Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

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

Nature Materials volume 18, pages 568–572 (2019)Cite this article

Subjects

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

Data availability

All relevant data are available from the authors.

References

  1. Zhou, C., Birner, S., Tang, Y., Heinselman, K. & Grayson, M. Driving perpendicular heat flow: (p × n)-type transverse thermoelectrics for microscale and cryogenic peltier cooling. Phys. Rev. Lett. 110, 227701 (2013).

    Article  Google Scholar 

  2. Tang, Y., Cui, B., Zhou, C. & Grayson, M. p x n-type transverse thermoelectrics: a novel type of thermal management material. J. Electron. Mater. 44, 2095–2104 (2015).

    Article  CAS  Google Scholar 

  3. Rowe, V. A. & Schroeder, P. A. Thermopower of Mg, Cd, and Zn between 1.2 degrees K and 300 degrees K. J. Phys. Chem. Solids 31, 1–8 (1970).

    Article  CAS  Google Scholar 

  4. Burkov, A. T., Vedernikov, M. V., Elenskii, V. A. & Kovtun, G. P. Anisotropy of thermo-EMF and electroconductivity of high-purity rhenium. Fiz. Tverd. Tela 28, 785–788 (1986).

    CAS  Google Scholar 

  5. Burkov, A. T. & Verdernikov, M. V. Anomalous aniosotropy of high temperature thermo-EMF in beryllium. Sov. Phys. Solid State 28, 3737–3739 (1986).

    CAS  Google Scholar 

  6. Gu, J. J., Oh, H. W., Inui, H. & Zhang, D. Anisotropy of mobility ratio between electron and hole along different orientations in ReGexSi1.75-x thermoelectric single crystals. Phys. Rev. B 71, 113201 (2005).

    Article  Google Scholar 

  7. Putley, E. H. The Hall Effect and Related Phenomena 85–90 (Butterworths, 1960).

  8. Caswell, A. E. The Hall, Ettingshausen, Nernst, and Leduc effects in cadmium, nickel, and zinc. Phys. Rev. 20, 280–282 (1922).

    Article  CAS  Google Scholar 

  9. Mangez, J. H., Issi, J.-P. & Heremans, J. P. Transport properties of bismuth in quantizing fields. Phys. Rev. B 14, 4381–4385 (1976).

    Article  CAS  Google Scholar 

  10. Ong, K. P., Singh, D. J. & Wu, P. Unusual transport and strongly anisotropic thermopower in PtCoO2 and PdCoO2. Phys. Rev. Lett. 104, 176601 (2010).

    Article  Google Scholar 

  11. Tanaka, M., Hasegawa, M. & Takei, H. Growth and anisotropic physical properties of PdCoO2 single crystals. J. Phys. Soc. Jpn 65, 3973–3977 (1996).

    Article  CAS  Google Scholar 

  12. Cutler, M. & Mott, N. F. Observation of Anderson localization in an electron gas. Phys. Rev. 181, 1336–1340 (1969).

    Article  CAS  Google Scholar 

  13. Harrison, W. Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond 34 (Dover, 1989).

  14. Jan, J.-P. Effective masses and curvature of the Fermi surface or energy bands. Helv. Phys. Acta 41, 957–959 (1968).

    Google Scholar 

  15. MacDonald, D. K. C. & Pearson, W. B. Thermo-electricity at low temperatures I. The ‘ideal’ metals: sodium, potassium, copper. Proc. R. Soc. Lond. A 219, 373–387 (1953).

    Article  CAS  Google Scholar 

  16. Anderson, H. G. Jr. Investigation of Thermoelectric Properties of Liquid Metals MACHLAB-254 (David W. Taylor Naval Ship Research and Development Center, 1969).

  17. Madsen, G. K. H. & Singh, D. J. BoltzTraP. A code for calculating band-structure dependent quantities. Comput. Phys. Commun. 175, 67–71 (2006).

    Article  CAS  Google Scholar 

  18. Arguilla, M. Q. et al. NaSn2As2: an exfoliatable layered van der Waals Zintl phase. ACS Nano 10, 9500–9508 (2016).

    Article  CAS  Google Scholar 

  19. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    Article  CAS  Google Scholar 

  20. Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal amorphous–semiconductor transition in germanium. Phys. Rev. B 49, 14251–14269 (1994).

    Article  CAS  Google Scholar 

  21. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996); erratum 78, 1396 (1997).

  22. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  Google Scholar 

  23. Ong, N. P. Geometric interpretation of the weak-field Hall conductivity in two-dimensional metals with arbitrary Fermi surface. Phys. Rev. B 43, 194–201 (1991).

    Article  Google Scholar 

  24. Førsvoll, K. & Holwech Sondheimer, I. Oscillations in the Hall effect of aluminium. Philos. Mag. 10, 921–930 (1964).

    Article  Google Scholar 

  25. Ravich, Y. I, Efimova, B. A. & Smirnov, I. A. Semiconducting Lead Chalcogenides 111–113 (Plenum, 1970).

  26. Fauqué, B. et al. Magnetoresistance of semi-metals: the case of antimony. Phys. Rev. Mater. 2, 114201 (2018).

    Article  Google Scholar 

  27. Lin, Z. et al. Thermal conductivities in NaSnAs, NaSnP, and NaSn2As2: effect of double lone-pair electrons. Phys. Rev. B 95, 165201 (2017).

    Article  Google Scholar 

  28. Heremans, J. P., Thrush, C. M. & Morelli, D. T. Thermopower enhancement in lead telluride nanostructures. Phys. Rev. B 70, 115334 (2004).

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Author notes

  1. These authors contributed equally: Bin He, Yaxian Wang.

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA

    Bin He & Joseph P. Heremans

  2. Department of Materials Science and Engineering, The Ohio State University, Columbus, OH, USA

    Yaxian Wang, Wolfgang Windl & Joseph P. Heremans

  3. Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA

    Maxx Q. Arguilla, Nicholas D. Cultrara, Michael R. Scudder & Joshua E. Goldberger

  4. Department of Physics, The Ohio State University, Columbus, OH, USA

    Wolfgang Windl & Joseph P. Heremans

Authors
  1. Bin He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yaxian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maxx Q. Arguilla
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nicholas D. Cultrara
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Michael R. Scudder
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Joshua E. Goldberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Wolfgang Windl
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Joseph P. Heremans
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding author

Correspondence to Joseph P. Heremans.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/s41563-019-0309-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-019-0309-4

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing