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Register a new userCatastrophe theory classification of Fermi surface topological transitions in two dimensions
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Anirudh Chandrasekaran
Publication date
2019
fields
Physics
and research's language is
English
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We classify all possible singularities in the electronic dispersion of two-dimensional systems that occur when the Fermi surface changes topology, using catastrophe theory. For systems with up to seven control parameters (i.e., pressure, strain, bias voltage, etc), the theory guarantees that the singularity belongs to to one of seventeen standard types. We show that at each of these singularities the density of states diverges as a power law, with a universal exponent characteristic of the particular catastrophe, and we provide its universal ratio of amplitudes of the prefactors of energies above and below the singularity. We further show that crystal symmetry restricts which types of catastrophes can occur at the points of high symmetry in the Brillouin zone. For each of the seventeen wallpaper groups in two-dimensions, we list which catastrophes are possible at each high symmetry point.
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We report a detailed magnetotransport study on single crystals of PrBi. The presence of $f$-electrons in this material raises the prospect of realizing a strongly correlated version of topological semimetals. PrBi shows a magnetic field induced metal insulator transition below $T sim 20$ K and a very large magnetoresistance ($approx 4.4 times 10^4~$) at low temperatures ($T= 2$ K). We have also probed the Fermi surface topology by de Haas van Alphen (dHvA) and Shubnikov de Haas (SdH) quantum oscillation measurements complimented with density functional theory (DFT) calculations of the band structure and the Fermi surface. Angle dependence of the SdH oscillations have been carried out to probe the possible signature of surface Dirac fermions. We find three frequencies corresponding to one electron ($alpha$) and two hole ($beta$ and $gamma$) pockets in experiments, consistent with DFT calculations. The angular dependence of these frequencies is not consistent with a two dimensional Fermi surface suggesting that the transport is dominated by bulk bands. Although the transport properties of this material originate from the bulk bands, the high mobility and small effective mass are comparable to other compounds in this series proposed as topologically nontrivial.
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Following over a decade of intense efforts to enable major progress in spintronics devices and quantum information technology by means of materials in which the electronic structure exhibits non-trivial topological properties, three key challenges are still unresolved. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, to identify generic topological degeneracies in large, multi-sheeted Fermi surfaces. Combining de Haas - van Alphen spectroscopy with density functional theory and band-topology calculations, we report here that the non-symmorphic symmetries in ferromagnetic MnSi generate nodal planes (NPs), which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs on the FS of MnSi that may be controlled with a magnetic field suggests the existence of similar properties, amenable for technological exploitation, in a large number of materials.
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