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A general method is presented to unfold band structures of first-principles super-cell calculations with proper spectral weight, allowing easier visualization of the electronic structure and the degree of broken translational symmetry. The…

Materials Science · Physics 2010-06-29 Wei Ku , Tom Berlijn , Chi-Cheng Lee

We present Wannier90, a program for calculating maximally-localised Wannier functions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread…

Materials Science · Physics 2011-05-18 A. A. Mostofi , J. R. Yates , Y. -S. Lee , I. Souza , D. Vanderbilt , N. Marzari

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis…

Band structure unfolding is a key technique for analyzing and simplifying the electronic band structure of large, internally distorted supercells that break the primitive cell's translational symmetry. In this work, we present an efficient…

Materials Science · Physics 2026-02-10 Jingkai Quan , Nikita Rybin , Matthias Scheffler , Christian Carbogno

We introduce a program named KPROJ that unfolds the electronic and phononic band structure of materials modeled by supercells. The program is based on the $\textit{k}$-projection method, which projects the wavefunction of the supercell onto…

Materials Science · Physics 2025-04-17 Jiaxin Chen , M. Weinert , Mingxing Chen

Unfolding the band structure of a supercell to a normal cell enables us to investigate how symmetry breakers such as surfaces and impurities perturb the band structure of the normal cell. We generalize the unfolding method, originally…

Materials Science · Physics 2013-08-07 Chi-Cheng Lee , Yukiko Yamada-Takamura , Taisuke Ozaki

The electronic band structure, describing the periodic dependence of electronic quantum states on lattice momentum in reciprocal space, is a fundamental concept in solid-state physics. However, it's only well-defined for static nuclei. To…

EPW (Electron-Phonon coupling using Wannier functions) is a program written in FORTRAN90 for calculating the electron-phonon coupling in periodic systems using density-functional perturbation theory and maximally-localized Wannier…

Other Condensed Matter · Physics 2015-05-19 Jesse Noffsinger , Feliciano Giustino , Brad D. Malone , Cheol-Hwan Park , Steven G. Louie , Marvin L. Cohen

The EPW (Electron-Phonon coupling using Wannier functions) software is a Fortran90 code that uses density-functional perturbation theory and maximally localized Wannier functions for computing electron-phonon couplings and related…

Materials Science · Physics 2016-11-23 Samuel Poncé , Elena R. Margine , Carla Verdi , Feliciano Giustino

Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…

Materials Science · Physics 2026-05-08 Christopher A. Bairnsfather , Ralph M. Kaufmann , Terry A. Loring , Alexander Cerjan

Over the last two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished.…

Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability…

Mesoscale and Nanoscale Physics · Physics 2008-03-19 Christopher R. Moon , Laila S. Mattos , Brian K. Foster , Gabriel Zeltzer , Wonhee Ko , Hari C. Manoharan

Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…

Quantum Physics · Physics 2007-05-23 Peter Hoyer

In this paper, a new method based on Greens function theory and Fourier transform analysis has been proposed for calculating band structure with high accuracy and low processing time. This method utilizes sampling of potential energy in…

Materials Science · Physics 2012-07-13 Milad Khoshnegar , Amir Hossein Hosseinia , Nima Arjmandi , Sina Khorasani

Modern computing facilities grant access to first-principles density-functional theory study of complex physical and chemical phenomena in materials, that require large supercell to properly model the system. However, supercells are…

Materials Science · Physics 2021-06-24 David Dirnberger , Georg Kresse , Cesare Franchini , Michele Reticcioli

An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…

Quantum Physics · Physics 2026-03-27 Daniel Pierce , Renuka Rajapakse

Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for…

Quantum Physics · Physics 2007-05-23 Jian-wu Wu , Chun-wen Li , Re-bing Wu

Wannier functions provide a localized representation of spectral subspaces of periodic Hamiltonians, and play an important role for interpreting and accelerating Hartree-Fock and Kohn-Sham density functional theory calculations in quantum…

Computational Physics · Physics 2018-01-29 Anil Damle , Antoine Levitt , Lin Lin

Spectrotemporal encoding of optical quantum information is emerging as a powerful tool in quantum information technology. Processing of spectrotemporal information has recently been demonstrated in multi-mode quantum memories, based on…

Quantum Physics · Physics 2025-11-19 Jesse L Everett

We present a simple view on band unfolding of the energy bands obtained from supercell calculations. It relies on the relationship between the local density of states in reciprocal space (qLDOS) and the fully unfolded band structure. This…

Materials Science · Physics 2020-01-24 Sara G. Mayo , Felix Yndurain , Jose M. Soler
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