Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3
The band structures and density of states (DOS) of all the three structural configurations of CsPbBr 3 without spin–orbit coupling (SOC = 0) and with the addition of spin–orbit coupling (SOC ≠ 0) effects were calculated, using density functional theory. Upon the inclusion of the spin–orbit coupling,...
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| Veröffentlicht in: | Journal of materials science 2021, Vol.56 (1), p.528-542 |
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| creator | Hussain, Mujtaba Rashid, Muhammad Saeed, Faisal Bhatti, A. S. |
| description | The band structures and density of states (DOS) of all the three structural configurations of CsPbBr
3
without spin–orbit coupling (SOC = 0) and with the addition of spin–orbit coupling (SOC ≠ 0) effects were calculated, using density functional theory. Upon the inclusion of the spin–orbit coupling, the bandgaps exhibit reductions of 1.27 eV, 1.16 eV and 1.08 eV for the cubic, tetragonal and orthorhombic phases, respectively. These calculations provide a positive split-off energy value of Δ
so
= 1.69 eV for the simple cubic phase. For the lower symmetry phases, the
p
-like fourfold degenerate
Γ
8
v
(
4
)
band has been observed to split to form two bands, in addition to the
Γ
6
v
(
2
)
split-off band. The calculated splitting energies between these bands are found to be in close agreement with previous experimentally measured values. The calculated electronic band structures show that CsPbBr
3
has a negative ‘inversion energy’ (Δ
i
|
| doi_str_mv | 10.1007/s10853-020-05298-8 |
| format | Article |
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3
without spin–orbit coupling (SOC = 0) and with the addition of spin–orbit coupling (SOC ≠ 0) effects were calculated, using density functional theory. Upon the inclusion of the spin–orbit coupling, the bandgaps exhibit reductions of 1.27 eV, 1.16 eV and 1.08 eV for the cubic, tetragonal and orthorhombic phases, respectively. These calculations provide a positive split-off energy value of Δ
so
= 1.69 eV for the simple cubic phase. For the lower symmetry phases, the
p
-like fourfold degenerate
Γ
8
v
(
4
)
band has been observed to split to form two bands, in addition to the
Γ
6
v
(
2
)
split-off band. The calculated splitting energies between these bands are found to be in close agreement with previous experimentally measured values. The calculated electronic band structures show that CsPbBr
3
has a negative ‘inversion energy’ (Δ
i
< 0). The magnitude of the inversion energy for the cubic phase is 2.36 eV for SOC = 0, which increased by 0.4–2.76 eV with the addition of the spin–orbit coupling. The arrangement of Bloch levels in the band structure of CsPbBr
3
has been found to resemble that of a typical topological semimetal, but with a nonzero bandgap opening, due to the presence of the inversion asymmetry within its molecular structure.</description><identifier>ISSN: 0022-2461</identifier><identifier>EISSN: 1573-4803</identifier><identifier>DOI: 10.1007/s10853-020-05298-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Asymmetry ; Band structure of solids ; Characterization and Evaluation of Materials ; Chemistry and Materials Science ; Classical Mechanics ; Computation & Theory ; Coupling (molecular) ; Crystallography and Scattering Methods ; Density functional theory ; Density of states ; Energy gap ; Energy levels ; Energy value ; Materials Science ; Mathematical analysis ; Molecular structure ; Polymer Sciences ; Solid Mechanics ; Spin-orbit interactions ; Splitting</subject><ispartof>Journal of materials science, 2021, Vol.56 (1), p.528-542</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-cbd4727eb8012218f11932867dc8aa06fcaeda1cb032ed9148e0e6663d5c76463</citedby><cites>FETCH-LOGICAL-c319t-cbd4727eb8012218f11932867dc8aa06fcaeda1cb032ed9148e0e6663d5c76463</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10853-020-05298-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10853-020-05298-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Hussain, Mujtaba</creatorcontrib><creatorcontrib>Rashid, Muhammad</creatorcontrib><creatorcontrib>Saeed, Faisal</creatorcontrib><creatorcontrib>Bhatti, A. S.</creatorcontrib><title>Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3</title><title>Journal of materials science</title><addtitle>J Mater Sci</addtitle><description>The band structures and density of states (DOS) of all the three structural configurations of CsPbBr
3
without spin–orbit coupling (SOC = 0) and with the addition of spin–orbit coupling (SOC ≠ 0) effects were calculated, using density functional theory. Upon the inclusion of the spin–orbit coupling, the bandgaps exhibit reductions of 1.27 eV, 1.16 eV and 1.08 eV for the cubic, tetragonal and orthorhombic phases, respectively. These calculations provide a positive split-off energy value of Δ
so
= 1.69 eV for the simple cubic phase. For the lower symmetry phases, the
p
-like fourfold degenerate
Γ
8
v
(
4
)
band has been observed to split to form two bands, in addition to the
Γ
6
v
(
2
)
split-off band. The calculated splitting energies between these bands are found to be in close agreement with previous experimentally measured values. The calculated electronic band structures show that CsPbBr
3
has a negative ‘inversion energy’ (Δ
i
< 0). The magnitude of the inversion energy for the cubic phase is 2.36 eV for SOC = 0, which increased by 0.4–2.76 eV with the addition of the spin–orbit coupling. The arrangement of Bloch levels in the band structure of CsPbBr
3
has been found to resemble that of a typical topological semimetal, but with a nonzero bandgap opening, due to the presence of the inversion asymmetry within its molecular structure.</description><subject>Asymmetry</subject><subject>Band structure of solids</subject><subject>Characterization and Evaluation of Materials</subject><subject>Chemistry and Materials Science</subject><subject>Classical Mechanics</subject><subject>Computation & Theory</subject><subject>Coupling (molecular)</subject><subject>Crystallography and Scattering Methods</subject><subject>Density functional theory</subject><subject>Density of states</subject><subject>Energy gap</subject><subject>Energy levels</subject><subject>Energy value</subject><subject>Materials Science</subject><subject>Mathematical analysis</subject><subject>Molecular structure</subject><subject>Polymer Sciences</subject><subject>Solid Mechanics</subject><subject>Spin-orbit interactions</subject><subject>Splitting</subject><issn>0022-2461</issn><issn>1573-4803</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kM9KxDAQh4MouK6-gKeA5-okaZP0qIv_YEFBvRradLp0qWlN0oW9-Q6-oU9i1wrevMwc5vf9Bj5CThmcMwB1ERjoTCTAIYGM5zrRe2TGMiWSVIPYJzMAzhOeSnZIjkJYA0CmOJuR16e-cV8fn50vm0htN_Rt41YU6xptpJ2j6NCvtrTFDbY0jNcYd4HCVbTcjRD9YOPgkTZugz40I9M4ugiP5ZUXx-SgLtqAJ797Tl5urp8Xd8ny4fZ-cblMrGB5TGxZpYorLDUwzpmuGcsF11JVVhcFyNoWWBXMliA4VjlLNQJKKUWVWSVTKebkbOrtffc-YIhm3Q3ejS8NTxVTqWCjnznhU8r6LgSPtel981b4rWFgdh7N5NGMHs2PR6NHSExQGMNuhf6v-h_qG9iHdwk</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Hussain, Mujtaba</creator><creator>Rashid, Muhammad</creator><creator>Saeed, Faisal</creator><creator>Bhatti, A. S.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>KB.</scope><scope>L6V</scope><scope>M7S</scope><scope>PDBOC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>2021</creationdate><title>Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3</title><author>Hussain, Mujtaba ; Rashid, Muhammad ; Saeed, Faisal ; Bhatti, A. S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-cbd4727eb8012218f11932867dc8aa06fcaeda1cb032ed9148e0e6663d5c76463</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Asymmetry</topic><topic>Band structure of solids</topic><topic>Characterization and Evaluation of Materials</topic><topic>Chemistry and Materials Science</topic><topic>Classical Mechanics</topic><topic>Computation & Theory</topic><topic>Coupling (molecular)</topic><topic>Crystallography and Scattering Methods</topic><topic>Density functional theory</topic><topic>Density of states</topic><topic>Energy gap</topic><topic>Energy levels</topic><topic>Energy value</topic><topic>Materials Science</topic><topic>Mathematical analysis</topic><topic>Molecular structure</topic><topic>Polymer Sciences</topic><topic>Solid Mechanics</topic><topic>Spin-orbit interactions</topic><topic>Splitting</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hussain, Mujtaba</creatorcontrib><creatorcontrib>Rashid, Muhammad</creatorcontrib><creatorcontrib>Saeed, Faisal</creatorcontrib><creatorcontrib>Bhatti, A. S.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Materials Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Journal of materials science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hussain, Mujtaba</au><au>Rashid, Muhammad</au><au>Saeed, Faisal</au><au>Bhatti, A. S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3</atitle><jtitle>Journal of materials science</jtitle><stitle>J Mater Sci</stitle><date>2021</date><risdate>2021</risdate><volume>56</volume><issue>1</issue><spage>528</spage><epage>542</epage><pages>528-542</pages><issn>0022-2461</issn><eissn>1573-4803</eissn><abstract>The band structures and density of states (DOS) of all the three structural configurations of CsPbBr
3
without spin–orbit coupling (SOC = 0) and with the addition of spin–orbit coupling (SOC ≠ 0) effects were calculated, using density functional theory. Upon the inclusion of the spin–orbit coupling, the bandgaps exhibit reductions of 1.27 eV, 1.16 eV and 1.08 eV for the cubic, tetragonal and orthorhombic phases, respectively. These calculations provide a positive split-off energy value of Δ
so
= 1.69 eV for the simple cubic phase. For the lower symmetry phases, the
p
-like fourfold degenerate
Γ
8
v
(
4
)
band has been observed to split to form two bands, in addition to the
Γ
6
v
(
2
)
split-off band. The calculated splitting energies between these bands are found to be in close agreement with previous experimentally measured values. The calculated electronic band structures show that CsPbBr
3
has a negative ‘inversion energy’ (Δ
i
< 0). The magnitude of the inversion energy for the cubic phase is 2.36 eV for SOC = 0, which increased by 0.4–2.76 eV with the addition of the spin–orbit coupling. The arrangement of Bloch levels in the band structure of CsPbBr
3
has been found to resemble that of a typical topological semimetal, but with a nonzero bandgap opening, due to the presence of the inversion asymmetry within its molecular structure.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10853-020-05298-8</doi><tpages>15</tpages></addata></record> |
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| subjects | Asymmetry Band structure of solids Characterization and Evaluation of Materials Chemistry and Materials Science Classical Mechanics Computation & Theory Coupling (molecular) Crystallography and Scattering Methods Density functional theory Density of states Energy gap Energy levels Energy value Materials Science Mathematical analysis Molecular structure Polymer Sciences Solid Mechanics Spin-orbit interactions Splitting |
| title | Spin–orbit coupling effect on energy level splitting and band structure inversion in CsPbBr3 |
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