DOI: 10.1038/s41567-020-0947-0. Berry curvature memory through electrically driven stacking transitions

Berry curvature memory through electrically driven stacking transitions

10.1038/s41567-020-0947-0

Crossref journal-article

Springer Science and Business Media LLC

Nature Physics (297)

Bibliography

Xiao, J., Wang, Y., Wang, H., Pemmaraju, C. D., Wang, S., Muscher, P., Sie, E. J., Nyby, C. M., Devereaux, T. P., Qian, X., Zhang, X., & Lindenberg, A. M. (2020). Berry curvature memory through electrically driven stacking transitions. Nature Physics, 16(10), 1028â1034.

Authors 12

Jun Xiao (first)
Ying Wang (additional)
Hua Wang (additional)
C. D. Pemmaraju (additional)
Siqi Wang (additional)
Philipp Muscher (additional)
Edbert J. Sie (additional)
Clara M. Nyby (additional)
Thomas P. Devereaux (additional)
Xiaofeng Qian (additional)
Xiang Zhang (additional)
Aaron M. Lindenberg (additional)

References 45 Referenced 181

Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018). (10.1038/nature26154) / Nature by Y Cao (2018)
Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015). (10.1038/nature15768) / Nature by AA Soluyanov (2015)
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015). (10.1038/nature14364) / Nature by L Ju (2015)
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019). (10.1038/s41567-018-0387-2) / Nat. Phys. by G Chen (2019)
Wang, J., Lian, B. & Zhang, S.-C. Electrically tunable magnetism in magnetic topological insulators. Phys. Rev. Lett. 115, 036805 (2015). (10.1103/PhysRevLett.115.036805) / Phys. Rev. Lett. by J Wang (2015)
Li, Y., Duerloo, K.-A. N., Wauson, K. & Reed, E. J. Structural semiconductor-to-semimetal phase transition in two-dimensional materials induced by electrostatic gating. Nat. Commun. 7, 10671 (2016). / Nat. Commun. by Y Li (2016)
Yan, B. & Felser, C. Topological materials: Weyl semimetals. Annu. Rev. Condens. Matter Phys. 8, 337–354 (2017). (10.1146/annurev-conmatphys-031016-025458) / Annu. Rev. Condens. Matter Phys. by B Yan (2017)
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018). (10.1103/RevModPhys.90.015001) / Rev. Mod. Phys. by NP Armitage (2018)
Suzuki, R. et al. Valley-dependent spin polarization in bulk MoS2 with broken inversion symmetry. Nat. Nanotechnol. 9, 611–617 (2014). (10.1038/nnano.2014.148) / Nat. Nanotechnol. by R Suzuki (2014)
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). (10.1038/nature26160) / Nature by Y Cao (2018)
Wang, H. & Qian, X. Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2. npj Comput. Mater. 5, 119 (2019). (10.1038/s41524-019-0257-1) / npj Comput. Mater. by H Wang (2019)
Kim, H.-J., Kang, S.-H., Hamada, I. & Son, Y.-W. Origins of the structural phase transitions in MoTe2 and WTe2. Phys. Rev. B 95, 180101 (2017). (10.1103/PhysRevB.95.180101) / Phys. Rev. B by H-J Kim (2017)
Yang, Q., Wu, M. & Li, J. Origin of two-dimensional vertical ferroelectricity in WTe2 bilayer and multilayer. J. Phys. Chem. Lett. 9, 7160–7164 (2018). (10.1021/acs.jpclett.8b03654) / J. Phys. Chem. Lett. by Q Yang (2018)
Lu, P. et al. Origin of superconductivity in the Weyl semimetal WTe2 under pressure. Phys. Rev. B 94, 224512 (2016). (10.1103/PhysRevB.94.224512) / Phys. Rev. B by P Lu (2016)
Xiao, J. et al. Intrinsic two-dimensional ferroelectricity with dipole locking. Phys. Rev. Lett. 120, 227601 (2018). (10.1103/PhysRevLett.120.227601) / Phys. Rev. Lett. by J Xiao (2018)
Zhang, W., Mazzarello, R., Wuttig, M. & Ma, E. Designing crystallization in phase-change materials for universal memory and neuro-inspired computing. Nat. Rev. Mater. 4, 150–168 (2019). (10.1038/s41578-018-0076-x) / Nat. Rev. Mater. by W Zhang (2019)
Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014). (10.1126/science.1256815) / Science by X Qian (2014)
Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677–682 (2017). (10.1038/nphys4091) / Nat. Phys. by Z Fei (2017)
Tang, S. et al. Quantum spin Hall state in monolayer 1T′-WTe2. Nat. Phys. 13, 683–687 (2017). (10.1038/nphys4174) / Nat. Phys. by S Tang (2017)
Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018). (10.1126/science.aan6003) / Science by S Wu (2018)
Fatemi, V. et al. Electrically tunable low-density superconductivity in a monolayer topological insulator. Science 362, 926–929 (2018). (10.1126/science.aar4642) / Science by V Fatemi (2018)
You, J.-S., Fang, S., Xu, S.-Y., Kaxiras, E. & Low, T. Berry curvature dipole current in the transition metal dichalcogenides family. Phys. Rev. B 98, 121109 (2018). (10.1103/PhysRevB.98.121109) / Phys. Rev. B by J-S You (2018)
Shi, L. K. & Song, J. C. W. Symmetry, spin-texture, and tunable quantum geometry in a WTe2 monolayer. Phys. Rev. B 99, 035403 (2019). (10.1103/PhysRevB.99.035403) / Phys. Rev. B by LK Shi (2019)
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015). (10.1103/PhysRevLett.115.216806) / Phys. Rev. Lett. by I Sodemann (2015)
Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019). (10.1038/s41586-018-0807-6) / Nature by Q Ma (2019)
Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019). (10.1038/s41563-019-0294-7) / Nat. Mater. by K Kang (2019)
Wang, Y., Xiao, J., Yang, S., Wang, Y. & Zhang, X. Second harmonic generation spectroscopy on two-dimensional materials. Opt. Mater. Express 9, 1136 (2019). (10.1364/OME.9.001136) / Opt. Mater. Express by Y Wang (2019)
Beams, R. et al. Characterization of few-layer 1T′ MoTe2 by polarization-resolved second harmonic generation and Raman scattering. ACS Nano 10, 9626–9636 (2016). (10.1021/acsnano.6b05127) / ACS Nano by R Beams (2016)
Kim, M. et al. Determination of the thickness and orientation of few-layer tungsten ditelluride using polarized Raman spectroscopy. 2D Mater. 3, 034004 (2016). (10.1088/2053-1583/3/3/034004) / 2D Mater. by M Kim (2016)
Chen, S.-Y., Goldstein, T., Venkataraman, D., Ramasubramaniam, A. & Yan, J. Activation of new Raman modes by inversion symmetry breaking in type II Weyl semimetal candidate T′-MoTe2. Nano Lett. 16, 5852–5860 (2016). (10.1021/acs.nanolett.6b02666) / Nano Lett. by S-Y Chen (2016)
Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61–66 (2019). (10.1038/s41586-018-0809-4) / Nature by EJ Sie (2019)
Varga, T. et al. Coexistence of weak ferromagnetism and ferroelectricity in the high pressure LiNbO3-type phase of FeTiO3. Phys. Rev. Lett. 103, 047601 (2009). (10.1103/PhysRevLett.103.047601) / Phys. Rev. Lett. by T Varga (2009)
Fei, Z. et al. Ferroelectric switching of a two-dimensional metal. Nature 560, 336–339 (2018). (10.1038/s41586-018-0336-3) / Nature by Z Fei (2018)
Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900–906 (2018). (10.1038/s41567-018-0189-6) / Nat. Phys. by S-Y Xu (2018)
Rehn, D. A., Li, Y., Pop, E. & Reed, E. J. Theoretical potential for low energy consumption phase change memory utilizing electrostatically-induced structural phase transitions in 2D materials. npj Comput. Mater. 4, 2 (2018). (10.1038/s41524-017-0059-2) / npj Comput. Mater. by DA Rehn (2018)
Zidan, M. A., Strachan, J. P. & Lu, W. D. The future of electronics based on memristive systems. Nat. Electron. 1, 22–29 (2018). (10.1038/s41928-017-0006-8) / Nat. Electron. by MA Zidan (2018)
Wang, Z., Wieder, B. J., Li, J., Yan, B. & Bernevig, B. A. Higher-order topology, monopole nodal lines, and the origin of large Fermi arcs in transition metal dichalcogenides XTe2 (X = Mo, W). Phys. Rev. Lett. 123, 186401 (2019). (10.1103/PhysRevLett.123.186401) / Phys. Rev. Lett. by Z Wang (2019)
Ezawa, M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Phys. Rev. Lett. 120, 026801 (2018). (10.1103/PhysRevLett.120.026801) / Phys. Rev. Lett. by M Ezawa (2018)
Park, M. J., Kim, Y., Cho, G. Y. & Lee, S. Higher-order topological insulator in twisted bilayer graphene. Phys. Rev. Lett. 123, 216803 (2019). (10.1103/PhysRevLett.123.216803) / Phys. Rev. Lett. by MJ Park (2019)
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996). (10.1103/PhysRevLett.77.3865) / Phys. Rev. Lett. by JP Perdew (1996)
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996). (10.1103/PhysRevB.54.11169) / Phys. Rev. B by G Kresse (1996)
Klimeš, J., Bowler, D. R. & Michaelides, A. Chemical accuracy for the van der Waals density functional. J. Phys. Condens. Matter 22, 022201 (2010). (10.1088/0953-8984/22/2/022201) / J. Phys. Condens. Matter by J Klimeš (2010)
Qian, X. et al. Quasiatomic orbitals for ab initio tight-binding analysis. Phys. Rev. B 78, 245112 (2008). (10.1103/PhysRevB.78.245112) / Phys. Rev. B by X Qian (2008)
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012). (10.1103/RevModPhys.84.1419) / Rev. Mod. Phys. by N Marzari (2012)
Krukau, A. V., Vydrov, O. A., Izmaylov, A. F. & Scuseria, G. E. Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 125, 224106 (2006). (10.1063/1.2404663) / J. Chem. Phys. by AV Krukau (2006)

Dates

Type	When
Created	5 years, 2 months ago (June 29, 2020, 12:04 p.m.)
Deposited	2 years, 3 months ago (May 20, 2023, 6:17 p.m.)
Indexed	1 week, 2 days ago (Aug. 27, 2025, 11:54 a.m.)
Issued	5 years, 2 months ago (June 29, 2020)
Published	5 years, 2 months ago (June 29, 2020)
Published Online	5 years, 2 months ago (June 29, 2020)
Published Print	4 years, 11 months ago (Oct. 1, 2020)

Funders 2

U.S. Department of Energy 10.13039/100000015
Region: Americas
gov (National government)
Labels8
1. Energy Department
2. Department of Energy
3. United States Department of Energy
4. ENERGY.GOV
5. US Department of Energy
6. USDOE
7. DOE
8. USADOE
Awards2
1. DE-AC02-76SF00515
2. DEAC02-05-CH11231
National Science Foundation 10.13039/100000001
Region: Americas
gov (National government)
Labels4
1. U.S. National Science Foundation
2. NSF
3. US NSF
4. USA NSF
Awards1
1. DMR-1753054

BibTeX

@article{Xiao_2020, title={Berry curvature memory through electrically driven stacking transitions}, volume={16}, ISSN={1745-2481}, url={http://dx.doi.org/10.1038/s41567-020-0947-0}, DOI={10.1038/s41567-020-0947-0}, number={10}, journal={Nature Physics}, publisher={Springer Science and Business Media LLC}, author={Xiao, Jun and Wang, Ying and Wang, Hua and Pemmaraju, C. D. and Wang, Siqi and Muscher, Philipp and Sie, Edbert J. and Nyby, Clara M. and Devereaux, Thomas P. and Qian, Xiaofeng and Zhang, Xiang and Lindenberg, Aaron M.}, year={2020}, month=jun, pages={1028–1034} }

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      "journal-title": "Nat. Phys."
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      "author": "P Lu",
      "year": "2016",
      "unstructured": "Lu, P. et al. Origin of superconductivity in the Weyl semimetal WTe2 under pressure. Phys. Rev. B 94, 224512 (2016).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "947_CR15",
      "doi-asserted-by": "crossref",
      "first-page": "227601",
      "DOI": "10.1103/PhysRevLett.120.227601",
      "volume": "120",
      "author": "J Xiao",
      "year": "2018",
      "unstructured": "Xiao, J. et al. Intrinsic two-dimensional ferroelectricity with dipole locking. Phys. Rev. Lett. 120, 227601 (2018).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR16",
      "doi-asserted-by": "crossref",
      "first-page": "150",
      "DOI": "10.1038/s41578-018-0076-x",
      "volume": "4",
      "author": "W Zhang",
      "year": "2019",
      "unstructured": "Zhang, W., Mazzarello, R., Wuttig, M. & Ma, E. Designing crystallization in phase-change materials for universal memory and neuro-inspired computing. Nat. Rev. Mater. 4, 150\u2013168 (2019).",
      "journal-title": "Nat. Rev. Mater."
    },
    {
      "key": "947_CR17",
      "doi-asserted-by": "crossref",
      "first-page": "1344",
      "DOI": "10.1126/science.1256815",
      "volume": "346",
      "author": "X Qian",
      "year": "2014",
      "unstructured": "Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344\u20131347 (2014).",
      "journal-title": "Science"
    },
    {
      "key": "947_CR18",
      "doi-asserted-by": "crossref",
      "first-page": "677",
      "DOI": "10.1038/nphys4091",
      "volume": "13",
      "author": "Z Fei",
      "year": "2017",
      "unstructured": "Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677\u2013682 (2017).",
      "journal-title": "Nat. Phys."
    },
    {
      "key": "947_CR19",
      "doi-asserted-by": "crossref",
      "first-page": "683",
      "DOI": "10.1038/nphys4174",
      "volume": "13",
      "author": "S Tang",
      "year": "2017",
      "unstructured": "Tang, S. et al. Quantum spin Hall state in monolayer 1T\u2032-WTe2. Nat. Phys. 13, 683\u2013687 (2017).",
      "journal-title": "Nat. Phys."
    },
    {
      "key": "947_CR20",
      "doi-asserted-by": "crossref",
      "first-page": "76",
      "DOI": "10.1126/science.aan6003",
      "volume": "359",
      "author": "S Wu",
      "year": "2018",
      "unstructured": "Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76\u201379 (2018).",
      "journal-title": "Science"
    },
    {
      "key": "947_CR21",
      "doi-asserted-by": "crossref",
      "first-page": "926",
      "DOI": "10.1126/science.aar4642",
      "volume": "362",
      "author": "V Fatemi",
      "year": "2018",
      "unstructured": "Fatemi, V. et al. Electrically tunable low-density superconductivity in a monolayer topological insulator. Science 362, 926\u2013929 (2018).",
      "journal-title": "Science"
    },
    {
      "key": "947_CR22",
      "doi-asserted-by": "crossref",
      "first-page": "121109",
      "DOI": "10.1103/PhysRevB.98.121109",
      "volume": "98",
      "author": "J-S You",
      "year": "2018",
      "unstructured": "You, J.-S., Fang, S., Xu, S.-Y., Kaxiras, E. & Low, T. Berry curvature dipole current in the transition metal dichalcogenides family. Phys. Rev. B 98, 121109 (2018).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "947_CR23",
      "doi-asserted-by": "crossref",
      "first-page": "035403",
      "DOI": "10.1103/PhysRevB.99.035403",
      "volume": "99",
      "author": "LK Shi",
      "year": "2019",
      "unstructured": "Shi, L. K. & Song, J. C. W. Symmetry, spin-texture, and tunable quantum geometry in a WTe2 monolayer. Phys. Rev. B 99, 035403 (2019).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "947_CR24",
      "doi-asserted-by": "crossref",
      "first-page": "216806",
      "DOI": "10.1103/PhysRevLett.115.216806",
      "volume": "115",
      "author": "I Sodemann",
      "year": "2015",
      "unstructured": "Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR25",
      "doi-asserted-by": "crossref",
      "first-page": "337",
      "DOI": "10.1038/s41586-018-0807-6",
      "volume": "565",
      "author": "Q Ma",
      "year": "2019",
      "unstructured": "Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337\u2013342 (2019).",
      "journal-title": "Nature"
    },
    {
      "key": "947_CR26",
      "doi-asserted-by": "crossref",
      "first-page": "324",
      "DOI": "10.1038/s41563-019-0294-7",
      "volume": "18",
      "author": "K Kang",
      "year": "2019",
      "unstructured": "Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324\u2013328 (2019).",
      "journal-title": "Nat. Mater."
    },
    {
      "key": "947_CR27",
      "doi-asserted-by": "crossref",
      "first-page": "1136",
      "DOI": "10.1364/OME.9.001136",
      "volume": "9",
      "author": "Y Wang",
      "year": "2019",
      "unstructured": "Wang, Y., Xiao, J., Yang, S., Wang, Y. & Zhang, X. Second harmonic generation spectroscopy on two-dimensional materials. Opt. Mater. Express 9, 1136 (2019).",
      "journal-title": "Opt. Mater. Express"
    },
    {
      "key": "947_CR28",
      "doi-asserted-by": "crossref",
      "first-page": "9626",
      "DOI": "10.1021/acsnano.6b05127",
      "volume": "10",
      "author": "R Beams",
      "year": "2016",
      "unstructured": "Beams, R. et al. Characterization of few-layer 1T\u2032 MoTe2 by polarization-resolved second harmonic generation and Raman scattering. ACS Nano 10, 9626\u20139636 (2016).",
      "journal-title": "ACS Nano"
    },
    {
      "key": "947_CR29",
      "doi-asserted-by": "crossref",
      "first-page": "034004",
      "DOI": "10.1088/2053-1583/3/3/034004",
      "volume": "3",
      "author": "M Kim",
      "year": "2016",
      "unstructured": "Kim, M. et al. Determination of the thickness and orientation of few-layer tungsten ditelluride using polarized Raman spectroscopy. 2D Mater. 3, 034004 (2016).",
      "journal-title": "2D Mater."
    },
    {
      "key": "947_CR30",
      "doi-asserted-by": "crossref",
      "first-page": "5852",
      "DOI": "10.1021/acs.nanolett.6b02666",
      "volume": "16",
      "author": "S-Y Chen",
      "year": "2016",
      "unstructured": "Chen, S.-Y., Goldstein, T., Venkataraman, D., Ramasubramaniam, A. & Yan, J. Activation of new Raman modes by inversion symmetry breaking in type II Weyl semimetal candidate T\u2032-MoTe2. Nano Lett. 16, 5852\u20135860 (2016).",
      "journal-title": "Nano Lett."
    },
    {
      "key": "947_CR31",
      "doi-asserted-by": "crossref",
      "first-page": "61",
      "DOI": "10.1038/s41586-018-0809-4",
      "volume": "565",
      "author": "EJ Sie",
      "year": "2019",
      "unstructured": "Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61\u201366 (2019).",
      "journal-title": "Nature"
    },
    {
      "key": "947_CR32",
      "doi-asserted-by": "crossref",
      "first-page": "047601",
      "DOI": "10.1103/PhysRevLett.103.047601",
      "volume": "103",
      "author": "T Varga",
      "year": "2009",
      "unstructured": "Varga, T. et al. Coexistence of weak ferromagnetism and ferroelectricity in the high pressure LiNbO3-type phase of FeTiO3. Phys. Rev. Lett. 103, 047601 (2009).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR33",
      "doi-asserted-by": "crossref",
      "first-page": "336",
      "DOI": "10.1038/s41586-018-0336-3",
      "volume": "560",
      "author": "Z Fei",
      "year": "2018",
      "unstructured": "Fei, Z. et al. Ferroelectric switching of a two-dimensional metal. Nature 560, 336\u2013339 (2018).",
      "journal-title": "Nature"
    },
    {
      "key": "947_CR34",
      "doi-asserted-by": "crossref",
      "first-page": "900",
      "DOI": "10.1038/s41567-018-0189-6",
      "volume": "14",
      "author": "S-Y Xu",
      "year": "2018",
      "unstructured": "Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900\u2013906 (2018).",
      "journal-title": "Nat. Phys."
    },
    {
      "key": "947_CR35",
      "doi-asserted-by": "crossref",
      "first-page": "2",
      "DOI": "10.1038/s41524-017-0059-2",
      "volume": "4",
      "author": "DA Rehn",
      "year": "2018",
      "unstructured": "Rehn, D. A., Li, Y., Pop, E. & Reed, E. J. Theoretical potential for low energy consumption phase change memory utilizing electrostatically-induced structural phase transitions in 2D materials. npj Comput. Mater. 4, 2 (2018).",
      "journal-title": "npj Comput. Mater."
    },
    {
      "key": "947_CR36",
      "doi-asserted-by": "crossref",
      "first-page": "22",
      "DOI": "10.1038/s41928-017-0006-8",
      "volume": "1",
      "author": "MA Zidan",
      "year": "2018",
      "unstructured": "Zidan, M. A., Strachan, J. P. & Lu, W. D. The future of electronics based on memristive systems. Nat. Electron. 1, 22\u201329 (2018).",
      "journal-title": "Nat. Electron."
    },
    {
      "key": "947_CR37",
      "doi-asserted-by": "crossref",
      "first-page": "186401",
      "DOI": "10.1103/PhysRevLett.123.186401",
      "volume": "123",
      "author": "Z Wang",
      "year": "2019",
      "unstructured": "Wang, Z., Wieder, B. J., Li, J., Yan, B. & Bernevig, B. A. Higher-order topology, monopole nodal lines, and the origin of large Fermi arcs in transition metal dichalcogenides XTe2 (X = Mo, W). Phys. Rev. Lett. 123, 186401 (2019).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR38",
      "doi-asserted-by": "crossref",
      "first-page": "026801",
      "DOI": "10.1103/PhysRevLett.120.026801",
      "volume": "120",
      "author": "M Ezawa",
      "year": "2018",
      "unstructured": "Ezawa, M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Phys. Rev. Lett. 120, 026801 (2018).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR39",
      "doi-asserted-by": "crossref",
      "first-page": "216803",
      "DOI": "10.1103/PhysRevLett.123.216803",
      "volume": "123",
      "author": "MJ Park",
      "year": "2019",
      "unstructured": "Park, M. J., Kim, Y., Cho, G. Y. & Lee, S. Higher-order topological insulator in twisted bilayer graphene. Phys. Rev. Lett. 123, 216803 (2019).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR40",
      "doi-asserted-by": "crossref",
      "first-page": "3865",
      "DOI": "10.1103/PhysRevLett.77.3865",
      "volume": "77",
      "author": "JP Perdew",
      "year": "1996",
      "unstructured": "Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865\u20133868 (1996).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "947_CR41",
      "doi-asserted-by": "crossref",
      "first-page": "11169",
      "DOI": "10.1103/PhysRevB.54.11169",
      "volume": "54",
      "author": "G Kresse",
      "year": "1996",
      "unstructured": "Kresse, G. & Furthm\u00fcller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169\u201311186 (1996).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "947_CR42",
      "doi-asserted-by": "crossref",
      "first-page": "022201",
      "DOI": "10.1088/0953-8984/22/2/022201",
      "volume": "22",
      "author": "J Klime\u0161",
      "year": "2010",
      "unstructured": "Klime\u0161, J., Bowler, D. R. & Michaelides, A. Chemical accuracy for the van der Waals density functional. J. Phys. Condens. Matter 22, 022201 (2010).",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "947_CR43",
      "doi-asserted-by": "crossref",
      "first-page": "245112",
      "DOI": "10.1103/PhysRevB.78.245112",
      "volume": "78",
      "author": "X Qian",
      "year": "2008",
      "unstructured": "Qian, X. et al. Quasiatomic orbitals for ab initio tight-binding analysis. Phys. Rev. B 78, 245112 (2008).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "947_CR44",
      "doi-asserted-by": "crossref",
      "first-page": "1419",
      "DOI": "10.1103/RevModPhys.84.1419",
      "volume": "84",
      "author": "N Marzari",
      "year": "2012",
      "unstructured": "Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419\u20131475 (2012).",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "947_CR45",
      "doi-asserted-by": "crossref",
      "first-page": "224106",
      "DOI": "10.1063/1.2404663",
      "volume": "125",
      "author": "AV Krukau",
      "year": "2006",
      "unstructured": "Krukau, A. V., Vydrov, O. A., Izmaylov, A. F. & Scuseria, G. E. Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 125, 224106 (2006).",
      "journal-title": "J. Chem. Phys."
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