Ab intio description of the electronic structure of high-temperature cupratesuperconductors: A Comparative Density Functional Study

Kanun Pokharel,1, ∗ Christopher Lane,2, 3, † James W. Furness,1 Ruiqi Zhang,1 Jinliang Ning,1

Bernardo Barbiellini,4, 5 Robert S. Markiewicz,5 Yubo Zhang,1 Arun Bansil,5, ‡ and Jianwei Sun1, §

1Department of Physics and Engineering Physics,Tulane University, Louisiana 70118 New Orleans, USA

2Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA3Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

4LUT University, P.O. Box 20, FI-53851, Lappeenranta, Finland5Physics Department, Northeastern University, Boston, Massachusetts 02115, USA

(Dated: April 20, 2020)

In this work we have studied the crystal, electronic, and magnetic structure of La2−xSrxCuO4

for x = 0.0 and x = 0.25 employing nine functionals, representing the local, semi-local, and hybriddensity functional approximations on the first four rungs of Jacob’s ladder. Our assessment findsthat the meta-generailized gradient approximation (meta-GGA) class of functionals perform well incapturing the key properties of the prototypical high-temperature superconductor. In contrast, thelocal spin density approximation (LDA), GGA, and the considered hybrid density functional fail tocapture the metal-insulator transition (MIT) under doping. We further explore the capability ofhybrid functionals to capture the MIT transition upon doping by varying the admixture parameterof its exact exchange component.

I. INTRODUCTION

Ever since the discovery of cuprates in 1986 by Bed-norz and Muller[1], the anomalous behavior of the pris-tine and especially the doped compounds have eludedtheoretical explanation and remain as a central unsolvedproblem in condensed matter physics. La2CuO4, in par-ticular, has been a significant challenge to capture withina single coherent theoretical framework. The Hohenberg-Kohn-Sham density functional theory (DFT)[2, 3] frame-work failed spectacularly to capture the insulating anti-ferromagnetic ground state, let alone the doped phase[4]. Specifically, the local spin-density approximation(LSDA) exchange-correlation functional incorrectly pre-dicts the parent compound to be a metal, yielding avastly underestimated value for copper magnetic momentof 0.1µB [5, 6] in comparison to the experimental valueof 0.5 µB [7, 8]. The generalized gradient approximation(GGA) still predicts it as a metal with a slightly improvedmagnetic moment of 0.2µB [9]. Studies using the Becke-3-Lee-Yang-Parr (B3LYP)[10–13] hybrid functional havebeen shown to correctly explain the AFM ground state inLCO but fail to capture the transition to a metal upondoping [14]. These failures have led to the belief thatDFT was insufficient to correctly capture the physics ofthe cuprates and other correlated materials. Therefore,methodologies “beyond DFT” such as quantum Montecarlo methods [15], DFT+U [16, 17], and DMFT[18–20]had to be introduced to handle the strong electron corre-lation effects. However these approaches typically intro-duce ad hoc parameters to tune the correlation strength,thereby limiting their predictive power.

Recent progress in constructing advanced density-functionals provides a new path forward in address-ing the electronic structures of correlated materi-

als at the first-principles level. In particular, thestrongly-constrained-and-appropriately-normed (SCAN)meta-GGA functional[21], which obeys all 17 known con-straints applicable to a meta-GGA functional, has beenshown to accurately predict many of the key properties ofthe undoped and doped La2CuO4 and YBa2Cu3O6 [22–24]. In La2CuO4, one correctly captures the size of theoptical band gap, value of the copper magnetic momentand its alignment in the cuprate plane, and the magneticform factor in good accord with the corresponding experi-mental results [23]. In near-optimally dopedYBa2Cu3O7,26 competing uniform and stripe phases are identified,where the treatment of charge, spin, and lattice degreesof freedom on the same footing was crucial in stabilizingthe stripe phases without invoking any free parameters.Furthermore, SCAN has been applied to Sr2IrO4 parentcompound yielding the subtle balance between electroncorrelations and strong spin-orbit coupling in excellentaccord with experimental observations.[25]

SCAN’s success in the copper and iridium oxide sys-tems is a significant achievement for DFT and suggestspromising results in the wider class of correlated materi-als. In light of these recent milestones, a few questionsarise. Is SCAN a unique density functional that is ableto correctly capture these properties of cuprates or doother meta-GGAs behave similarly? Furthermore, howdo hybrid functionals behave in comparison?

In this paper the accuracy of nine density functionals,including LSDA [26, 27], PBE[28], SCAN[21], SCANL[29], TPSS[30], RTPSS[31], MS0[32], MS2[33], M06L[34], and HSE06[35–39], are assessed with respect to theexperimental crystal, electronic, and magnetic structureof pristine and doped prototypical high-temperature su-perconductor La2−xSrxCuO4. The various functionalsemployed span the first four rungs of the so-called DFTJacob’s Ladder [40] allowing us to judge the performance

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of each functional class for the description of correlatedcondensed matter systems.

II. COMPUTATIONAL DETAILS

The calculations were performed using the pseudopo-tential projector-augmented wave method [41] imple-mented in the Vienna ab initio simulation package(VASP)[42, 43]. The energy cutoff for the plane-wavebasis set was taken to be 550 eV for all meta-GGA calcu-lation whereas 520 eV for HSE functional. To sample theBrillouin zone, for meta-GGAs, 8 × 8 × 4 Γ-centered k-point mesh was used while a smaller mesh of 6×6×2 wasused for HSE functional. The structures were initiallyrelaxed for meta-GGAs using conjugate gradient algo-rithm with an atomic force tolerance of eV/Ao and totalenergy tolerance of 10−5 eV. For HSE06 functional, theunrelaxed experimental structure was used for calcula-tions. The pristine system used conjugate gradient algo-rithm while the doped system uses damped algorithm inHSE06 calculations. The computational cost for HSE06increases drastically as compared to meta-GGA calcula-tions so smaller energy, smaller k-point and unrelaxedstructure were used. Also, only LTO phase calculationfor HSE06 for the doped system was performed. Theunit cell was rotated to obtain

√2 ×√

2 AFM structure[44] where Sr was doped in place of one La to obtain adoped structure. In the AFM structure obtained, due tothe crystal symmetry, lanthanum substitution positionwas equivalent at all position so replacing one La by Srresulted in an effective average doping of 25%.

III. COMPARATIVE STUDY OF DIFFERENTFUNCTIONALS

Ground State Crystal Structure

The phase diagram of the cuprates displays a com-plex intertwining of magnetic and charge ordered statesthat evolve with doping to reveal a superconductingdome. Interestingly, structural phase transitions asso-ciated with various octahedral tilt modes[7, 8] mainlyfollow the electronic phase boundaries.[45] At high tem-peratures LCO is found to be tetragonal (HTT) withall CuO6 octahedra aligned axially. A phase transitionoccurs upon lowering the temperature resulting in a low-temperature orthorhombic (LTO) phase where the octa-hedra are tilted along the (110) zone diagonal. An ad-ditional low-temperature tetragonal (LTT) phase arisesupon substituting La by Ba or Nd, which has the octa-hedral tilts aligned along the (100) and (010) directionsin alternating CuO2 layers. Therefore, to properly dis-entangle the connection between the electronic and thephysical properties of the high-Tc cuprates it is impera-tive to capture the correct ground state crystal structure.

FIG. 1. (a) Theoretical predicted crystal structure ofLa2−xSrxCuO4 in the LTO phase for x = 0.0 and 0.25. Thecopper, oxygen, lanthanum, and strontium atoms are repre-sented by blue, green and yellow spheres, respectively. Oc-tahedral faces are shaded in blue (orange) to denote spin-up (down). Black dotted lines mark the unit cell. (b) ) Aschematic of the NM and AFM Brillouin zones; where thepath followed in the electronic dispersions in Fig. 6 is marked.

To calculate the total energy of each crystalline phase,we consider the

√2 ×√

2 supercell of the body-centered-tetragonal I4/mmm primitive unit-cell to accommodateboth the octahedral tilts and (π, π) AFM order originat-ing within the CuO2 plane. We treat the doping withinthe relatively simple “δ- doping” scheme where a singleLa is replaced by Sr in the supercell. This approach hasbeen recently reported for doping LSCO via molecularbeam epitaxy techniques[44]. Overall, this scheme yieldsan average hole-doing of 25%[22]. Figure 1 (a) shows thecrystal structures of LCO and LSCO in the LTO phasewhere the CuO6 octahedra have been shaded blue andorange following the AFM order. The Sr doping site isalso indicated.

Figure 2 (a) and (d) presents the relative energy be-tween the AFM and NM phases for pristine and dopedLa2−xSrxCuO4 in each crystal structure for the variousdensity fuctionals. Firstly, we note LDA does not sta-bilize an AFM order over the Cu sites, whereas in GGAthe AFM phase is marginally more stable, consistent withprevious studies[22]. The meta-GGA functionals all findthe AFM phase to be the ground state, displaying a rangeof −0.2 to −0.9 eV separating the AFM and NM states inthe pristine structure, whereas in doped case the energydifference reduces by a factor of two. These trends areconsistent across the various crystal structures.

Figure 2 (b-c) and (e-f) presents the relative energybetween the HTT, LTT, and LTO crystal structures forpristine and doped La2−xSrxCuO4 obtained within var-ious density functional approximations. Across all den-sity functionals the HTT phase lies at much higher ener-gies compared to the LTO and LTT phases. The differ-ence between LTO and LTT appears more delicate. ForSCAN, SCANL, and M06L, the LTO phase is correctlypredicted in the undoped case, while TPSS, RTPSS,MS0, and MS2 incorrectly predict the LTT phase as theground state. We note that the LTO and LTT phases

3

FIG. 2. (a) The energy difference between the G-AFM and NM phases for the HTT (green upside-down triangle), LTO (whitedimond), and LTT (blue triangle) crystal structures for various density functionals. The relative energy per formula unit forAFM between LTO and HTT (b) and LTO and LTT (c) structures for pristine LCO. (d), (e) and (f) same as (a), (b), and(a) except for LSCO.

are found experimentally to be virtually degenerate withmultiple domains displaying the coexistence of these twophases. This suggests that SCANL and M06L over es-timate the stability of the LTO phase, while the neardegeneracy predicted by SCAN is in favor with the ex-perimental observations. In the doped case, all function-als rightly predict the ground state to be LTT phase[46],with SCAN and SCANL displaying a marginal energydifference with respect to LTO.

Figure 3 shows the equilibrium lattice constants forLCO in the HTT, LTT, and LTO phases using variousdensity functionals. The LSDA and PBE values weretaken from reference [22] and experimental values wereobtained from [47–49]. Firstly, we observe that LSDAunderestimates the values of lattice constants, by overbinding the atoms, for all crystal structures. PBE, onthe other hand, under-binds the atoms yielding an ex-aggerated orthorhombicity in the LTO phase, similar tothe super-tetragonality spuriously predicted by PBE forferroelectric materials [50]. TPSS, RTPSS, MS0, andMS2 correct upon the GGA results by reducing the blattice constant in line with the experimental value inLTO and LTT. Curiously, all functionals under estimatethe lattice parameters in the HTT phase, except for GGAand M06L. Furthermore, the emperical M06L functional

predicts all lattice constants for each crystal phase withbetter accuracy than the other functionals. We notethat HTT is a high-temperature phase and the experi-menatl lattice constant should be corrected by removingthe finite temperature expansion and the zero-point vi-brational expansion for comparison with DFT results.Figure 4 is the same as Fig. 3, except compares the oc-tahedra tilt angles. Here, the M06L finds a reduced tiltangle, whereas all other functionals tend to over estimatethe angle within a few degrees. However, we should notethat the calculated and experimental tilt angles should beregarded as average values. That is, the CuO6 octahedraare not rigid objects, but can dynamically deform andshould couple strongly to various phonon modes. There-fore, to capture the octahedra tilts more accurately amolecular dynamics or phonon calculation should be per-formed.

Electronic And Magnetic Structure

Figure 5 compares the theoretically predicted elec-tronic band gap (a) and copper magntic moment (b)within the various density functional approximations forall three crystal phases of pristine LCO. The experimen-

4

FIG. 3. Comparison of the theoretically obtained and experi-mental lattice constants for the HTT, LTT, and LTO crystalstructures using various density functionals for La2CuO4.

tal band gap and copper magnetic moment of 1.0 eV and0.5 µB , respectively, are marked by the grey dashed lines.Clearly, LDA and GGA spectacularly underestimate theband gap and magnetic moments, due to the failure tostabilize the AFM order. Moving up Jacob’s ladder, alarge variation in behavior amongst the meta-GGAs isobserved. Specifically, TPSS and RTPSS both underes-timate the band gap and magnetic moments, while theMS family of functionals, yield the experimental values orslightly over estimate them. SCAN gives accurate resultsin both cases, whereas SCANL predicts a reduced bandgap by almost a factor of two. M06L under estimatesboth the moment and the gap value, possibly due to itsbias towards molecular systems during its empirical con-struction. Finally, the hybrid HSE06 functional, predictsa 3 eV band gap completely out of step with experiment.

Figure 6 shows the electronic band dispersions of pris-tine and doped La2CuO4 in the LTO crystal struc-ture for the AFM phase for various density functionals.The copper (red circles) and planar oxygen (blue dots)atomic weights are overlayed. For all functionals LCOis clearly seen to be an insulator. At the valence edge,SCAN produces a significant avoided crossing betweenthe dx2−y2 and in-plane oxygen dominated bands along

FIG. 4. Theoretically predicted values of octahedra tilt angleusing various density functionals for LCO. The LSDA andPBE value are taken from reference [22] The octahedra tiltvalues for LTO, LTT and HTT are divided by correspondingexperimental values.

Γ − M and M − Γ. Comparing this feature across thevarious functionals, it is reduced in SCANL and virtu-ally non-existent in M06L. In SCAN, the gap is indirect,with the lowest energetic transition occurring at M ± δand M for the valence and conduction bands (δ is a smalldisplacement away from M), respectively. In contrast,SCANL and M06L predict indirect transitions connectingvalence and conduction between X and M. These slightdifferences in alignment between the oxygen and copperstates suggest that the various functionals are capturingan effective on-site potential to a varying degree, whichis possibly derived from the reduced magnetic momentfound by each functional.

For the doped system, all meta-GGAs capture transi-tion to a metal, with each functional producing slightlydifferent band splittings around the Fermi level. In con-trast, HSE06 maintains a small gap and predicts a nearlyflat impurity-like band just above the Fermi level, consis-tent with the B3LYP result [14]. Moreover, the conduc-tion bands display significant spin splitting indicative ofa strong uncompensated ferrimagnetic order.

IV. WHY DOES HSE06 OPEN A GAP FOR THEDOPED LSCO

The exchange-correlation energy for the screened hy-brid functional of Heyd, Scuseria and Ernzerhof (HSE)is given by

EHSExc = αEHF,SR

x (µ) + (1− α)EPBE,SRx (µ)

+EPBE,LRx (µ) + EPBE

c (µ)

where “α” is the exact exchange admixing parameterwhose value is 1/4 [51]. EHF,SR

x (µ) is the short-range

5

FIG. 5. Bar graph of the theoretical predicted values of (a)electronic band gap (b) copper magnetic moment for all threephases of pristine LCO obtained within various density func-tional approximations. The dotted grey lines represent exper-imental values for the respective values. The LSDA and PBEvalues are taken from reference [22]

HF exact exchange, EPBE,SRx (µ) and EPBE,LR

x (µ) arethe short and long-range components respectively ofthe PBE exchange functional. Hybrid density function-als were originally designed to combine semilocal den-sity functionals with the Hartree-Fock approximation forthermochemical properties of molecules, the former andthe latter of which typically overbinds and underbindsmolecules, respectively. The admixing parameter valueof 1/4 has been justified for molecular thermochemicalproperties based on a perturbation consideration [52].HSE06 with the admixing parameter value of 1/4 laterturned out to work well for band gap predictions of semi-conductors. This can be understood from its better deal-ing with the orbital localization by neutralizing the over-delocalization of PBE due to their self-interaction errorswith the over-localization of Hartree-Fock [53, 54]. How-ever, due to its over-localization error, Hartree-Fock is

FIG. 6. Electronic band structure and density of states ofLCO and LSCO in the LTO phase using (a) SCAN (b)SCANL (c) M06L (d)HSE06. The contribution of Cu-dx2−y2

and O -px + py are marked by the red and blues shadings,respectively. The path followed by the dispersion in the Bril-louin zone is shown in Fig 1(b).

well known for not being applicable for metallic systemswhere no band gap is present to separate the occupiedfrom unoccupied bands. Therefore, hybrid functionalsare not recommended for metallic systems even if only afraction of the exact exchange is mixed in.

Consistently, the HSE06 functional correctly capturesLCO as insulator but fails to capture the metallic tran-sition under doping in LSCO. Figure 7 shows the bandstructures of HSE06 by varying the mixing parameter

6

FIG. 7. Band structure comparison by varying mixing pa-rameter for (a) α = 0 (b) α = 0.05 (c) α = 0.15 and (d) α= 0.25 in doped LTO phase. The blue filled and red emptycircles correspond to oxygen px+py orbitals and the copperdx2−y2 orbitals respectively. The projection strength is shownby marker size.

“α”. For α = 0, HSE06 is reduced to PBE, and thus pre-dicts LSCO to be metallic. As the mixing parameter is in-creased to α =0.05, a slight change in the band structureis observed. The conduction bands are slightly pushed upand split due to the stabilization of magnetic moments ofCu. Also, the bands around Fermi level at point X startto separate from one another. Further increasing thevalue to 0.15 results in larger band separation and split-ting of conduction bands. The two valence bands nearFermi level are separated out with some portion of bothbands crossing the Fermi level. Finally, at the standardvalue of α= 0.25, bands completely split into conductionband at around 0.2 eV and valence band below Fermilevel with a small gap, resulting in the doped system be-ing an insulator. From the band structures it can be seenthat at lower admixing values, the conductions band andvalence bands around Fermi level are more dominated bycopper orbitals at M point with color of projection beingmore red. As the value of admixing parameter increases,the oxygen orbitals gain more weight and color changesfrom red dominant to mixture of red and blue, indicatingmore characteristic of charge transfer. This implies thatelectrons are more localized around oxygen atoms, as ex-pected for higher portions of exact exchange in HSE06.

V. CONCLUDING REMARKS

Our results show that all meta-GGAs behave sim-ilarly by predicting the pristine LCO as an insulatorand capturing the metallic transition with Sr doping.

Among different meta-GGAs considered, SCAN’s perfor-mance on structural, electronic, and magnetic propertiesof LCO/LSCO is closest to experimental results. The hy-brid functional (HSE06) in contrast, captures the pristinesystem as an insulator, predicting a very large values ofband gap and copper magnetic moment and completelyincorrectly predicting the doped system as an insulator.The incorrect prediction of doped system is linked to thestandard value of the admixing parameter, which has tobe adjusted for the metal-insulator transition predictionof LCO under doping. We have shown that the standardvalue of 25% mixing needs to be revisited while consid-ering the metallic system.

VI. ACKNOWLEDGMENTS

The work at Tulane University was supported bythe US Department of Energy under EPSCoR GrantNo. DE-SC0012432 with additional support from theLouisiana Board of Regents, and by the U.S. DOE, Of-fice of Science, Basic Energy Sciences grant number DE-SC0019350. Calculations were partially done using theNational Energy Research Scientific Computing Centersupercomputing center and the Cypress cluster at Tu-lane University. The work at Northeastern Universitywas supported by the US Department of Energy (DOE),Office of Science, Basic Energy Sciences grant numberDE-FG02-07ER46352 (core research), and benefited fromNortheastern University’s Advanced Scientific Computa-tion Center (ASCC), the NERSC supercomputing cen-ter through DOE grant number DE-AC02-05CH11231,and support (testing efficacy of advanced functionals)from the DOE EFRC: Center for Complex Materialsfrom First Principles (CCM) under grant number DE-SC0012575. C.L. was supported by the U.S. DOE NNSAunder Contract No. 89233218CNA000001 and by theCenter for Integrated Nanotechnologies, a DOE BES userfacility, in partnership with the LANL Institutional Com-puting Program for computational resources. Additionalsupport was provided by DOE Office of Basic Energy Sci-ences Program E3B5. B.B. acknowledges support fromthe COST Action CA16218.

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Ab intio description of the electronic structure ofhigh-temperature cuprate superconductors: A

Comparative Density Functional Study

Kanun Pokharel,1,∗ Christopher Lane,2,3,James W. Furness,1Ruiqi Zhang,1

Jinliang Ning,1, Bernardo Barbiellini,4,5 Robert S. Markiewicz,5 YuboZhang,1 Arun Bansil,∗5 Jianwei Sun∗1

1Department of Physics and Engineering Physics, Tulane University, New Orleans, LA

70118, USA

2Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545,

USA3Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos,

New Mexico 87545, USA4LUT University, P.O. Box 20, FI-53851, Lappeenranta, Finland

5Physics Department, Northeastern University, Boston, Massachusetts 02115, USA∗To whom correspondence should be addressed; E-mail: jsun@tulane.edu and

ar.bansil@neu.edu

April 20, 2020

This supplementary material includes 3 tables and 3 figures:Table 1 represents the the theoretically predicted values of lattice constants using

various meta-GGAs for all three phases of pristine LCO and hope doped LSCO.Table 2 represents the theoretically predicted values of electronic band gap and

copper magnetic moment by various functionals considered for calculation.Table 3 represents the theoretically predicted values of octahedra tilt for parent LCO

by various functionals considered for calculation.Figure 1 represents the eletronic structure plots for three different functionals SCAN,

SCANL and M06L repectively for the LTT phase of both parent LCO and doped LSCOsystems.

Figure 2 represents the eletronic structure plots for three different functionals SCAN,SCANL and M06L repectively for the HTT phase of both parent LCO and doped LSCOsystems.

Figure 3 represents the spin density plot of the conduction band for the mixing valueof 0.25 and form factor comparison of copper atoms for SCAN and HSE06 functional.

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Table 1: Theoretically predicted values of lattice constants using various meta-GGAs forthree different phases of pristince LCO and doped LSCO systems

pristine LCO doped LSCOMeta-GGA Phase Lattice constant Lattice constant

a(A) b(A) c(A) V(A3) a(A) b(A) c(A) V(A

3)

LTO 5.335 5.421 13.107 379.1 - - - -Experimental LTT 5.360 5.360 13.236 380.3 - - - -

HTT 5.391 5.391 13.219 384.2 - - - -

LTO 5.324 5.453 13.090 380.06 5.318 5.394 13.097 375.79SCAN LTT 5.389 5.388 13.083 379.97 5.350 5.360 13.099 375.72

HTT 5.349 5.349 13.123 375.51 5.335 5.333 13.112 373.12

LTO 5.310 5.436 13.176 380.91 5.293 5.371 13.232 376.29SCANL LTT 5.368 5.368 13.182 379.92 5.332 5.330 13.226 375.94

HTT 5.355 5.355 13.193 378.40 5.313 5.311 13.253 374.07

LTO 5.329 5.495 13.062 382.6 5.327 5.430 13.090 378.7TPSS LTT 5.414 5.414 13.064 383.04 5.373 5.375 13.100 378.44

HTT 5.370 5.370 13.116 378.34 5.352 5.350 13.122 375.86

LTO 5.328 5.472 13.042 380.28 5.324 5.415 13.062 376.65RTPSS LTT 5.402 5.402 13.042 380.64 5.369 5.363 13.071 376.47

HTT 5.366 5.366 13.088 376.95 5.349 5.347 13.087 374.43

LTO 5.342 5.504 13.039 383.41 5.333 5.452 13.052 379.57MS0 LTT 5.424 5.424 13.044 383.88 5.394 5.410 13.028 380.23

HTT 5.370 5.370 13.080 377.28 5.359 5.357 13.063 375.08

LTO 5.315 5.464 13.024 378.35 5.312 5.407 13.044 374.78MS2 LTT 5.392 5.391 13.031 378.88 5.356 5.369 13.045 375.25

HTT 5.348 5.348 13.065 373.74 5.331 5.330 13.073 371.53

LTO 5.38 5.41 13.248 386.17 5.360 5.367 13.273 381.95M06L LTT 5.399 5.399 13.248 386.22 5.363 5.364 13.273 381.92

HTT 5.389 5.389 13.255 385 5.363 5.361 13.275 381.74

2

Table 2: Theoretically predicted values of octahedra tilt using various meta-GGAs for threedifferent phases of parent LCO system

Meta-GGA Phase Octahedral Tiltaxial (deg)

LTO 7SCAN LTT 6.87

HTT 0

LTO 6SCANL LTT 4.9

HTT 0

LTO 6.9TPSS LTT 6.88

HTT 0

LTO 6.43RTPSS LTT 6.50

HTT 0

LTO 8.32MS0 LTT 8.28

HTT 0

LTO 7.32MS2 LTT 7.35

HTT 0

LTO 3.54M06L LTT 3.53

HTT 0

3

Table 3: Theoretically predicted values of electronic band gap and copper magnetic momentby various functionals considered

Meta-GGA Phase Cu magnetic moment (µB) electronic bandgap (eV)

LTO 0.491 0.98SCAN LTT 0.491 1.01

HTT 0.480 0.917

LTO 0.402 0.422SCANL LTT 0.401 0.544

HTT 0.399 0.469

LTO 0.312 0.18TPSS LTT 0.315 0.24

HTT 0.305 0.21

LTO 0.320 0.21RTPSS LTT 0.322 0.26

HTT 0.313 0.24

LTO 0.538 1.22MS0 LTT 0.539 1.27

HTT 0.528 1.20

LTO 0.506 1.02MS2 LTT 0.507 1.06

HTT 0.500 0.99

LTO 0.377 0.432M06L LTT 0.376 0.439

HTT 0.377 0.434

LTO 0.641 3.2HSE06 LTT 0.638 3.1

HTT 0.642 3.0

4

Figure 1: Electronic structure results for (a) SCAN (b) SCANL (c) M06L for pristine LCOand doped LSCO systems for LTT phase. The crystal structure can be found in reference [?]

5

Figure 2: Electronic structure results for (a) SCAN (b) SCANL (c) M06L for pristine LCOand doped LSCO systems for HTT phase. The crystal structure can be found in reference [?]

6

Figure 3: (a) represents spin density plot for the conduction band at α = 0.25. Yellowcolor denotes the positive spin density, black lines mark the unit cell. The red, blue anddots represent the oxygen and copper atoms respectively. One green dot represent the holedoped Strontium atom. Lanthanum atoms are not shown here. The doped hole is foundto be localized within oxygen and copper atoms shown by yellow iso-surface which is dz2

in nature. (b) Represents form factor comparison of copper atoms for SCAN and HSE06functional

7