Readme file for data relating to "Decoupling structural and electronic dimensionality: 2D transport in a 3D honeycomb chiral stacking"


Experimental Raw Data:


Single crystal growth of HfSn2:
Single crystal growth of HfSn2 was achieved with the metal flux method using Sn as a self-flux with the addition of Cr in a ratio of Hf:Cr:Sn = 3:18:96. When placing Hf, Cr, and Sn inside the flux reaction mixture, two single crystal materials are formed, HfSn2 and a secondaryphase. Cooling the reaction mixture at 2 °C/hr favours the formation of the competingsecondary phase, where crystals of HfSn2 grow to less than 1 mm along the longest dimension. Lowering the temperature at which the tubes are centrifuged below 700 °C does not increase the size of the HfSn2 crystals (600 °C and 500 °C were attempted). Using a slower cooling rate of 1 °C/hr and separating the flux from the crystals at 700 °C favours the formation of large, rod-shaped HfSn2 crystals around 4 mm in length and 1 mm wide. Growth is preferred along the c-axis at this flux composition.

Single crystal X-ray diffraction:
The single crystal X-ray diffraction (SXRD) was performed on a
Bruker Venture D8 diffractometer using a Mo Kα (λ = 0.71073 Å) rotating anode source and a Bruker PHOTON 100 CMOS detector with data collected at 100 K. A small single crystal was broken off and loaded with Parabar oil. The structure was solved using SHELXT as implemented in Olex 2. 
The SXRD raw data and the refined cif files are presented in the HfSn2_SCXRD.zip. Files are readable in Olex 2.0 available at https://www.olexsys.org/olex2/.

Energy Dispersion X-ray:
The compositional analysis was undertaken via the energy dispersive X-ray (EDX) technique on the scanning electronic microscope (SEM). To remove the thin layer of Sn deposited on the crystal surface after the synthesis, Ga-Focus Ion Beam (FIB) was used to dig a few 20 μm × 20 μm square trenches about 1-2 μm deep, using a 30 keV beam with currents ranging from 3 to 10 nA.
Data is presented HfSn2_EDX.zip, including the SEM image and the EDX spectrum.

Electron Backscatter Diffraction:
The electron backscatter diffraction (EBSD) characterisation was carried out in a ZEISS GeminiSEM 450 instrument at room temperature on multiple HfSn2 single crystals, labelled by CryX. For each single crystal, the experimental electron backscatter patterns (EBSP) were measured in an area of 0.5 μm2 on the (1010) orientation and was reproduced several times, labelled by EPSPX. For crystal 5, we carried out EBSD chirality mapping over a large area of 13 μm × 7.5 μm, using 0.5 μm step size) and collected 390 EBSP images. Automated quantitative comparison between each experimental EBSP image and dynamically simulated EBSPs (for both P6222 and P6422 structures) was carried out using AZtec Crystal with the MapSweeper pattern matching option and returned corresponding values of the cross-correlation coefficient R.
The EBSP images are presented in HfSn2_EBSD.zip.

Electrical transport:
Electrical transport measurements (resistivity, Hall effect and AMR) were performed on a horizontal rotator on the Quantum Design PPMS-DynaCool, applying a DC current of 2000 μA along the c-axis. Due to the small misalignment of the c crystallographic axis during sample mounting, the angle θ of 90° is calibrated by using the position of the maximum out-of-plane AMR at 14 T. 
The electrical transport data is presented in HfSn2_ElectricalTransport.zip in columns format. The physical parameters were labelled in the first row and the measurement conditions were presented in the second row. 
Sheet "AMR" includes the raw data of angular-dependent magnetoresistance at various magnetic fields at 2 K. The external magnetic field B is applied rotating away from the c-axis (angle θ) with an angle increment of 0.5 degree.
Sheet "AMR_2" includes the raw data of angular-dependent magnetoresistance at various magnetic fields at 2 K. The external magnetic field B is applied rotating away from the c-axis (angle θ) with an angle increment of 0.25 degree.
Sheet "AMR_3" includes the raw data of angular-dependent magnetoresistance at various temperatures at 14 T. The external magnetic field B is applied rotating away from the c-axis (angle θ) with an angle increment of 0.5 degree.
Sheet "AMR_4" includes the raw data of angular-dependent magnetoresistance at various temperatures at 14 T. The external magnetic field B is applied rotating in the ab plane (angle φ) with an angle increment of 0.5 degree.
Sheet "MRHall" includes the raw data of four separated measurements of magnetic-field-dependent magnetoresistance at 6 K. The final Rxx and Rxy were obtained by averaging the four results. The Hall contacts were applied on the ab-plane.
Sheet "RT" inculdes the raw data of temperature-dependent resistance at zero magnetic field.
All the raw data files are in the folder RawData.

Heat capacity:
Heat capacity was measured below room temperature using the heat capacity option on the Quantum Design physical properties measurement system (PPMS-DynaCool) using the relaxation method with the crystal mounted on the sample puck with N-grease. The contribution measured from the puck and the grease was subtracted from the results to obtain the heat capacity of the material.
Data is presented in HfSn2_HeatCapacity.zip in clolums format. The temerpature dependence of heat capacity is Sample Temp (Kelvin) versus Samp HC (J/mole-K) with the error bar in Samp HC Err (J/mole-K). It can be readable on the software MultiVu PPMS Quatum Design. 

Magnetic torque:
Magnetic torque was measured between 0 T and 35 T for various angles as illustrated at the High Field Magnet Laboratory at Radboud University, Nijmegen. The external magnetic field is applied from the c-axis with an angle θ, which  was calibrated by Hall signals.
Data is presented in HfSn2_Torque.xlsx in HfSn2_Torque.zip in columns. The calibrated angles for each measurement was presented in the third row. The Cap AH (pF) is probed by the capacitive torque magnetometers and proportional to the magnetic torque measured. All the raw data and measrurement conditions are attached in the folder RawData_Torque.


Theoretical Calculations:

All the DFT calculations results are in DFT_calculations.zip. This zip file contains the VASP-DFT calculations input and output files for C40 compounds: HfSn2, TiSi2, ZrSn2, VSi2, NbSi2, NbGe2, TaSi2, TaGe2, CrSi2, MoSi2, and WSi2. The relaxation, static, band structure, and Fermi surface calculations are inside each subfolder with the compound name. 

The FPLO calculations of HfSn2 is in HfSn2_FPLO.zip. This zip file contains the FPLO input (named as =.in) and tight-binding Hamiltonian (named as +hamdata) of HfSn2. 

The theoretical fermiology calculation is in HfSn2_dHvA.zip. This zip file contains the FPLO-calculated angular-dependent dHvA results. Inside the folder one can find the folder names 'b000xx_p000y': 'xx' represents the Fermi surface number from 33 to 40, corresponding to α, α', β, β', γ, γ', δ, and δ' Fermi surfaces, and 'y' represents the separate fragments of the Fermi surfaces in the Brillouin zone for dHvA calculations. Within the folder 'b000xx_p000y', one can find the folder names as 'iphi000zz' for the phi angles of the dHvA, in which the electron extremal area and mass are enclosed for different slices of the Fermi surfaces along the phi angle direction. 

The theoretical electrical transport calculation is in HfSn2_OHE.zip. This zip file contains the WannierTools-calculated angular-dependent magnetoresistance results. Inside the folder one can find the folder names band_xx, where xx represents the Fermi surface number from 33 to 40, corresponding to α, α', β, β', γ, γ', δ, and δ' Fermi surfaces. Within the folder, there are calculated results for different phi and theta angles, the conductivity data is named as 'sigma_bands_mu_0.00eV.dat' for each phi and theta angle.