Identifying the Van Hove singularity in overdoped Bi-2201 using k-means clustering

Cuprates are mysterious materials with many not yet understood properties. One of these properties is the Van Hove singularity, which enhances the electron-electron interactions where it occurs. This Van Hove singularity would be expected to appear in all cuprates, but has only been shown to appear in a single cuprate: Bi-2201. The Van Hove singularity presents as a peak in the graph of the density of states. To identify the locations in the material featuring the Van Hove singularity the dimension was reduced by using principal component analysis and calculating the mean squared distance to the mean of intervals to reduce the dimension of the data. After this dimension reduction a k-means clustering algorithm was used to find relations in the data. When analysing the clusters found by the algorithm it was found that the Van Hove singularities are localised a striped pattern on the sample and that the singularity varies a lot in the energy spectra. This variation in the energy...Show moreCuprates are mysterious materials with many not yet understood properties. One of these properties is the Van Hove singularity, which enhances the electron-electron interactions where it occurs. This Van Hove singularity would be expected to appear in all cuprates, but has only been shown to appear in a single cuprate: Bi-2201. The Van Hove singularity presents as a peak in the graph of the density of states. To identify the locations in the material featuring the Van Hove singularity the dimension was reduced by using principal component analysis and calculating the mean squared distance to the mean of intervals to reduce the dimension of the data. After this dimension reduction a k-means clustering algorithm was used to find relations in the data. When analysing the clusters found by the algorithm it was found that the Van Hove singularities are localised a striped pattern on the sample and that the singularity varies a lot in the energy spectra. This variation in the energy spectra can be explained by putting the Van Hove singularity on the Fermi level and then displacing it because of a combination of inhomogeneity of doping and the formation of a superconducting gap.Show less

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Identifying the Van Hove singularity in overdoped Bi-2201 using k-means clustering