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Topological quantization and gauge invariance of charge transport in liquid insulators

Nature Physics volume 15, pages 967–972 (2019)Cite this article

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Abstract

According to the Green–Kubo theory of linear response, the conductivity of an electronically gapped liquid can be expressed in terms of the time correlations of the adiabatic charge flux, which is determined by the atomic velocities and Born effective charges. We show that topological quantization of adiabatic charge transport and gauge invariance of transport coefficients allow one to rigorously express the electrical conductivity of an insulating fluid in terms of integer-valued, scalar, and time-independent atomic oxidation numbers, instead of real-valued, tensor and time-dependent Born charges.

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Fig. 1: Paths in the periodic nuclear configuration space.
Fig. 2: Time series of the Born effective-charge tensor.
Fig. 3: Closed paths and charge-transport quantization.
Fig. 4: Dipole mean square displacements versus time.

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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Green, M. S. Markoff random processes and the statistical mechanics of time-dependent phenomena. J. Chem. Phys. 20, 1281–1295 (1952).

    Article  ADS  MathSciNet  Google Scholar 

  2. Kubo, R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn 12, 570–586 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  3. Green, M. S. Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids. J. Chem. Phys. 22, 398–413 (1954).

    Article  ADS  MathSciNet  Google Scholar 

  4. Kubo, R., Yokota, M. & Nakajima, S. Statistical-mechanical theory of irreversible processes. II. Response to thermal disturbance. J. Phys. Soc. Jpn 12, 1203–1211 (1957).

    Article  ADS  MathSciNet  Google Scholar 

  5. Baroni, S., de Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001).

    Article  ADS  Google Scholar 

  6. Resta, R. Electrical polarization and orbital magnetization: the modern theories. J. Phys. Condens. Matter 22, 123201 (2010).

    Article  ADS  Google Scholar 

  7. Vanderbilt, D. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge Univ. Press, 2018)

  8. French, M., Hamel, S. & Redmer, R. Dynamical screening and ionic conductivity in water from ab initio simulations. Phys. Rev. Lett. 107, 185901 (2011).

    Article  ADS  Google Scholar 

  9. Jiang, L., Levchenko, S. V. & Rappe, A. M. Rigorous definition of oxidation states of ions in solids. Phys. Rev. Lett. 108, 1–5 (2012).

    Google Scholar 

  10. Marcolongo, A., Umari, P. & Baroni, S. Microscopic theory and ab initio simulation of atomic heat transport. Nat. Phys. 12, 80–84 (2016).

    Article  Google Scholar 

  11. Ercole, L., Marcolongo, A., Umari, P. & Baroni, S. Gauge invariance of thermal transport coefficients. Low Temp. Phys. 185, 79–86 (2016).

    Article  ADS  Google Scholar 

  12. Baroni S., Bertossa R., Ercole L., Grasselli F. & Marcolongo A. in Handbook of Materials Modeling: Applications: Current and Emerging Materials 2nd edn (eds Andreoni, W. & Yip, S.) 1–36 (Springer, 2018).

  13. Helfand, E. Transport coefficients from dissipation in a canonical ensemble. Phys. Rev. 119, 1–9 (1960).

    Article  ADS  MathSciNet  Google Scholar 

  14. Marcolongo, A. Theory and Ab Initio Simulation of Atomic Heat Transport. PhD thesis, Scuola Internazionale Superiore di Studi Avanzati (2014).

  15. Resta, R. in The Physics of Correlated Insulators, Metals, and Superconductors. Modeling and Simulation Vol. 7 (eds Pavarini, E. et al.) 3.5 (Verlag des Forschungszentrum Jülich, 2017).

  16. Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  17. Pendry, J. B. & Hodges, C. H. The quantisation of charge transport in ionic systems. J. Phys. C 17, 1269–1279 (1984).

    Article  ADS  Google Scholar 

  18. Resta, R. Quantum-mechanical position operator in extended systems. Phys. Rev. Lett. 80, 1800–1803 (1998).

    Article  ADS  Google Scholar 

  19. Rowland T. and Weisstein E. W. Fundamental group. MathWorld–A Wolfram Web Resource http://mathworld.wolfram.com/FundamentalGroup.html (2019).

  20. Kirshenbaum, A. D., Cahill, J. A., McGonigal, P. J. & Grosse, A. V. The density of liquid NaCl and KCl and an estimate of their critical constants together with those of the other alkali halides. J. Inorg. Nucl. Chem. 24, 1287–1296 (1962).

    Article  Google Scholar 

  21. Giannozzi, P. et al. Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  22. Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).

    Article  Google Scholar 

  23. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  Google Scholar 

  24. Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015).

    Article  ADS  Google Scholar 

  25. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519 (1984).

    Article  ADS  Google Scholar 

  26. Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697 (1985).

    Article  ADS  Google Scholar 

  27. Jónsson, H., Mills, G. & Jacobsen, K. W. in Classical and Quantum Dynamics in Condensed Phase Simulations (eds Berne, B. J. et al.) 385–404 (World Scientific, 1998).

  28. Ercole, L., Marcolongo, A. & Baroni, S. Accurate thermal conductivities from optimally short molecular dynamics simulations. Sci. Rep. 7, 15835 (2017).

    Article  ADS  Google Scholar 

  29. Janz, G. J., Dampier, F. W., Lakshminarayanan, G. R., Lorenz, P. K. & Tomkins, R. P. T. Molten Salts: Volume I. Electrical Conductance, Density, and Viscosity Data (ed. Astin, A. V.) 48 (US National Bureau of Standards, 1968).

  30. Armand, M., Endres, F., MacFarlane, D. R., Ohno, H. & Scrosati, B. Ionic-liquid materials for the electrochemical challenges of the future. Nat. Mater. 8, 621–629 (2009).

    Article  ADS  Google Scholar 

  31. Marcolongo, A. & Marzari, N. Ionic correlations and failure of Nernst–Einstein relation in solid-state electrolytes. Phys. Rev. Mater. 1, 025402 (2017).

    Article  Google Scholar 

  32. Kahle, L., Marcolongo, A. & Marzari, N. Modeling lithium-ion solid-state electrolytes with a pinball model. Phys. Rev. Mater. 2, 065405 (2018).

    Article  Google Scholar 

  33. Resta, R. & Vanderbilt, D. Theory of polarization: A modern approach Physics of Ferroelectrics: A Modern Perspective 51–52 (Springer, 2007).

Download references

Acknowledgements

We are grateful to R. Resta for insightful discussions and to R. Bertossa for technical assistance. This work was partially funded by the EU through the max Centre of Excellence for supercomputing applications (project nos. 676598 and 824143).

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  1. SISSA–Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

    Federico Grasselli & Stefano Baroni

  2. CNR–IOM DEMOCRITOS @SISSA, Trieste, Italy

    Stefano Baroni

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  1. Federico Grasselli
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  2. Stefano Baroni
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Correspondence to Stefano Baroni.

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Grasselli, F., Baroni, S. Topological quantization and gauge invariance of charge transport in liquid insulators. Nat. Phys. 15, 967–972 (2019). https://doi.org/10.1038/s41567-019-0562-0

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