Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA + U

Sterling, Tyler C.; Reznik, Dmitry

doi:10.1103/physrevb.104.134311

Title: Effect of the electronic charge gap on LO bond-stretching phonons in undoped La₂CuO₄ calculated using LDA + U

Abstract

Typical density-functional theory calculations that wrongly predict undoped cuprates to be metallic also predict Cu-O half- and full-breathing phonon energies that are significantly softer than observed, presumably because of weak on-site Coulomb repulsion on the Cu 3d orbitals. We used DFT+U calculations with antiferromagnetic supercells of La2CuO4 to establish correlation between the on-site repulsion strength, tuned via adjusting the value of U, and phonon dispersions. We find that breathing and half-breathing phonons reach experimental values when U is tuned to obtain the correct optical gap and magnetic moments. We demonstrate that using distorted supercells within DFT+U is a promising framework to model phonons in undoped cuprates and other perovskite oxides with complex, interrelated structural and electronic degrees of freedom.

Authors:

^[1]; Reznik, Dmitry ^[1]

Univ. of Colorado, Boulder, CO (United States)

Publication Date:: Mon Oct 25 00:00:00 EDT 2021

Research Org.:: Univ. of Colorado, Boulder, CO (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1834320

Alternate Identifier(s):: OSTI ID: 1829750; OSTI ID: 1842470

Grant/Contract Number:: SC0006939

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 104; Journal Issue: 13; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; phonons; correlated electrons; density functional theory; antiferromagnetism; cuprates; band gap; electron-phonon coupling; first-principles calculations; optical phonons; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Sterling, Tyler C., and Reznik, Dmitry. Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA + U.  United States: N. p., 2021. 
Web.  doi:10.1103/physrevb.104.134311.

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                    Sterling, Tyler C., & Reznik, Dmitry. Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA + U.  United States.  https://doi.org/10.1103/physrevb.104.134311

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                    Sterling, Tyler C., and Reznik, Dmitry. Mon .  
"Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA + U".  United States.  https://doi.org/10.1103/physrevb.104.134311.  https://www.osti.gov/servlets/purl/1834320.

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@article{osti_1834320,

  title        = {Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA + U},

  author       = {Sterling, Tyler C. and Reznik, Dmitry},

  abstractNote = {Typical density-functional theory calculations that wrongly predict undoped cuprates to be metallic also predict Cu-O half- and full-breathing phonon energies that are significantly softer than observed, presumably because of weak on-site Coulomb repulsion on the Cu 3d orbitals. We used DFT+U calculations with antiferromagnetic supercells of La2CuO4 to establish correlation between the on-site repulsion strength, tuned via adjusting the value of U, and phonon dispersions. We find that breathing and half-breathing phonons reach experimental values when U is tuned to obtain the correct optical gap and magnetic moments. We demonstrate that using distorted supercells within DFT+U is a promising framework to model phonons in undoped cuprates and other perovskite oxides with complex, interrelated structural and electronic degrees of freedom.},

  doi          = {10.1103/physrevb.104.134311},

  journal      = {Physical Review B},

  number       = 13,

  volume       = 104,

  place        = {United States},

  year         = {Mon Oct 25 00:00:00 EDT 2021},

  month        = {Mon Oct 25 00:00:00 EDT 2021}

}

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https://doi.org/10.1103/physrevb.98.121104

Full Text Available
Phonon spectrum of underdoped HgBa₂CuO_4+δ investigated by neutron scattering

Journal Article Ahmadova, I. ; Sterling, T. C. ; Sokolik, A. C. ; ... - Physical Review B

The cuprates exhibit a prominent charge-density-wave (CDW) instability with a wave vector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, the signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wave vector approximately halfway through the Brillouin zone. Most of this work is focused on moderately doped cuprates, for which the CDW order is robust, or on optimally doped samples, for which themore »« less
Cited by 6
https://doi.org/10.1103/physrevb.101.184508

Full Text Available
Charge instabilities due to breathing mode electron-phonon coupling in the single-band Hubbard theory for cuprate superconductors

Conference Fedro, A J ; Schuettler, H B

We study possible phonon-driven charge instabilities in the cuprate superconductors within the frame-work of a single-band two- dimensional extended Hubbard electron system with on-site electron-phonon (EP) coupling to the in- and out-of-plane oxygen breathing mode motion. We identify the relevant competing phases in the ionic (t=0) limit and predict the existence of a novel, dopant induced, coexistent charge density wave (CDW) and spin density wave (SDW) ordered state near {1/4}-filling, with a CDW {radical}{bar 2} {times} {radical}{bar 2}{minus} and an SDW 2{times}2-supercell, respectively. We then develop a systematic strong-coupling expansion, to 2nd order in the delocalization energy t, which allowsmore »« less
Angle-resolved photoemission study of untwinned PrBa{sub 2}Cu{sub 3}O{sub 7}: Undoped CuO{sub 2} plane and doped CuO{sub 3} chain

Journal Article Mizokawa, T ; Kim, C ; Shen, Z ; ... - Physical Review, B: Condensed Matter

We have performed an angle-resolved photoemission study on untwinned PrBa{sub 2}Cu{sub 3}O{sub 7}, which has low resistivity but does not show superconductivity. We have observed a dispersive feature with a band maximum around ({pi}/2,{pi}/2), indicating that this band is derived from the undoped CuO{sub 2} plane. We have observed another dispersive band exhibiting one-dimensional character, which we attribute to signals from the doped CuO{sub 3} chain. The overall band dispersion of the one-dimensional band agrees with the prediction of the t-J model calculation with parameters relevant to cuprates except that the intensity near the Fermi level is considerably suppressed inmore »« less
https://doi.org/10.1103/PhysRevB.60.12335
Spin-bags, polarons and impurity potentials in La{sub 2{minus}x}Sr{sub x}CuO{sub 4} from first principles

Journal Article Anisimov, V L ; Zaanen, J ; Andersen, O K - Bulletin of the American Physical Society

A quantitative electronic structure theory is vital in the study of electron-phonon interactions. The otherwise successful local density approximation band structure theory (LDA) has serious flaws if used to study doped Mott-Hubard insulators like the High-T{sub c} Cuprates. Based on the success of the so-called constrained LDA calculations, the authors recently proposed a generalization of LDA ({open_quote}LDA + U{close_quote}) which they showed to give a much improved description of the insulators. Using LDA + U in combination with large supercells to study spin and lattice relaxations, the authors found little tendency for the formation of small polarons involving in planemore »« less

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Title: Effect of the electronic charge gap on LO bond-stretching phonons in undoped La2CuO4 calculated using LDA + U

Abstract

Citation Formats

Electron-Phonon Renormalization in Cuprate Superconductors journal, February 2007

Doping-induced in-plane anisotropy of bond-stretching phonon softening in oxychloride Ca 2 − x CuO 2 Cl 2 compounds journal, January 2020

Anomalous Dispersion of LO Phonons in La 1.85 Sr 0.15 CuO 4 at Low Temperatures journal, January 1999

Reinvestigation of crystal symmetry and fluctuations in La 2 CuO 4 journal, July 2021

Projector augmented-wave method journal, December 1994

Temperature-dependent phonon spectra of magnetic random solid solutions journal, February 2018

Effect of the insulator-metal transition on the phonon anomalies in La 2 CuO 4 journal, June 2000

Competing stripe and magnetic phases in the cuprates from first principles journal, December 2019

Unfolding the complexity of phonon quasi-particle physics in disordered materials journal, January 2020

Electronic band properties and superconductivity in La 2 − y X y CuO 4 journal, March 1987

Extracting E versus k ⃗ effective band structure from supercell calculations on alloys and impurities journal, February 2012

Recovering hidden Bloch character: Unfolding electrons, phonons, and slabs journal, February 2013

Electronically driven instabilities and superconductivity in the layered La 2 − x Ba x CuO 4 perovskites journal, March 1987

First-principles local density approximation+U and generalized gradient approximation+U study of plutonium oxides journal, February 2008

Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism journal, August 1992

Local-spin-density calculations of antiferromagnetic YBa2Cu3O6 and La2CuO4 journal, January 1991

Spin dynamics in the two-dimensional quantum antiferromagnet La 2 CuO 4 journal, September 1989

Phonon spectrum of underdoped HgBa 2 CuO 4 + δ investigated by neutron scattering journal, May 2020

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

Phonon anomalies and dynamic stripes journal, November 2012

Phonon broadening in high entropy alloys journal, September 2017

Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study journal, January 1998

First-principles LDA + U and GGA + U study of cerium oxides: Dependence on the effective U parameter journal, January 2007

Mode decomposition based on crystallographic symmetry in the band-unfolding method journal, January 2017

Origin of phonon anomalies in La 2 CuO 4 journal, February 1997

Fermi-surface pockets in YBa 2 Cu 3 O 6.5 : Comparison of ab initio techniques journal, February 2009

Phonon renormalization and c -axis phonon-plasmon mixing in La 2 CuO 4 journal, August 1995

Hidden competing phase revealed by first-principles calculations of phonon instability in the nearly optimally doped cuprate La 1.875 Sr 0.125 CuO 4 journal, August 2021

Confirmation of antiferromagnetism in La 2 CuO 4 − y with polarized neutrons journal, July 1987

Ab initiomolecular dynamics for liquid metals journal, January 1993

An accurate first-principles treatment of doping-dependent electronic structure of high-temperature cuprate superconductors journal, March 2018

Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation journal, November 2013

Probing the short-range order and dynamics of phase transitions using neutron powder diffraction journal, October 1996

Magnetic, transport, and optical properties of monolayer copper oxides journal, July 1998

Reconciliation of local and long-range tilt correlations in underdoped La 2 − x Ba x CuO 4 ( 0 ≤ x ≤ 0.155 ) journal, February 2015

Antiferromagnetic ground state of La 2 CuO 4 : A parameter-free ab initio description journal, September 2018

Unfolding First-Principles Band Structures journal, May 2010

Optical studies of gap, exchange, and hopping energies in the insulating cuprates journal, December 1990

Strongly Constrained and Appropriately Normed Semilocal Density Functional journal, July 2015

Lattice instability and soft phonons in single-crystal La 2 − x Sr x Cu O 4 journal, July 1988

Oxygen phonon branches in overdoped La 1.7 Sr 0.3 Cu 3 O 4 journal, November 2006

DFT + U study of magnetic order in doped La 2 CuO 4 crystals journal, August 2011

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set journal, July 1996

Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO journal, January 2018

Large calculated electron-phonon interactions in La 2 − x M x CuO 4 journal, January 1993

Electronic structure of La 2 CuO 4 and YBa 2 Cu 3 O 6 : A local-spin-density approximation with on-site Coulomb- U correlation calculations journal, May 1994

Role of Static Displacements in Stabilizing Body Centered Cubic High Entropy Alloys journal, January 2021

Spin bags, polarons, and impurity potentials in La 2 − x Sr x CuO 4 from first principles journal, January 1992

Theory of Fermi-surface pockets and correlation effects in underdoped Y Ba 2 Cu 3 O 6.5 journal, February 2008

First-principles calculations of phonon dispersion and lattice dynamics in La 2 CuO 4 journal, April 1999

Influence of ionic charge and dipole fluctuations on the lattice dynamics, dielectric properties, and infrared response of La2CuO4 journal, January 2002

Gradient-corrected density-functional studies of CaCuO 2 journal, October 1991

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

First principles phonon calculations in materials science journal, November 2015

Unmasking the Origin of Kinks in the Photoemission Spectra of Cuprate Superconductors journal, April 2021

Electron-phonon coupling effects explored by inelastic neutron scattering journal, January 2005

Incommensurate Phonon Anomaly and the Nature of Charge Density Waves in Cuprates journal, January 2018

Evidence for a charge collective mode associated with superconductivity in copper oxides from neutron and x-ray scattering measurements of La 2 − x Sr x CuO 4 journal, January 2014

Nonlocal electron-phonon coupling of ionic charge-fluctuation type and phonon anomalies in high-temperature superconductors journal, July 2001

Effective Band Structure of Random Alloys journal, June 2010

Optical spectra of La 2 − x Sr x CuO 4 : Effect of carrier doping on the electronic structure of the CuO 2 plane journal, April 1991

The effect of the heat treatments on the antiferromagnetism in La2CuO4-δ single crystals journal, November 1987

First-Principles Phonon Calculations for La 2 Cu O 4 journal, June 1990

Temperature dependence of the bond-stretching phonon anomaly in YBa 2 Cu 3 O 6.95 journal, September 2008

Phonons in La2CuO4: Local density calculations journal, May 1996

Antiferromagnetism in Y Ba 2 Cu 3 O 6 + x journal, August 1988

Effect of charge fluctuations on the phonon dispersion and electron-phonon interaction in La 2 CuO 4 journal, March 1993

Soft-phonon behavior and transport in single-crystal La 2 CuO 4 journal, September 1987

Chiral phonons in the pseudogap phase of cuprates journal, July 2020

Strong charge fluctuations manifested in the high-temperature Hall coefficient of high- T c cuprates journal, January 2007

Antiferromagnetism in La 2 CuO 4 − y journal, June 1987

Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors journal, July 2019

Weak Ferromagnetism and Tricriticality in Pure La 2 Cu O 4 journal, August 1994

Fermi surfaces and quantum oscillations in the underdoped high- T c superconductors YBa 2 Cu 3 O 6.5 and YBa 2 Cu 4 O 8 journal, July 2011

Self-interaction correction to density-functional approximations for many-electron systems journal, May 1981

Computation of stripes in cuprates within the LDA + U method journal, November 2004

Improved tetrahedron method for Brillouin-zone integrations journal, June 1994

Title: Effect of the electronic charge gap on LO bond-stretching phonons in undoped La₂CuO₄ calculated using LDA + U

Electron-Phonon Renormalization in Cuprate Superconductors
journal, February 2007

Doping-induced in-plane anisotropy of bond-stretching phonon softening in oxychloride ${Ca}_{2 - x} {CuO}_{2} {Cl}_{2}$ compounds
journal, January 2020

Anomalous Dispersion of LO Phonons in ${La}_{1.85} {Sr}_{0.15} {CuO}_{4}$ at Low Temperatures
journal, January 1999

Reinvestigation of crystal symmetry and fluctuations in ${La}_{2} {CuO}_{4}$
journal, July 2021

Projector augmented-wave method
journal, December 1994

Temperature-dependent phonon spectra of magnetic random solid solutions
journal, February 2018

Effect of the insulator-metal transition on the phonon anomalies in ${La}_{2} {CuO}_{4}$
journal, June 2000

Competing stripe and magnetic phases in the cuprates from first principles
journal, December 2019

Unfolding the complexity of phonon quasi-particle physics in disordered materials
journal, January 2020

Electronic band properties and superconductivity in ${La}_{2 - y}$ $X_{y}$ ${CuO}_{4}$
journal, March 1987

Extracting $E$ versus $\vec{k}$ effective band structure from supercell calculations on alloys and impurities
journal, February 2012

Recovering hidden Bloch character: Unfolding electrons, phonons, and slabs
journal, February 2013

Electronically driven instabilities and superconductivity in the layered ${La}_{2 - x}$ ${Ba}_{x}$ ${CuO}_{4}$ perovskites
journal, March 1987

First-principles local density approximation+U and generalized gradient approximation+U study of plutonium oxides
journal, February 2008

Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism
journal, August 1992

Local-spin-density calculations of antiferromagnetic YBa2Cu3O6 and La2CuO4
journal, January 1991

Spin dynamics in the two-dimensional quantum antiferromagnet ${La}_{2}$ ${CuO}_{4}$
journal, September 1989

Phonon spectrum of underdoped ${HgBa}_{2} {CuO}_{4 + δ}$ investigated by neutron scattering
journal, May 2020

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

Phonon anomalies and dynamic stripes
journal, November 2012

Phonon broadening in high entropy alloys
journal, September 2017

Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
journal, January 1998

First-principles $LDA + U$ and $GGA + U$ study of cerium oxides: Dependence on the effective U parameter
journal, January 2007

Mode decomposition based on crystallographic symmetry in the band-unfolding method
journal, January 2017

Origin of phonon anomalies in ${La}_{2}$ ${CuO}_{4}$
journal, February 1997

Fermi-surface pockets in ${YBa}_{2} {Cu}_{3} O_{6.5}$ : Comparison of ab initio techniques
journal, February 2009

Phonon renormalization and c -axis phonon-plasmon mixing in ${La}_{2}$ ${CuO}_{4}$
journal, August 1995

Hidden competing phase revealed by first-principles calculations of phonon instability in the nearly optimally doped cuprate ${{La}_{1.875} {Sr}_{0.125} CuO}_{4}$
journal, August 2021

Confirmation of antiferromagnetism in ${La}_{2}$ ${CuO}_{4 - y}$ with polarized neutrons
journal, July 1987

Ab initiomolecular dynamics for liquid metals
journal, January 1993

An accurate first-principles treatment of doping-dependent electronic structure of high-temperature cuprate superconductors
journal, March 2018

Inelastic X-ray scattering in YBa2Cu3O6.6 reveals giant phonon anomalies and elastic central peak due to charge-density-wave formation
journal, November 2013

Probing the short-range order and dynamics of phase transitions using neutron powder diffraction
journal, October 1996

Magnetic, transport, and optical properties of monolayer copper oxides
journal, July 1998

Reconciliation of local and long-range tilt correlations in underdoped ${La}_{2 - x} {Ba}_{x} {CuO}_{4} (0 \leq x \leq 0.155)$
journal, February 2015

Antiferromagnetic ground state of ${La}_{2} {CuO}_{4}$ : A parameter-free ab initio description
journal, September 2018

Unfolding First-Principles Band Structures
journal, May 2010

Optical studies of gap, exchange, and hopping energies in the insulating cuprates
journal, December 1990

Strongly Constrained and Appropriately Normed Semilocal Density Functional
journal, July 2015

Lattice instability and soft phonons in single-crystal ${La}_{2 - x} {Sr}_{x} Cu O_{4}$
journal, July 1988

Oxygen phonon branches in overdoped ${La}_{1.7} {Sr}_{0.3} {Cu}_{3} O_{4}$
journal, November 2006

DFT + $U$ study of magnetic order in doped La $_{2}$ CuO $_{4}$ crystals
journal, August 2011

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996

Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO
journal, January 2018

Large calculated electron-phonon interactions in ${La}_{2 - x}$ $M_{x}$ ${CuO}_{4}$
journal, January 1993

Electronic structure of ${La}_{2}$ ${CuO}_{4}$ and ${YBa}_{2}$ ${Cu}_{3}$ $O_{6}$ : A local-spin-density approximation with on-site Coulomb- U correlation calculations
journal, May 1994

Role of Static Displacements in Stabilizing Body Centered Cubic High Entropy Alloys
journal, January 2021

Spin bags, polarons, and impurity potentials in ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$ from first principles
journal, January 1992

Theory of Fermi-surface pockets and correlation effects in underdoped $Y {Ba}_{2} {Cu}_{3} O_{6.5}$
journal, February 2008

First-principles calculations of phonon dispersion and lattice dynamics in ${La}_{2} {CuO}_{4}$
journal, April 1999

Influence of ionic charge and dipole fluctuations on the lattice dynamics, dielectric properties, and infrared response of La2CuO4
journal, January 2002

Gradient-corrected density-functional studies of ${CaCuO}_{2}$
journal, October 1991

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

First principles phonon calculations in materials science
journal, November 2015

Unmasking the Origin of Kinks in the Photoemission Spectra of Cuprate Superconductors
journal, April 2021

Electron-phonon coupling effects explored by inelastic neutron scattering
journal, January 2005

Incommensurate Phonon Anomaly and the Nature of Charge Density Waves in Cuprates
journal, January 2018

Evidence for a charge collective mode associated with superconductivity in copper oxides from neutron and x-ray scattering measurements of La $_{2 - x}$ Sr $_{x}$ CuO $_{4}$
journal, January 2014

Nonlocal electron-phonon coupling of ionic charge-fluctuation type and phonon anomalies in high-temperature superconductors
journal, July 2001

Effective Band Structure of Random Alloys
journal, June 2010

Optical spectra of ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$ : Effect of carrier doping on the electronic structure of the ${CuO}_{2}$ plane
journal, April 1991

The effect of the heat treatments on the antiferromagnetism in La2CuO4-δ single crystals
journal, November 1987

First-Principles Phonon Calculations for ${La}_{2}$ Cu $O_{4}$
journal, June 1990

Temperature dependence of the bond-stretching phonon anomaly in ${YBa}_{2} {Cu}_{3} O_{6.95}$
journal, September 2008

Phonons in La2CuO4: Local density calculations
journal, May 1996

Antiferromagnetism in $Y {Ba}_{2} {Cu}_{3} O_{6 + x}$
journal, August 1988

Effect of charge fluctuations on the phonon dispersion and electron-phonon interaction in ${La}_{2}$ ${CuO}_{4}$
journal, March 1993

Soft-phonon behavior and transport in single-crystal ${La}_{2}$ ${CuO}_{4}$
journal, September 1987

Chiral phonons in the pseudogap phase of cuprates
journal, July 2020

Strong charge fluctuations manifested in the high-temperature Hall coefficient of high- $T_{c}$ cuprates
journal, January 2007

Antiferromagnetism in ${La}_{2}$ ${CuO}_{4 - y}$
journal, June 1987

Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors
journal, July 2019

Weak Ferromagnetism and Tricriticality in Pure ${La}_{2}$ Cu $O_{4}$
journal, August 1994

Fermi surfaces and quantum oscillations in the underdoped high- $T_{c}$ superconductors YBa $_{2}$ Cu $_{3}$ O $_{6.5}$ and YBa $_{2}$ Cu $_{4}$ O $_{8}$
journal, July 2011

Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981

Computation of stripes in cuprates within the $LDA + U$ method
journal, November 2004

Improved tetrahedron method for Brillouin-zone integrations
journal, June 1994

Photoemission kinks and phonons in cuprates
journal, October 2008

Mott gapping in $3 d A B O_{3}$ perovskites without Mott-Hubbard interelectronic repulsion energy U
journal, July 2019