BoltzWann: A code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis

We present a new code to evaluate thermoelectric and electronic transport properties of extended systems with a maximally-localized Wannier function basis set. The semiclassical Boltzmann transport equations for the homogeneous infinite system are solved in the constant relaxation-time approximation and band energies and band derivatives are obtained via Wannier interpolations. Thanks to the exponential localization of the Wannier functions obtained, very high accuracy in the Brillouin zone integrals can be achieved with very moderate computational costs. Moreover, the analytical expression for the band derivatives in the Wannier basis resolves any issues that may occur when evaluating derivatives near band crossings. The code is tested on binary and ternary skutterudites CoSb3 and CoGe3/2 S-3/2. Program summary Program title: BoltzWann Catalogue identifier: AEQX_v1_0 Program summaiy URL: http://cpc.cs.qub.ac.uk/summaries/AEQX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 710 810 No. of bytes in distributed program, including test data, etc.: 8 337 000 Distribution format: tar.gz Programming language: Fortran 90. Computer: Any architecture with a Fortran 90 compiler. Operating system: Linux, Windows, Solaris, AIX, Tru64 Unix, OSX. Has the code been vectorized or parallelized?: Yes. RAM: The example requires approximately 10 MB. Classification: 7.3, 7.9. External routines: BLAS and LAPACK (available on http://www.netlib.org/); MPI libraries (optional) for parallel execution Nature of problem: Obtain electronic and thermoelectric transport properties for crystals. Solution method: The Boltzmann transport equations in the constant relaxation-time approximation are used. These equations require the integration of the band velocities over all the Brillouin zone; this is done numerically on a sufficiently dense k grid. Band energies and band derivatives are obtained by interpolation using the maximally-localized Wannier functions basis obtained with a preliminary run of the Wannier90 code. Unusual features: The maximally-localized Wannier functions interpolation scheme allows the use of analytical formulas (instead of finite-difference methods) to obtain the band derivatives. Additional comments: This is a package that is tightly integrated with the Wannier90 code (http://www.wannier.org). The Wannier90 code is included in the distribution package. Running time: The example runs (in its serial version) in less than 2 min. (C) 2013 Elsevier B.V. All rights reserved.

[1]  Jean-Pierre Fleurial,et al.  Properties of single crystalline semiconducting CoSb3 , 1996 .

[2]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[3]  D. Vanderbilt,et al.  Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. , 1990, Physical review. B, Condensed matter.

[4]  N. Marzari,et al.  Maximally localized Wannier functions for entangled energy bands , 2001, cond-mat/0108084.

[5]  John S. Tse,et al.  Calculations of transport properties with the linearized augmented plane-wave method , 2000 .

[6]  David J. Singh,et al.  BoltzTraP. A code for calculating band-structure dependent quantities , 2006, Comput. Phys. Commun..

[7]  Steven G. Louie,et al.  EPW: A program for calculating the electron-phonon coupling using maximally localized Wannier functions , 2010, Comput. Phys. Commun..

[8]  Stefano de Gironcoli,et al.  QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[10]  Ali Shakouri,et al.  Nanostructured Thermoelectrics: Big Efficiency Gains from Small Features , 2010, Advanced materials.

[11]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[12]  M. Kanatzidis,et al.  High-performance bulk thermoelectrics with all-scale hierarchical architectures , 2012, Nature.

[13]  Nicola Marzari,et al.  Phonon anharmonicities in graphite and graphene. , 2007, Physical review letters.

[14]  T. Arias,et al.  Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co , 1992 .

[15]  N. Marzari,et al.  Band structure and quantum conductance of nanostructures from maximally localized Wannier functions: the case of functionalized carbon nanotubes. , 2005, Physical review letters.

[16]  J. Ziman.  Principles of the Theory of Solids , 1965 .

[17]  Boris Kozinsky,et al.  Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: a first-principles study. , 2011, Physical review letters.

[18]  University of Cambridge,et al.  THERMAL CONTRACTION AND DISORDERING OF THE AL(110) SURFACE , 1999 .

[19]  Jorge O. Sofo,et al.  Transport coefficients from first-principles calculations , 2003 .

[20]  Tadeusz Paszkiewicz,et al.  Physics of Phonons , 1987 .

[21]  G. J. Snyder,et al.  Complex thermoelectric materials. , 2008, Nature materials.

[22]  Pickett,et al.  Smooth Fourier interpolation of periodic functions. , 1988, Physical review. B, Condensed matter.

[23]  D. Vanderbilt,et al.  Spectral and Fermi surface properties from Wannier interpolation , 2007, cond-mat/0702554.

[24]  N. Marzari,et al.  Maximally localized generalized Wannier functions for composite energy bands , 1997, cond-mat/9707145.

[25]  G. Madsen,et al.  Automated search for new thermoelectric materials: the case of LiZnSb. , 2006, Journal of the American Chemical Society.

[26]  Gerbrand Ceder,et al.  Screening for high-performance piezoelectrics using high-throughput density functional theory , 2011 .

[27]  Paz Vaqueiro,et al.  Structure and electrical transport properties of the ordered skutterudites MGe1.5S1.5 (M = Co, Rh, Ir) , 2008 .

[28]  R. Venkatasubramanian,et al.  Thin-film thermoelectric devices with high room-temperature figures of merit , 2001, Nature.

[29]  Weishu Liu,et al.  High-performance nanostructured thermoelectric materials , 2010 .

[30]  Boris Kozinsky,et al.  Electronic, vibrational, and transport properties of pnictogen-substituted ternary skutterudites , 2011, 1112.1749.

[31]  N. Marzari,et al.  Maximally-localized Wannier Functions: Theory and Applications , 2011, 1112.5411.

[32]  Andrew G. Glen,et al.  APPL , 2001 .

[33]  Kenji Shiraishi,et al.  Momentum-matrix-element calculation using pseudopotentials , 1997 .

[34]  G. D. Mahan.  Chapter 1.8 Transport properties , 2006 .

[35]  G. Mahan,et al.  The best thermoelectric. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Stefano Curtarolo,et al.  Assessing the Thermoelectric Properties of Sintered Compounds via High-Throughput Ab-Initio Calculations , 2011 .

[37]  Pickett,et al.  Anisotropic normal-state transport properties predicted and analyzed for high-Tc oxide superconductors. , 1988, Physical review. B, Condensed matter.

[38]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[39]  M. Dresselhaus,et al.  High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys , 2008, Science.

[40]  Boris Kozinsky,et al.  Effects of filling in CoSb3: Local structure, band gap, and phonons from first principles , 2010 .

[41]  Anton Kokalj,et al.  Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale , 2003 .

[42]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[43]  Patrick Martin,et al.  Thermoelectric properties of CoSb3 and related alloys , 1995 .

[44]  N. Marzari,et al.  Exponential localization of Wannier functions in insulators. , 2006, Physical review letters.

[45]  Read,et al.  Calculation of optical matrix elements with nonlocal pseudopotentials. , 1991, Physical review. B, Condensed matter.

[46]  Louie,et al.  Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators. , 1987, Physical review. B, Condensed matter.

[47]  H. Monkhorst,et al.  SPECIAL POINTS FOR BRILLOUIN-ZONE INTEGRATIONS , 1976 .

[48]  Cohen,et al.  Phonon Softening and Superconductivity in Tellurium under Pressure. , 1996, Physical review letters.

[49]  Anthony Papagiannis.  Intern , 2010, BMJ : British Medical Journal.

[50]  Walter Kohn,et al.  Quantum Density Oscillations in an Inhomogeneous Electron Gas , 1965 .

[51]  Qingjie Zhang,et al.  Unique nanostructures and enhanced thermoelectric performance of melt-spun BiSbTe alloys , 2009 .

[52]  G. V. Chester,et al.  Solid State Physics , 2000 .

[53]  R. Martin,et al.  Electronic Structure: Basic Theory and Practical Methods , 2004 .

[54]  Hubert Scherrer,et al.  Transport in doped skutterudites: Ab initio electronic structure calculations , 2005 .

[55]  D. Hamann,et al.  Maximally localized Wannier functions for GW quasiparticles , 2008, 0810.3616.

[56]  S. Louie,et al.  Electron-phonon interaction using Wannier functions , 2007 .

[57]  Paxton,et al.  High-precision sampling for Brillouin-zone integration in metals. , 1989, Physical review. B, Condensed matter.