblemLead::expk_p
protected

The wave numbers of the eigenstates, that propagates or decays in the positive direction.

Definition at line 49 of file EigenProblemLead.m.

◆ fazis_mtx_H0

Property CreateLeadHamiltonians::fazis_mtx_H0
protectedinherited

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
protectedinherited

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
protectedinherited

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
protectedinherited

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
protectedinherited

The Hamiltonian of a unit cell.

Definition at line 73 of file CreateLeadHamiltonians.m.

◆ H00

Property CreateLeadHamiltonians::H00
protectedinherited

Obsolete.

Definition at line 82 of file CreateLeadHamiltonians.m.

◆ H1

Property CreateLeadHamiltonians::H1
protectedinherited

The coupling Hamiltonian between the unit cells.

Definition at line 76 of file CreateLeadHamiltonians.m.

◆ H1_skew_left

Property CreateLeadHamiltonians::H1_skew_left
protectedinherited

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
protectedinherited

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
protectedinherited

The transverse coupling between the slabs for transverse calculations.

Definition at line 85 of file CreateLeadHamiltonians.m.

◆ H1adj

Property CreateLeadHamiltonians::H1adj
protectedinherited

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
protectedinherited

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

Definition at line 115 of file CreateLeadHamiltonians.m.

◆ HamiltoniansDecimated

Property CreateLeadHamiltonians::HamiltoniansDecimated
protectedinherited

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
protectedinherited

The id number of the current lead.

Definition at line 43 of file CreateLeadHamiltonians.m.

◆ is_SVD_transformed

Property SVDregularizationLead::is_SVD_transformed
protectedinherited

true if the Hamiltonians were SVD transformed, false otherwise

Definition at line 37 of file SVDregularizationLead.m.

◆ K0

Property CreateLeadHamiltonians::K0
protectedinherited

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

Definition at line 61 of file CreateLeadHamiltonians.m.

◆ K1

Property CreateLeadHamiltonians::K1
protectedinherited

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
protectedinherited

K1_transverse=H1_transverse-E*S1_transverse.

Definition at line 70 of file CreateLeadHamiltonians.m.

◆ K1adj

Property CreateLeadHamiltonians::K1adj
protectedinherited

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
protectedinherited

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
protectedinherited

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
protectedinherited

The number of the sites in the cross section.

Definition at line 46 of file CreateLeadHamiltonians.m.

◆ MagneticFieldApplied

Property CreateLeadHamiltonians::MagneticFieldApplied
protectedinherited

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

Definition at line 124 of file CreateLeadHamiltonians.m.

◆ modusmtx

Property EigenProblemLead::modusmtx
protected

The unsorted right-sided eigenstates.

Definition at line 37 of file EigenProblemLead.m.

◆ modusmtx_left

Property EigenProblemLead::modusmtx_left
protected

The unsorted left-sided eigenstates.

Definition at line 40 of file EigenProblemLead.m.

◆ modusmtx_m

Property EigenProblemLead::modusmtx_m
protected

The right-sided wave functions of the eigenstates, that propagates or decays in the negative direction.

Definition at line 64 of file EigenProblemLead.m.

◆ modusmtx_m_left

Property EigenProblemLead::modusmtx_m_left
protected

The left-sided wave functions of the eigenstates, that propagates or decays in the negative direction.

Definition at line 70 of file EigenProblemLead.m.

◆ modusmtx_p

Property EigenProblemLead::modusmtx_p
protected

The right sided wave functions of the eigenstates, that propagates or decays in the positive direction.

Definition at line 61 of file EigenProblemLead.m.

◆ modusmtx_p_left

Property EigenProblemLead::modusmtx_p_left
protected

The left-sided wave numbers of the eigenstates, that propagates or decays in the positive direction.

Definition at line 67 of file EigenProblemLead.m.

◆ Neff

Property SVDregularizationLead::Neff
protectedinherited

Effective number of sites after the elimination of the singular values.

Definition at line 55 of file SVDregularizationLead.m.

◆ next_SVD_cycle

Property SVDregularizationLead::next_SVD_cycle
protectedinherited

Somethimes it is needed to perform another SVD cycle to regularize the H1 matrix.

Definition at line 52 of file SVDregularizationLead.m.

◆ open_channels

Property EigenProblemLead::open_channels
protected

A structure open_channels containing info on the open channels.

Definition at line 82 of file EigenProblemLead.m.

◆ Opt

Property Messages::Opt
protectedinherited

An instance of structure Opt.

Definition at line 31 of file Messages.m.

◆ OverlapApplied

Property CreateLeadHamiltonians::OverlapApplied
protectedinherited

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

Definition at line 121 of file CreateLeadHamiltonians.m.

◆ param

Property CreateLeadHamiltonians::param
protectedinherited

An instance of the structure param.

Definition at line 37 of file CreateLeadHamiltonians.m.

◆ params

Property CreateLeadHamiltonians::params
protectedinherited

An instance of the structure lead_param.

Definition at line 49 of file CreateLeadHamiltonians.m.

◆ q

Property CreateLeadHamiltonians::q
protectedinherited

The tranverse momentum for transverse computations.

Definition at line 52 of file CreateLeadHamiltonians.m.

◆ retarted

Property EigenProblemLead::retarted
protected

true for calculating the retarded Green function, or false for the advanced Green function.

Definition at line 34 of file EigenProblemLead.m.

◆ S

Property SVDregularizationLead::S
protectedinherited

S matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407.

Definition at line 43 of file SVDregularizationLead.m.

◆ S0

Property CreateLeadHamiltonians::S0
protectedinherited

The overlap integrals of a unit cell.

Definition at line 94 of file CreateLeadHamiltonians.m.

◆ S1

Property CreateLeadHamiltonians::S1
protectedinherited

The overlap integrals between the unit cells.

Definition at line 97 of file CreateLeadHamiltonians.m.

◆ S1_transverse

Property CreateLeadHamiltonians::S1_transverse
protectedinherited

The overlap integrals between the slabs for transverse calculations.

Definition at line 103 of file CreateLeadHamiltonians.m.

◆ S1adj

Property CreateLeadHamiltonians::S1adj
protectedinherited

The adjungate of the overlap integrals between the unit cells.

Definition at line 100 of file CreateLeadHamiltonians.m.

◆ sort_tolerance

Property EigenProblemLead::sort_tolerance
protected

A real number corresponding to the tolerance used to sort the left and right moving (decaying) modes.

Definition at line 79 of file EigenProblemLead.m.

◆ tolerance

Property SVDregularizationLead::tolerance
protectedinherited

SVD tolerance to identify singular values.

Definition at line 49 of file SVDregularizationLead.m.

◆ U

Property SVDregularizationLead::U
protectedinherited

U matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407.

Definition at line 40 of file SVDregularizationLead.m.

◆ V

Property SVDregularizationLead::V
protectedinherited

V matrix from the SVD decompozition, see Eq (41) of PRB 78, 035407.

Definition at line 46 of file SVDregularizationLead.m.

◆ varargin

Property CreateLeadHamiltonians::varargin
protectedinherited

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

Definition at line 130 of file CreateLeadHamiltonians.m.

◆ vcsop_m

Property EigenProblemLead::vcsop_m
protected

The group velocities of the eigenstates, that propagates or decays in the negative direction.

Definition at line 58 of file EigenProblemLead.m.

◆ vcsop_p

Property EigenProblemLead::vcsop_p
protected

The group velocities of the eigenstates in form exp(1i*k), that propagates or decays in the positive direction.

Definition at line 55 of file EigenProblemLead.m.


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