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Title: Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
Authors: Jan Biedermann and Lukas Janssen
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Description:
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The archive contains the data used to construct Figs. 2-6, 7(b), and 9-11 of the paper "Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides" by Jan Biedermann and Lukas Janssen.

All data is stored in the form of one or two-dimensional arrays in the .txt format. Rows correspond to the first axis. Columns, if they exist, correspond to the second axis. The arrays may be conveniently accessed using the numpy.loadtxt function of Python's NumPy library.

The data is organized in nine folders, corresponding to the nine figures.


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Parameters:
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Noninteracting continuum model:
    WSe2 lattice constant: a_0 = 0.328nm
    Effective electron mass: m^* = 1.2 m_e, with m_e the free electron mass
    Phase shift: phi = -0.17
    Intralayer hoppings: (V_1, V^0_2, V^1_2) = (200, -159, -8)meV
    Interlayer hoppings: (V_{12}, V^0_{23}, V^1_{23}) = (184, 356, -9)meV

Interaction:
    Gate distance: d = 12.5nm
    Effective permittivity: epsilon_{eff} = 10 ... 200
    Gate type: double gated
    Number of active bands per spin and valley: N_bands = 2 for Fig. 2, N_bands = 6 otherwise

Numerics:
    Grid size: L = 12, 15, 18 (unless otherwise specified, a value of L = 18 is used)
    Plane-wave cutoff: |G| <= 4 * |G1| (corresponds to 244 noninteracting bands)
    Coulomb potential cutoff: |G| <= 2 * |G1|
    Hartree-Fock threshold: max_k( ||P_{n + 1}(k) - P_n(k)|| ) <= 1e-6,
        where P is the density matrix, n labels the Hartree-Fock iteration,
        k denotes momentum in the moiré Brillouin Zone and ||.|| is the Frobenius norm

Uniaxial heterostrain:
    Poisson ratio of WSe2: nu = 0.2
    Strain angle: phi = 0rad
    Strain amount: epsilon = 0 for Figs. (2 - 5) and Fig. 8, epsilon = 0.5% for Fig. 6


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Fig2:
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The folder contains the files energies_epsilon=40.txt and energies_epsilon=110.txt, where epsilon is the effective permittivity. Both files contain results for the Hartree-Fock energy in units of meV.

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the Slater determinant state (index 0: FM, index 1: AFM, index 2: noninteracting ground state). The second dimension corresponds to the twist angle.


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Fig3:
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The folder contains the six subfolders "a", "b", "c", "d", "e" and "f", corresponding to the six subfigures.


The subfolders "a", "b" and "c" each contain the files density.txt and s_z.txt, containing the number density in units of 1 / nm^2 and the out-of-plane spin expectation value in units of (hbar / 2) * (1 / nm^2).

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the x-axis, the second dimension corresponds to the y-axis.


The subfolders "d", "e" and "f" each contain the files spectrum.txt and spectrum_noninteracting.txt. The former contains the spectrum of the Hartree-Fock Hamiltonian for the self-consistent solution in units of meV. The latter contains the spectrum of the Hartree-Fock Hamiltonian for the noninteracting ground state in units of meV.

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the band index, the second dimension corresponds to the k-point index.


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Fig4:
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The folder contains the three subfolders "a", "b" and "c", corresponding to the three subfigures.


The subfolders "a" and "b" each contain the files AFM_OP.txt and FM_OP.txt, containing results for the AFM and FM order parameters in units of Bohr magneton / nm^2.

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the system size (index 0: L = 12, index 1: L = 15, index 2: L = 18). The second dimension corresponds to the twist angle.


The subfolder "c" contains the following files, with <L> = 12, 15, 18 determining the system size:
AFM_OP_L=<L>.txt (AFM order parameter in units of Bohr magneton / nm^2)
FM_OP_L=<L>.txt (FM order parameter in units of Bohr magneton / nm^2)
gaps_L=<L>.txt (band gap in units of meV)
HF_energies_L=<L>.txt (Hartree-Fock energies in units of meV)
HF_energies_P0_L=<L>.txt (Hartree-Fock energies of the noninteracting ground state in units of meV)

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the twist angle. The second dimension corresponds to the effective permittivity.


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Fig5:
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The folder contains the files AFM_OP_theta=<theta>.txt and gaps_theta=<theta>.txt, where <theta> = 2.75 is the twist angle in degrees. The former contains results for the AFM order parameter in units of Bohr magneton / nm^2, the latter contains results for the band gap in units of meV.

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the system size (index 0: L = 12, index 1: L = 15, index 2: L = 18). The second dimension corresponds to the applied pressure.


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Fig6:
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The folder contains the two subfolders "a" and "b", corresponding to the two subfigures.


The subfolder "a" contains the files density.txt and s_z.txt, containing the number density in units of 1 / nm^2 and the out-of-plane spin expectation value in units of (hbar / 2) * (1 / nm^2).

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the x-axis, the second dimension corresponds to the y-axis.


The subfolder "b" contains the following files, with <L> = 12, 15, 18 determining the system size:
AFM_OP_L=<L>.txt (AFM order parameter in units of Bohr magneton / nm^2)
FM_OP_L=<L>.txt (FM order parameter in units of Bohr magneton / nm^2)
gaps_L=<L>.txt (band gap in units of meV)
HF_energies_L=<L>.txt (Hartree-Fock energies in units of meV)
HF_energies_P0_L=<L>.txt (Hartree-Fock energies of the noninteracting ground state in units of meV)

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the twist angle. The second dimension corresponds to the effective permittivity.

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Fig7:
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The folder contains the subfolder "b", corresponding to the respective subfigure.

The subfolder contains the following files:
v_F_over_v_B.txt (velocity ratio)
z.txt (effective dynamical critical exponent)

All file contents are in the form of one-dimensional arrays. The first dimension corresponds to the renormalization group scale 1/b in the range 0.01 to 1.00.


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Fig9:
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The folder contains the following files:
t_bar.txt (Kinetic energy scale in units of meV)
U_S.txt (Chiral interaction energy scale in units of meV)
U_A.txt (Antichiral interaction energy scale in units of meV)
F_A_over_F_S.txt (Ratio of the magnitudes of the antisymmetric and symmetric contributions to the overlap matrices)

All file contents are in the form of one-dimensional arrays. The first dimension corresponds to the twist angle.


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Fig10:
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The folder contains the file epsilon_effs.txt, containing results for the effective permittivity.

All file contents are in the form of one-dimensional arrays. The first dimension corresponds to the twist angle.


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Fig11:
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The folder contains the files AFM_OP_theta=<theta>.txt and gaps_theta=<theta>.txt, where <theta> = 2.8 is the twist angle in degrees. The former contains results for the AFM order parameter in units of Bohr magneton / nm^2, the latter contains results for the band gap in units of meV.

All file contents are in the form of two-dimensional arrays. The first dimension corresponds to the system size (index 0: L = 12, index 1: L = 15, index 2: L = 18). The second dimension corresponds to the applied pressure.
