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Overview of KITE

KITE is a user-friendly open source software suite for simulating electronic structure and quantum transport properties of large-scale molecular and condensed systems with up to tens of billions of atomic orbitals (\(N\sim 10^{10}\)). In a nutshell, KITE takes real-space tight-binding models of arbitrary complexity as an input that can be promptly defined by the user through its versatile Python interface. Then, its memory-efficient and heavily-parallelized C++ code employs extremely accurate Chebyshev spectral expansions1 in order to study equilibrium electronic properties (DOS, LDOS and spectral functions), response functions (linear and nonlinear conductivities) and even dynamical effects arising from the time-evolution of electronic wave-packets. The scope of KITE extends beyond periodic systems, with its true power revealed through the study of more realistic lattice models. These systems include randomly distributed dilute impurities, structural defects, ad-atoms, mechanical strain and external magnetic fields. Some illustrative examples may be found in KITE’s presentation paper2. See the Tutorial section for a quick-start guide.

KITE's latest release (version 1.1) contains the following functionalities:

  • Average density of states (DOS) and local DOS
  • \(\mathbf{k}\)-space spectral functions and ARPES response
  • Linear DC conductivity tensor (using the Kubo-Greenwood formula)
  • First and second-order optical (AC) conductivities
  • Spin dynamics by time-evolution of gaussian wave-packets

These calculations can now be applied to arbitrary two- and three-dimensional tight-binding models that have:

  • Generic multi-orbital local (on-site) and bond disorder
  • User-defined local potential profile and structural disorder
  • Different boundary conditions (periodic, open and twisted)
  • Applied perpendicular magnetic field (limited use in 3D)

Refer to the About section for more information about the current release.

A Short Background Story

The seeds for KITE’s project were planted in 2014, when an exact spectral expansion of the broadened lattice Green's function was discovered by Aires Ferreira (University of York, UK) in collaboration with Eduardo R. Mucciolo (University of Central Florida)3 and, independently, by A. Braun and P. Schmitteckert (Karlsruhe Institute of Technology)4. Aires Ferreira then developed a large-RAM "single-shot" recursive algorithm that enabled for the first time the study of huge tight-binding systems containing billions of atomic orbitals entirely in real space (previous approaches had been limited to a few million atoms). At the time, this method proved essential to numerically demonstrate that zero-energy modes in graphene with dilute vacancy defects benefit from a finite (non-zero) conductivity in the large system limit, thereby overcoming Anderson localization 3.

In the following years, the utility of real-space spectral methods5 has been extended to studies of the linear conductivity tensor at finite temperature/frequency6 7 (proposed by L. Covaci and T. G. Rappoport in collaboration with José H. García (ICN2)) and the non-linear optical response (proposed by S. M. João and J. M. Viana Parente Lopes8). It was the conjunction of all these proposals that resulted in the joint venture that led to the pre-release of KITE in 2018 and its official release (v1.0) in 2020 2.

From its inception, KITE was built to handle real-space models of realistic complexity and sizes. Thereby, its architecture allies a versatile and user-friendly \(\texttt{Python}\) interface, with an efficient \(\texttt{C++}\) code (developed by J. M. Viana Parente Lopes) that handles the heavy spectral computations. The interface is based on Pybinding’s syntax9 which allows the user to input an arbitrary (2D or 3D) lattice model decorated with a myriad of non-periodic perturbations, such as on-site disorder, personalized structural defects, and strain. The model Hamiltonian is then passed to the \(\texttt{C++}\) code (\(\texttt{KITEx}\)) which implements a matrix-free Chebyshev iteration. It combines a domain-decomposition of the lattice with a "tile-by-tile" matrix-vector multiplication strategy in order to minimize memory-transfer overheads and thus boost the parallelization and calculational efficiency2. Such an approach has enabled unprecedented large-scale studies of electronic structure and non-equilibrium phenomena in a variety of systems, including disordered semi-metals, topological insulators, and superconductors, among others 10 11. Finally, a convenient post-processing tool (\(\texttt{KITE-tools}\)), developed by S. M. João, was also included in the package, thereby turning KITE into an all-round, ready-to-use tool for practical applications.

  1. Kernel polynomial method, A. Weiße, G. Wellein, A. Alvermann and H. Fehske, Rev. Mod. Phys. 78, 275 (2016) ↩

  2. KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures, S. M. João, M. Anđelković, L. Covaci, T. G. Rappoport, João M. Viana Parente Lopes, and A. Ferreira, R. Soc. open sci. 7, 191809 (2020) ↩↩↩

  3. Critical delocalization of chiral zero energy modes in graphene, A. Ferreira and E. Mucciolo, Phys. Rev. Lett. 115, 106601 (2015) ↩↩

  4. Numerical evaluation of Green's functions based on the Chebyshev expansion, A. Braun and P. Schmitteckert, Phys. Rev. B 90, 165112 (2014) ↩

  5. Efficient multiscale lattice simulations of strained and disordered graphene, N. Leconte, A. Ferreira, and J. Jung. Semiconductors and Semimetals 95, 35 (2016) ↩

  6. Real-space calculation of the conductivity tensor for disordered topological matter, J. H. García, L. Covaci, and T. G. Rappoport, Phys. Rev. Lett. 114, 116602 (2015) ↩

  7. Numerical calculation of the Casimir-Polder interaction between a graphene sheet with vacancies and an atom, T. P. Cysne, T. G. Rappoport, A.Ferreira, J. M. Viana Parente Lopes, and N. M. R. Peres, Phys. Rev. B 94, 235405 (2016) ↩

  8. Basis-independent spectral methods for non-linear optical response in arbitrary tight-binding models, S. M. João and J. M. Viana Parente Lopes, J. Phys.: Condens. Mat. 32 (12), 125901 (2019) ↩

  9. Pybinding V0.9.4: a python package for tight-binding calculations, D. Moldovan, M. Anđelković, and F. M. Peeters, Zenodo (2017). ↩

  10. High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity, S. M. João, J. M. Viana Parente Lopes, and A. Ferreira, J. Phys. Mater. 5 045002 (2022) ↩

  11. Anomalous Transport Signatures in Weyl Semimetals with Point Defects, J. P. Santos Pires, S. M. João, A. Ferreira, B. Amorim, and J. M. Viana Parente Lopes, Phys. Rev. Lett. 129, 196601 (2022) ↩