The folder contains all data produced to obtain the figures reported in R. Favata, N. Baù, A. Marrazzo, Fluctuations and correlations of local topological order parameters in disordered two-dimensional topological insulators. 

-- Folders 'Fig1', 'Fig2', 'Fig4' and 'Fig5' contains data produced to obtain corresponding figures in the main text of the manuscript (included the Appendices), where the Haldane model is considered.

The names of the files contain the following information:
- L : the linear size of the supercell
- delta : the on-site energy of the Haldane model
- phi : it is defined such that -pi/phi is the phase of the complex second-nearest neighbor hopping of the Haldane model
- w : the Anderson disorder strength
- rho : the relative density of vacancies
- M : number of realizations at fixed disorder strength / density of vacancies

Other parameters of the Haldane model are set to:
- t = -4, where t indicates the first nearest-neighbor real hopping
- t2 = 1, where t2 is the amplitude of the complex second-nearest neighbor hopping 

Files named as 'L{ }_delta{ }_w/rho{ }_phi{ }_M{ }.txt' in Fig1, Fig4 and Fig5 folders contain:
- C_mean : mean value of results obtained for the single-point Chern calculation using the "symmetric" formula, over M realizations of disorder/vacancies
- std_C : standard deviation of results obtained for the single-point Chern calculation using the "symmetric" formula, over M realizations of disorder/vacancies

Files named as 'corr_L{ }_delta{ }_w{ }_M{ }.txt' in Fig2 folder contain:
- r : radial distance (in units of the lattice parameter) between sites in the honeycomb lattice
- G(r) : the connected Chern-Chern correlation function at distance r
The data shown in the inset of the right-hand panel in Fig2 are obtained by extracting the correlation lengths from correlation functions contained in the folder 'correlation_length_inset', by the fit with the Ornstein-Zernike formula (Eq. 6 in the manuscript).

Files in 'maps' folders contain obc/pbc local Chern markers (lcm) used to plot real-space maps appearing in the manuscript.
The values of the local Chern markers contained in these files are reported as before macroscopic average over cutoff radius r_c is performed.

-- Folder 'SM' contains data produced to obtain the supplementary figures in the Supplementary Material.

Subfolder SM1 contains data for the supplementary Fig1 in "Fluctuations and correlations of local topological order parameters in disordered two-dimensional topological insulators" section, where the Kane-Mele model in the presence of Anderson disorder strength w is considered.

    The parameters of the Kane-Mele model are set to:
    - L = 75, where L is the linear size of the supercell
    - t = 1, where t indicates the first nearest-neighbor real hopping
    - lambda_SOC = 0.05, where lambda_SOC is the amplitude of the complex second-nearest neighbor hopping with a spin-dependent amplitude representing the diagonal Kane-Mele spin-orbit coupling (SOC) 
    - e/lambda_SOC = 3.0, where e is the staggered on-site potential
    - lambda_R/lambda_SOC = 1.0, where lambda_R is the Rashba SOC term, a complex nearest-neighbor hopping with off-diagonal spin components

    Files in the 'SM1' subfolder contain pbc local spin Chern markers (lscm) C_+ (p) and C_- (m) used to plot real-space maps appearing in the supplementary material. 
    The values of the local spin Chern markers contained in these files are reported as before macroscopic average over cutoff radius r_c is performed.

Subfolder SM2 contains data for the supplementary Fig2 in "Correlation functions, exponent and finite-size effects" section, where radial Chern-Chern correlation functions for increasing system sizes L at the topological-to-trivial transition driven by disorder (w=26.0) in the Haldane model are considered.

-- Folder 'Fig3' contains data produced to obtain the corresponding figure in the main text of the manuscript, where both the Haldane (QAHI) and Kane-Mele (QSHI) models are considered.

The parameters are dubbed and set as before.

Files named as 'qahi/qshi_corr_L{ }_delta/e{ }_w{ }_M{ }.txt' in Fig3 folder contain:
- r : radial distance (in units of the lattice parameter) between sites in the honeycomb lattice
- G(r) : the connected Chern-Chern/spin Chern-spin Chern correlation function at distance r

In the following, we list the values of the parameters for the different phase transitions which are discussed in the main text.

Haldane model:
Disorder-driven transitions
	QAHI to trivial: L=96, delta=5.0, phi=-pi/2, w=26.0
	Trivial to TAI: L=96, delta=5.5, phi=-pi/2, w=7.0
	TAI to trivial: L=96, delta=5.5, phi=-pi/2, w=26.0
Vacancy-driven transition
	QAHI to trivial: L=57, delta=0.0, phi=-pi/8,, rho=0.22

Kane-Mele model:
Disorder-driven transitions
	QSHI to trivial: L=72, e/lambda_SOC=3.0, w=4.0
	Trivial to TAI: L=72, e/lambda_SOC=5.3, w=1.4
	TAI to trivial: L=72, e/lambda_SOC=5.3, w=4.0