2P117
෼ࢠ಺෦ͷ༗ޮి৔ͱిࢠͷి‫ؾ‬૒‫ࢠۃ‬Ϟʔϝϯτʹ‫ى‬Ҽ͢ΔεϐϯτϧΫ
ʢ‫ژ‬େӃɾ޻ʣ ીզ ߁ଠɺ෱ా কେɺ੉೾ େ౔ɺཱՖ ໌஌
Effective electric field and spin torque induced by electron electric dipole moment in molecules
(Kyoto Univ.) Kota Soga, Masahiro Fukuda, Masato Senami, Akitomo Tachibana
ʲংʳిࢠͷӬ‫ؾిٱ‬૒‫ࢠۃ‬Ϟʔϝϯτ (Electric Dipole Moment, EDM) ͸ɺͦͷεϐϯʹ෇ਵ͢Δిՙ෼
෍ͷภΓΛද͢ϕΫτϧྔͰ͋Δɻ‫ؒ࣌ʹܥ‬൓స (T) ม‫׵‬Λࢪͯ͠΋ిՙ෼෍͸ෆมʢ͢ͳΘͪɺEDM
΋ෆมʣͰ͋ΔҰํɺεϐϯ͸ͦͷ޲͖Λม͑Δɻ͕ͨͬͯ͠ɺnon-zero ͷ EDM ͕ଘࡏ͢Ε͹ T ରশੑ
͸ഁΕΔɻT ରশੑͷഁΕΛࣔ͢‫ݱ‬৅͸ɺ࣌ؒͷෆՄ‫ٯ‬ੑ΍Ӊ஦ʹ͓͚Δ෺࣭ɾ൓෺࣭ͷඇରশੑΛཧ
ղ͢Δ্Ͱॏཁͳ‫ͳͱݤ‬ΔͨΊɺEDM ͷ୳ࠪΛ‫ؚ‬Ίɺ͜Ε·Ͱʹ‫؍‬ଌͷࢼΈ͕਺ଟ͘ߦΘΕ͖ͯͨ΋ͷ
ͷɺ௚઀ͷ‫؍‬ଌʹ͸ࢸ͍ͬͯͳ͍ɻ
ૉཻࢠͷඪ४໛‫͕ܕ‬༧‫͢ݴ‬Δిࢠ EDM ͷ஋ (d e ) ͸ඇৗʹখ͘͞ɺ‫ࡏݱ‬ͷ‫؍‬ଌ‫ݶ‬քΛ௒͍͑ͯΔɻ͠
͔͠ɺ௒ରশ໛‫ܕ‬Λ͸͡Ίͱͨ͠ඪ४໛‫ʹܕ‬ର͢Δଟ͘ͷ֦ுཧ࿦Ͱ͸ɺ‫ࡏݱ‬ͷ࣮‫ݧ‬ਫ਼౓Ͱ‫؍‬ଌՄೳͳ
΄Ͳେ͖ͳ d e ͕༧‫͞ݴ‬Ε͍ͯΔɻඇৗʹߴਫ਼౓ͷ࣮‫ ࢠి͍͓͑ͯ͞ʹݧ‬EDM ͷଘࡏ͕‫؍‬ଌ͞Εͳ͍৔
߹ɺ֦ுཧ࿦͸࣍ʑʹഉআ͞Ε͍ͯ͘͜ͱʹͳΔ͕ɺ΋͠ EDM ͷଘࡏ͕‫ݕ‬ग़͞ΕΕ͹ඪ४໛‫ʹܕ‬ର͢Δ
৽ཧ࿦ͷඞཁੑ͕࣮‫ݧ‬తʹࣔ͞Εͨ͜ͱʹͳΔɻ͢ͳΘͪɺnon-zero ͷిࢠ EDM ͷଘࡏ͸ T ରশੑͷഁ
Εͷ௚઀తͳূ‫ͳͱڌ‬Δ͚ͩͰͳ͘ɺඪ४໛‫ܕ‬Λ௒͑ͨ৽͍͠෺ཧΛ୳ࡧ͢Δࢦ਑ʹ΋ͳΔɻ
ిࢠ EDM ͷ୳ࠪʹ͸ɺ෼ࢠ಺෦ͷ༗ޮి৔ͱͦΕʹґଘ͢Δిࢠεϐϯͷࡀࠩӡಈ͕த৺తͳ໾ׂ
ΛՌͨ͢ɻNon-zero ͷిࢠ EDM ͕ଘࡏ͢Δ͜ͱͰͲͷΑ͏ͳεϐϯτϧΫ͕ੜ͡Δ͔Λ໌Β͔ʹ͠ɺͦ
Εʹ൐͏ిࢠεϐϯͷμΠφϛΫεΛਖ਼֬ʹ༧ଌ͢Δ͜ͱ͸ɺEDM ‫ݕ‬ग़ͷͨΊʹෆՄܽͰ͋Δɻզʑͷ
‫ڀݚ‬άϧʔϓͰ͸ɺEDM ༗ޮి৔ͷ‫ʹࢉܭ‬Ճ͑ɺ৔ͷཧ࿦ʹ‫ͮ͘ج‬εϐϯμΠφϛΫεͷ‫ ڀݚ‬1 ΋ߦͬ
͍ͯΔɻຊ‫Ͱڀݚ‬͸ɺྔࢠిࢠεϐϯӔཧ࿦ 2−4 ʹΑͬͯಋ͔ΕΔ৔ͷཧ࿦ʹ‫ॴہͮ͘ج‬తͳిࢠεϐϯ
ͷӡಈํఔࣜʹɺEDM ͷଘࡏʹ‫ى‬Ҽ͢ΔεϐϯτϧΫ͕ՃΘΔ͜ͱΛࣔ͠ɺ࣌ࠁ t = 0 Ͱఆৗঢ়ଶʹ͋
Δ‫֎ʹܥ‬෦੩ి࣓৔ΛҹՃͨ͠ࡍʹ༠‫͞ى‬ΕΔ‫ॴہ‬෺ཧྔͷ෼෍Λௐ΂ͨɻ
ˆ
ʲཧ࿦ʳ৔ͷཧ࿦ʹ͓͍ͯɺిࢠεϐϯ sˆe (x) ͷ࣌ؒൃల͸εϐϯτϧΫ tˆe (x) ͱπΣʔλྗ ζe (x) ʹΑͬ
ͯࢧ഑͞ΕΔɻ
∂ ˆ
ˆ
s e (x) = tˆe (x) + ζe (x)
∂t
(1)
ͦΕͧΕͷ෺ཧྔ͸ిࢠ৔ ψ̂(x) ͱޫࢠ৔ Â μ (x) Λ༻͍ͯ࣍ͷΑ͏ʹఆٛ͞ΕΔɻ
†
ic
ŝ ei = ψ̂ † Σ i ψ̂, tˆei = −
ε i j k ψ̂ † γ 0 γ k ∂ j ψ̂ − ∂ j ψ̂ γ 0 γ k ψ̂ − (Ze e) ε i j k ψ̂ † γ 0 γ k  j ψ̂
2
2
μ
i
jˆ0, jˆ5 = Ze ecψ̄ˆ γ μ γ5 ψ̂, γ5 = iγ 0 γ 1 γ 2 γ 3, e = |e|, Ze = −1
ζˆe = −∂i φ̂5, φ̂5 =
2Ze e 5
(2)
(3)
, c, e ͸ͦΕͧΕϓϥϯΫఆ਺ɺਅۭதͰͷޫ଎ɺૉిՙͰ͋Γɺγ μ , Σ i ͸ͦΕͧΕΨϯϚߦྻɺ4 ࣍
Λ૬ର࿦Խ͢Δ
‫ݩ‬ύ΢ϦߦྻͰ͋Δɻ௿ΤωϧΪʔͰͷ༗ޮ EDM ϋϛϧτχΞϯ HEDM = −de · E
i ˆ
μν
͜ͱͰಘΒΕΔ૬ର࿦త༗ޮ EDM ϥάϥϯδΞϯ L̂ EDM (x) = −d e 2 ψ̄ (x)σ γ5 F̂μν (x) ψ̂(x) F̂μν (x) =
∂μ Âν (x) − ∂ν Â μ (x), σ μν = 2i [γ μ , γν ] Λ༻͍Δ͜ͱͰɺిࢠεϐϯͷӡಈํఔࣜ (1) ͷӈลʹ࣍ࣜͰ༩͑
ˆEDM (x) ͕ิਖ਼߲ͱͯ͠ՃΘΔɻ
ΒΕΔ EDM ͷଘࡏʹ‫ى‬Ҽ͢ΔεϐϯτϧΫ T
ˆ
ˆ ele
ˆ mag
TEDM (x) = TEDM
(x) + TEDM
(x)
(4)
ˆ ele
mag
ˆ ψ̂(x), TˆEDM
ˆ ψ̂(x)
× B(x)
TEDM
(x) = d e ψ̄ˆ (x)Σ × E(x)
(x) = d e i ψ̄ˆ (x)γ 0 γ
(5)
ˆ
ˆ
૬ର࿦Խʹ൐͍ɺి৔ E(x)
͚ͩͰͳ࣓͘৔ B(x)
ͱ΋૬‫͢༻࡞ޓ‬Δ͜ͱ͕Θ͔Δɻ
ຊൃදͰ͸ɺYbF, ThO, BaF ෼ࢠΛର৅ʹɺզʑͷ‫ڀݚ‬άϧʔϓ͕։ൃΛߦ͍ͬͯΔ QE Dynamics5 Λ
༻͍ͯߦͬͨ EDM ༗ޮి৔ɺ͓Αͼ‫ॴہ‬෺ཧྔͷ‫݁ࢉܭ‬ՌΛࣔ͢ɻ
M = (1, 0, 0) [a.u.] ΛҹՃͨ͠ͱ͖ͷ BaF ෼ࢠ
M = (1, 0, 0), B
ʲ݁Ռͱߟ࡯ʳ࣌ࠁ t = 0 ʹ֎෦੩ి࣓৔ E
ele
EDM
ɺ࣓৔ʹ‫ى‬Ҽ͢Δ EDM τϧΫີ౓
಺෦ͷεϐϯ֯ӡಈྔີ౓ s e ɺి৔ʹ‫ى‬Ҽ͢Δ EDM τϧΫີ౓ T
mag
ͷ෼෍ΛͦΕͧΕਤ 1-3 ࣔ͢ɻਤதͷ໼͕֤఺ʹ͓͚ΔϕΫτϧΛද͠ɺϊϧϜͷ஋Λͦͷ৭ʹΑͬ
TEDM
ͯ‫ࢠݪ‬୯ҐͰද‫͍ͯ͠ݱ‬Δɻ·ͨɺਤதͷ੺͍‫ ͕ٿ‬Ba ‫֩ࢠݪ‬Λɺ੨͍‫ ͕ٿ‬F ‫֩ࢠݪ‬Λද͍ͯ͠Δɻ
εϐϯ֯ӡಈྔີ౓͸‫͔֩ࢠݪ‬Β΍΍཭ΕͨҐஔʹภͬͯ෼෍͍ͯ͠Δ͜ͱ͕Θ͔Δɻి৔‫ى‬Ҽͷ EDM
τϧΫີ౓ͷ෼෍͸εϐϯ֯ӡಈྔີ౓ͷ෼෍ͱࣅ௨͍ͬͯΔ͕ɺ͜Ε͸ࣜ (5) ͔ΒཧղͰ͖Δɻ͢ͳΘͪɺ
x ࣠ํ޲ʹҰ༷ͳి৔ΛҹՃ͍ͯ͠ΔͨΊɺ1/c ͷ࣍਺·ͰΛऔΓѻ͏ඇ૬ର࿦‫ݶۃ‬ΛͱΕ͹ɺి৔‫ى‬Ҽͷ
EDM τϧΫີ౓ͷϊϧϜ͸εϐϯ֯ӡಈྔີ౓ͷϊϧϜʹൺྫ͍ͯ͠ΔɻҰํɺ࣓৔‫ى‬Ҽͷ EDM τϧΫ
ີ౓͸‫֩ࢠݪ‬ͷपғΛӔ‫͘ר‬Α͏ʹ෼෍͍ͯ͠Δ͜ͱ͕Θ͔Δɻࣜ (5) Λม‫͢ܗ‬Δ͜ͱʹΑΓɺ࣓৔‫ى‬Ҽͷ
EDM τϧΫີ౓ͷओཁ߲͸ిࢠີ౓ͷޯ഑ͱҹՃ࣓৔ͷ֎ੵͰॻ͚Δ͜ͱΛࣔͤΔɻిࢠີ౓ͷޯ഑͸
‫֩ࢠݪ‬Λத৺ʹ์ࣹঢ়ͷ෼෍Λ͍ͯ͠ΔͨΊɺҰ༷࣓৔ͱͷ֎ੵʹΑΓӔঢ়ͷ෼෍ʹͳͬͨͱཧղͰ͖Δɻ
෼෍ύλʔϯ͔ΒΘ͔ΔΑ͏ʹɺશۭؒʹ͓͚Δ‫ظ‬଴஋
ʹؔͯ͠͸ಉ͡ํ޲Λ޲͍͍ͯΔి৔‫ى‬ҼͷτϧΫͷํ
͕࣓৔‫ى‬ҼͷτϧΫΑΓ΋ͣͬͱେ͖͘ͳΔɻ͔͠͠ɺ‫ہ‬
ॴతͳྖҬʹ஫໨͢Δͱɺ֓ͯ͠‫͑ݴ‬͹࣓৔‫ى‬Ҽͷτϧ
Ϋͷํ͕ి৔‫ى‬ҼͷτϧΫΑΓ΋େ͖͍ޮՌΛ༩͑Δɻ
͜ͷΑ͏ʹɺ৔ͷཧ࿦ʹ‫ʹີݫͮ͘ج‬ఆٛ͞Εͨ‫ॴہ‬త
ͳ෺ཧྔΛऔΓѻ͏͜ͱʹΑΓɺશۭؒͰͷ‫ظ‬଴஋ͷΈ
ΛऔΓѻ͏ྔࢠྗֶͰ͸༧ଌͰ͖ͳ͍෺ཧతੑ࣭Λཧղ
͢Δ͜ͱ͕Ͱ͖Δɻ
εϐϯ֯ӡಈྔີ౓ s e ͸εϐϯτϧΫ t eɾπΣʔλྗ
mag
ele
+ TEDM
ʹ
ζe ɺͦͯ͜͜͠Ͱࣔͨ͠ EDM τϧΫີ౓ TEDM
ਤ 1 εϐϯ֯ӡಈྔີ౓ s e
Αͬͯ‫ۦ‬ಈ͞Εɺ࣌ؒͷ‫ܦ‬աͱͱ΋ʹࡀࠩӡಈΛߦ͏͜
ͱʹͳΔɻ
ele
ਤ 2 ి৔ʹ‫ى‬Ҽ͢Δ EDM τϧΫີ౓ T
EDM
ਤ 3 ࣓৔ʹ‫ى‬Ҽ͢Δ EDM τϧΫີ౓ T
EDM
mag
ʲࠓ‫ޙ‬ͷల๬ʳ্Ͱड़΂ͨεϐϯμΠφϛΫεͷ࿮૊Έ͸৔ͷཧ࿦ʹཱ‫ͨ͠٭‬΋ͷͰ͋ΓɺͦΕΏ͑‫ॴہ‬
తͳ৘ใ͕ࣦΘΕΔ͜ͱ͸ͳ͍ɻকདྷతͳ࣮‫ݧ‬ͷߴਫ਼౓ɾߴ෼ղೳԽʹ൐ͬͯɺશۭؒͰͷ‫ظ‬଴஋ͷΈΛ
‫ه‬ड़͢Δैདྷͷྔࢠྗֶతͳ‫ࢉܭ‬ख๏Ͱ͸༧ଌͰ͖ͳ͍ɺ‫ॴہ‬తͳޮՌ͕‫؍‬ଌ͞ΕΔ͜ͱ͕‫ظ‬଴͞ΕΔɻ
1. A. Tachibana, J. Mol. Model. 11, 301-311 (2005); J. Mol. Struct.: THEOCHEM 943, 138-151 (2010).
2. A. Tachibana, J. Math. Chem. 50, 669-688 (2012).
3. A. Tachibana, In Concepts and Methods in Modern Theoretical Chemistry,
S. K. Ghosh and P. K. Chattaraj Eds., CRC Press, Florida (2013), pp 235-251.
4. A. Tachibana, J. Comput. Chem. Jpn. 13, 18-31 (2014).
5. QEDynamics, M. Senami, K. Ichikawa, A. Tachibana,
http://www.tachibana.kues.kyoto-u.ac.jp/qed/index.html.