Charge waves and dynamical signatures of topological phases in Su–Schrieffer–Heeger chains

The file main. f90 contains the program code written in Fortran90 for numerical calculations of stationary LDOS (Local Density of States) and charge distribution along atomic SSH chains placed on a mettalic surface. The calculations are performed within the tight-binding Hamiltonian framework and the Green function technique. The file main2. f90 contains the program code written in Fortran90 for numerical calculations of time dependent LDOS and dynamics of charge distribution along atomic SSH chains placed on a mettalic surface. The calculations are performed within the tight-binding Hamiltonian framework and the evolution operator method. The attached files contain the data used to produce the figures presented in the paper: T. Kwapinski, M. Kurzyna, L. E. F. Foa Torres, Charge waves and dynamical signatures of topological phases in SSH chains, accepted for publication in Physical Review B. Data for figure fig01. eps of this repository (fig1 in the main text of the paper). The files 'fig01A₀lad' (data for panel A), 'fig01B₀lad' (data for panel B) and 'fig01C₀lad' (data for panel C) include charge occupancies along the normal chain (panel A), SSH0 chain (panel B) and SSH1 chain (panel C) of the length N=50 as a function of the site number for differnt values of the on-site energies ranging from e₀=-5 up to +5: column1: site numbercolumn2: charge at each site of the chaincolumn3: normalization of LDOS functioncolumn4: on-site energy Data for figure fig02. jpg of this repository (fig2 in the main text of the paper). The files 'fig02Aᵥlad1ₙ3', 'fig02Aᵥlad11ₙ3' (data for panel A) 'fig02Bᵥlad1ₙ5', 'fig02Bᵥlad11ₙ5' (data for panel B) 'fig02Cᵥlad1ₙ7', 'fig02Cᵥlad11ₙ7' (data for panel C) and'fig02Cᵥlad1ₙ10', 'fig02Cᵥlad11ₙ10' (data for panel D) include charge occupancies along the SSH1 chain of length N=30 (panels A and B) and N=50 (panels C and D) as a function of the site number for the average filling of the chain equals: 1/3, 1/5, 1/7 and 1/10: column1: site numbercolumn2: charge at each site of the chaincolumn3: normalization of LDOS function Data for figure fig03. jpg of this repository (fig10 in the main text of the paper). The files 'fig03Aᵥlad1ₙ5', 'fig03AAᵥlad1ₙ5' and fig03AAAᵥlad1ₙ5 (data for panel A) include charge occupancies along the SSH1 chain of length N=30 (panels A) as a function of the site number for different geometry of the system as described in the text: column1: site numbercolumn2: charge at each site of the chaincolumn3: normalization of LDOS functionThe files 'fig03Bᵥdos1ₙ5', 'fig03BBᵥdos1ₙ5' and fig03BBBᵥdos1ₙ5 (data for panel B) include normalized Local Density of States as a function of energy for a chain of N=30 linear atoms corresponding to data from panel A: column1: energycolumn2: LDOS function at each site of the chaincolumn3: site number Data for figure fig04. eps of this repository (fig3 in the main text of the paper). The file 'fig04A₀dos14' includes normalized LDOS as a function of energy for a chian of N=30 linear atoms coupled directly with the surface with the couplig parameters t₁=1 and t₂=4 for th on-site energies e₁=0 and e₂=0: column1: energycolumn2: Local Density of States for e1 sitecolumn3: Local Density of States for e2 sitecolumn4: Local Density of States for e15 sitecolumn5: Local Density of States for e3 sitecolumn6: Local Density of States for e4 sitecolumn7: Local Density of States for e5 sitecolumn8: Local Density of States for e7 siteThe file 'fig04A₀dos14e2' includes normalized LDOS as a function of energy for a chian of N=30 linear atoms coupled directly with the surface with the couplig parameters t₁=1 and t₂=4 for th on-site energies e₁=0 and e₂=2: column1: energycolumn2: Local Density of States for e1 sitecolumn3: Local Density of States for e2 sitecolumn4: Local Density of States for e15 sitecolumn5: Local Density of States for e3 sitecolumn6: Local Density of States for e4 sitecolumn7: Local Density of States for e5 sitecolumn8: Local Density of States for e7 siteThe file 'fig04A₀dos14e4' includes normalized LDOS as a function of energy for a chian of N=30 linear atoms coupled directly with the surface with the couplig parameters t₁=1 and t₂=4 for th on-site energies e₁=0 and e₂=4: column1: energycolumn2: Local Density of States for e1 sitecolumn3: Local Density of States for e2 sitecolumn4: Local Density of States for e15 sitecolumn5: Local Density of States for e3 sitecolumn6: Local Density of States for e4 sitecolumn7: Local Density of States for e5 sitecolumn8: Local Density of States for e7 site Data for figure fig05. eps of this repository (fig4 in the main text of the paper). The files 'fig05Aₓlad1ₙ7', 'fig05Aₓlad1e4ₙ7' and 'fig05Aₓlad1e4ₙ10' include charge occupancies along the SSH1 chain of length N=50 as a function of the site number for the average filling of the chain equals: 1/7 or 1/10: column1: site numbercolumn2: charge at each site of the chaincolumn3: normalization of LDOS function Data for figure fig06. jpg of this repository (fig5 in the main text of the paper). The file 'fig06ABCdos14t'includes local DOS for a chain of N = 30 sites, evaluated at sites i = 1, 2 and 15 (panel a, b and c) as a function of energy and time, following a sudden change in the coupling parameters at t = 30: column1: timecolumn2: energycolumn3: LDOS function at 1-st sitecolumn4: LDOS function at 2-st sitecolumn5: LDOS function at 15-st site Data for figure fig08. eps of this repository (fig7 in the main text of the paper). The files 'fig08Aₗad14' (data for panel A) and 'fig08Bₗad14' (data for panel B) include time evolution of the charge occupancies, nᵢ (t) at sites i = 1, 2, 3, 4 in a chain of length N = 30 following a sudden change in the coupling parameters at time t = 30. Initially, the system is a uniform chain with couplings tᵢ = 2 (panel a) and tᵢ = 4 (panel b), and after the quench, the couplings are changed to those of the SSH1 chain with (t1, t2) = (1, 4): column1: timecolumn2: charge at each chain sitecolumn3: normalized chargecolumn4: site number of the chain Data for figure fig09. eps of this repository (fig8 in the main text of the paper). The files 'fig09ₗad14', 'fig09ₗad14x1', 'fig09ₗad14x2', 'fig09ₗad14x3', 'fig09ₗad14x4' and 'fig09ₗad14x5' include time evolution of the charge occupancy at the end atom, n₁ (t), following a sudden change in the coupling parameters at time t = 30, in a chain of length N = 30, for different on-site energies eᵢ = −2. 5, 0, 2. 5, and 4. 4 and for the transition from a normal chain to the SSH1 (SSH0) topological phase, i. e. , the couplings change from tᵢ = 4 to (t1, t2) = (1, 4) or (4, 1): column1: timecolumn2: charge at each chain sitecolumn3: normalized chargecolumn4: site number of the chain Data for figure fig10. eps of this repository (fig9 in the main text of the paper). The files 'fig10Aₗad14x' (data for panel A) and 'fig10ₗad14x' (data for panel B) include time-dependent occupancies ni (t) at the first four sites (i = 1, 2, 3, 4) in a chain of length N = 30, following a sudden change in the coupling parameter t₂3 (between sites 2 and 3), which was set to zero in the time interval from t = 30 up to t = 40. Initially, the system is in the topologically trivial (panel a) and nontrivial (panel b) phase, with couplings (t1, t2) = (4, 1) and (t1, t2) = (1, 4), respectively, and the on-site energies are eᵢ = 4. 4: column1: timecolumn2: charge at each chain sitecolumn3: normalized chargecolumn4: site number of the chain **************************** END OF FILE