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The Fermi surface geometrical origin of axis-dependent conduction polarity in layered materials


Electronic materials generally exhibit a single isotropic majority carrier type, electrons or holes. Some superlattice1,2 and hexagonal3,4,5 materials exhibit opposite conduction polarities along in-plane and cross-plane directions due to multiple electron and hole bands. Here, we uncover a material genus with this behaviour that originates from the Fermi surface geometry of a single band. NaSn2As2, a layered metal, has such a Fermi surface. It displays in-plane electron and cross-plane hole conduction in thermopower and exactly the opposite polarity in the Hall effect. The small Nernst coefficient and magnetoresistance preclude multi-band transport. We label this direction-dependent carrier polarity in single-band systems ‘goniopolarity’. We expect to find goniopolarity and the Fermi surface geometry that produces it in many metals and semiconductors whose electronic structure is at the boundary between two and three dimensions. Goniopolarity may enable future explorations of complex transport phenomena that lead to unprecedented device concepts.

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Fig. 1: Analytical model of a goniopolar material.
Fig. 2: Crystal and band structures of NaSn2As2.
Fig. 3: Goniopolar Seebeck and Hall effects of NaSn2As2.
Fig. 4: Resistivity, magnetoresistance, Nernst coefficient and thermal conductivity of NaSn2As2.

Data availability

All relevant data are available from the authors.


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Primary funding for the synthesis (M.Q.A., N.D.C., M.R.S. and J.E.G.) and transport measurements (B.H. and J.P.H.) was provided by NSF EFRI-1433467. Primary funding for the DFT simulations was provided by the Center for Emergent Materials: an NSF MRSEC under Award DMR-1420451 (Y.W.) and AFOSR FA9550-18-1-0335 (W.W.). J.E.G. acknowledges the Camille and Henry Dreyfus Foundation for partial support. R. Ripley is acknowledged for editing text and figures.

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Measurements were carried out by B.H. and J.P.H.; the theory was developed by Y.W., J.P.H. and W.W.; the sample synthesis was carried out by M.Q.A., N.D.C., M.R.S. and J.E.G.; and all DFT computations were carried out by Y.W. and W.W. The paper was primarily written by B.H., Y.W., J.E.G., W.W. and J.P.H.

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Correspondence to Joseph P. Heremans.

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Supplementary Figures 1–6, Supplementary Notes 1–5, Supplementary References 1–10

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He, B., Wang, Y., Arguilla, M.Q. et al. The Fermi surface geometrical origin of axis-dependent conduction polarity in layered materials. Nat. Mater. 18, 568–572 (2019).

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