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Motivated by the famous and pioneering mathematical works by Perelman, Hamilton, and Thurston, we introduce the concept of using modern geometrical mathematical classifications of multi-dimensional manifolds to characterize electronic structures and predict non-trivial electron transport phenomena. Here we develop the Fermi Surface Geometry Effect (FSGE), using the concepts of tangent bundles and Gaussian curvature as an invariant. We develop an index, $mathbb{H}_F$, for describing the the hyperbolicity of the Fermi Surface (FS) and show a universal correlation (R$^2$ = 0.97) with the experimentally measured intrinsic anomalous Hall effect of 16 different compounds spanning a wide variety of crystal, chemical, and electronic structure families, including where current methods have struggled. This work lays the foundation for developing a complete theory of geometrical understanding of electronic (and by extension magnonic and phononic) structure manifolds, beginning with Fermi surfaces. In analogy to the broad impact of topological physics, the concepts begun here will have far reaching consequences and lead to a paradigm shift in the understanding of electron transport, moving it to include geometrical properties of the E vs k manifold as well as topological properties.
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We report measurements of the de Haas-van Alphen effect in CeIn3 in magnetic fields extending to ~90 T, well above the Neel critical field of Hc ~61 T. The unreconstructed Fermi surface a-sheet is observed in the high magnetic field polarized paramagnetic limit, but with its effective mass and Fermi surface volume strongly reduced in size compared to that observed in the low magnetic field paramagnetic regime under pressure. The spheroidal topology of this sheet provides an ideal realization of the transformation from a `large Fermi surface accommodating f-electrons to a `small Fermi surface when the f-electron moments become polarized.
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.
In this study an extended low energy phase diagram for NaxCoO2 is experimentally established with emphasis on the high x range. It is based on systematic heat capacity studies on both polycrystalline and single crystalline samples and on uSR measurements. Main features are the existence of mass enhancement, spin fluctuations without long-range order, and magnetic order with associated Fermi surface gapping. The latter is seen in the electronic density of states (DOS) and suppression of nuclear specific heat. While there is agreement between the band structure and the low energy DOS in the low x range, in the high x range (x > 0.6) the thermodynamically determined DOS is approximately three times that deduced from the angle-resolved photoemission spectroscopy (ARPES)-measured band dispersion or local-density approximation (LDA) calculations.
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.
We report on the electronic and thermodynamic properties of the antiferromagnetic metal uranium mononitride with a Neel temperature $T_Napprox 53,$K. The fabrication of microstructures from single crystals enables us to study the low-temperature metamagnetic transition at approximately $58,$T by high-precision magnetotransport, Hall-effect, and magnetic-torque measurements. We confirm the evolution of the high-field transition from a broad and complex behavior to a sharp first-order-like step, associated with a spin flop at low temperature. In the high-field state, the magnetic contribution to the temperature dependence of the resistivity is suppressed completely. It evolves into an almost quadratic dependence at low temperatures indicative of a metallic character. Our detailed investigation of the Hall effect provides evidence for a prominent Fermi-surface reconstruction as the system is pushed into the high-field state.
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