mikhail kiselev ginzburg-landau glimpse on...
TRANSCRIPT
Mikhail Kiselev
Ginzburg-Landau glimpse on coexistingmagnetic/superconducting phases of
unconventional superconductors
Kourovka - XXXVII, February 28, 2018
Outline
• unconventional superconductors: phase diagram and coexisting phases
• Landau theory 1: SDW vs SC
• Landau theory 2: effects of disorder
• Landau theory 3: nematic phase
• Landau theory 4: topological superconductivity
• Landau theory 5: stripes vs checkerboard
• from Landau theory to Ginzburg - Landau theory
• open questions and perspectives
CrystalstructureofIron-basedsuperconductors
11 111 122 1111
AfterPaglione,Greene,Nature
CrystalStructure:TetragonalI4/mmm
Fe,Ni
As,PLa,Sm,Ce
O• 2D square lattice of Fe• Fe - magnetic moment • As-similar then O in cuprates
But As not in plane!
Fe
As
Cuprates vs pnictidesafter Chubukov and Basov, Nature Physics(2010)
Mott insulator/Heisenberg AFM
metal
para-magneticmetal
magnetictransition(collinearAForder)
structuraltransition(tetragonal-orthorhomic)
Ba(Fe1-xCox)2As2
Measuredphasediagram
S.Nandietal,PRL(2010)
Ba1-xKxFe2As2
magnetictransition(collinearAForder)
para-magneticmetal
Wen,Li,Annu.Rev.Condens.MatterPhys.(2011)
phasediagramtakenfromμSR
H.Luetkenssetal,Nat.Matt.8,305(2009)
para-magneticmetal
LaO1-xFxFeAs
magnetictransition(collinearAForder)
structuraltransition(tetragonal-orthorhomic)
Phasediagram
NdFeAs(O1-xFx) (x=0.1)A. Kaminski et al.
Hole pockets near (0,0) Electron pockets near (p,p)
dHVaARPES
LaFeOPA. Coldea et al,
Ba06K04Fe2As2H. Ding et al.
A. Kordyuk et alLiFeAs
Itinerantpicture:LDAelectronicstructure(LaFeAsO)
Fe2+ 3d6-states
S.Lebegue,PRB75,035110(2007);D.J.Singhand M.-H.Du,PRL100,237003(2008);I.I.Mazin etal.,PRL101,057003(2008)
Weak CEF splitting: all 5 orbitals (dx2-y2, d3z2-r2, dxy, dxz+dyz) are near the Fermi level
1. Both electron and hole pockets do exist (quantum oscillations, ARPES)
2. There is a Fermi surface even at zero doping (ARPES)
h
eΓ
M
A.A.Kordyuk,LowTemp.Phys.(2012)
Proposedmultibandpairinggapsymmetries
AfterPaglione,Greene(2010)
Optimaldoping
Landau theory
cT T>cT T<
[ ] 2 3 40 1 2 3 4 ...j j j j jF =F +F +F +F +F +
1 0F = 3 0F =
2 ( )ca T TF = -
4 0constF = >
Landautheoryof2ndorderphasetransitions
0D ¹
M
0M ¹
DMagnets Superconductors
Vorontsov-Vavilov-Chubukov theory
A)PureSCstate
B)PureSDWstate
C)MixedSC+SDWstate
Vorontsov,Vavilov,Chubukov PRB2010
Vorontsov-Vavilov-Chubukov theory
Vorontsov,Vavilov,Chubukov PRB2010
Universalsuppressionofmagneticorder
Ph.Materne etal,PRB2015
Ca1�x
Nax
Fe2As2
Universalsuppressionofmagneticorder
Ph.Materne etal,PRB2015
Universalsuppressionofmagneticorder
Ph.Materne etal,PRB2015
Hoyer-Syzranov-Schmalian theoryRoleofdisorder
nocoexistence,1stordertransition coexistencepossible,2ndordertransition
Hoyer,Syzranov,Schmalian,PRB2014
g =�
pumus
� 1<latexit sha1_base64="9+k4jm7xORsgAaNeHgkdJ2MAsZw=">AAACCXicbVBNS8NAEN34WetX1KOX1SJ4sSQiqAeh6MVjBWMLTQib7aZduruJuxuhhJy9+Fe8eFDx6j/w5r9x2+agrQ8GHu/NMDMvShlV2nG+rbn5hcWl5cpKdXVtfWPT3tq+U0kmMfFwwhLZjpAijAriaaoZaaeSIB4x0ooGVyO/9UCkoom41cOUBBz1BI0pRtpIob3Xu/BjiXDu9xDnqMh9dS91noUcZqEqiiM3tGtO3RkDzhK3JDVQohnaX343wRknQmOGlOq4TqqDHElNMSNF1c8USREeoB7pGCoQJyrIx68U8MAoXRgn0pTQcKz+nsgRV2rII9PJke6raW8k/ud1Mh2fBTkVaaaJwJNFccagTuAoF9ilkmDNhoYgLKm5FeI+Mslok17VhOBOvzxLvOP6ed25Oak1Lss0KmAX7IND4IJT0ADXoAk8gMEjeAav4M16sl6sd+tj0jpnlTM74A+szx9LoJrX</latexit><latexit sha1_base64="9+k4jm7xORsgAaNeHgkdJ2MAsZw=">AAACCXicbVBNS8NAEN34WetX1KOX1SJ4sSQiqAeh6MVjBWMLTQib7aZduruJuxuhhJy9+Fe8eFDx6j/w5r9x2+agrQ8GHu/NMDMvShlV2nG+rbn5hcWl5cpKdXVtfWPT3tq+U0kmMfFwwhLZjpAijAriaaoZaaeSIB4x0ooGVyO/9UCkoom41cOUBBz1BI0pRtpIob3Xu/BjiXDu9xDnqMh9dS91noUcZqEqiiM3tGtO3RkDzhK3JDVQohnaX343wRknQmOGlOq4TqqDHElNMSNF1c8USREeoB7pGCoQJyrIx68U8MAoXRgn0pTQcKz+nsgRV2rII9PJke6raW8k/ud1Mh2fBTkVaaaJwJNFccagTuAoF9ilkmDNhoYgLKm5FeI+Mslok17VhOBOvzxLvOP6ed25Oak1Lss0KmAX7IND4IJT0ADXoAk8gMEjeAav4M16sl6sd+tj0jpnlTM74A+szx9LoJrX</latexit><latexit sha1_base64="9+k4jm7xORsgAaNeHgkdJ2MAsZw=">AAACCXicbVBNS8NAEN34WetX1KOX1SJ4sSQiqAeh6MVjBWMLTQib7aZduruJuxuhhJy9+Fe8eFDx6j/w5r9x2+agrQ8GHu/NMDMvShlV2nG+rbn5hcWl5cpKdXVtfWPT3tq+U0kmMfFwwhLZjpAijAriaaoZaaeSIB4x0ooGVyO/9UCkoom41cOUBBz1BI0pRtpIob3Xu/BjiXDu9xDnqMh9dS91noUcZqEqiiM3tGtO3RkDzhK3JDVQohnaX343wRknQmOGlOq4TqqDHElNMSNF1c8USREeoB7pGCoQJyrIx68U8MAoXRgn0pTQcKz+nsgRV2rII9PJke6raW8k/ud1Mh2fBTkVaaaJwJNFccagTuAoF9ilkmDNhoYgLKm5FeI+Mslok17VhOBOvzxLvOP6ed25Oak1Lss0KmAX7IND4IJT0ADXoAk8gMEjeAav4M16sl6sd+tj0jpnlTM74A+szx9LoJrX</latexit>
Hoyer-Syzranov-Schmalian theoryRoleofdisorder
nocoexistenceofSDWandSC
coexistenceofSDWandSCispossible
Hoyer,Syzranov,Schmalian,PRB2014
Interplaybetweentetragonalmagneticorder,stripemagnetismandsuperconductivity
Kang,Wang,Chubukov,Fernandes,PRB2015
C_2orthorhombicC_4tetragonal ~M2
1 = ~M22
~M1 = 0, or ~M2 = 0
Chubukov,Fernandes,Schmalian PRB2015
Nematic orderinFeSe
Nematic orderinFeSe
Chubukov,Fernandes,Schmalian PRB2015
FepnictidesFeSe
Nematic orderinpnictides
Fernandes,Chubukov,Schmalian NaturePhysics2014
Nematic orderinpnictides
Fernandes,Chubukov,Schmalian NaturePhysics2014
Nematic orderinpnictides
Fernandes,Chubukov,Schmalian NaturePhysics2014
Nematic orderinpnictides
Fernandes,Chubukov,Schmalian NaturePhysics2014
Nematic orderinpnictides
Fernandes,Chubukov,Schmalian NaturePhysics2014
HowmanyQPC?
Fernandes,Maiti,Woelfle,Chubukov PRL2013
TopologicalSCandunconventionalpairing
Scheurer,Schmalian NatureCommunications2014
TopologicalSCandunconventionalpairing:scatteringprocesses
TopologicalSCandunconventionalpairing:RG
Scheurer,Schmalian NatureCommunications2014
TopologicalSCandunconventionalpairing
Scheurer,Schmalian NatureCommunications2014
TopologicalSCandunconventionalpairing
Scheurer,Schmalian NatureCommunications2014
�f =X
V sc↵��0↵0(k,p)hc�p�0cp↵0i
�c =X
V sc↵��0↵0(k,p)hf�p�0fp↵0i
m↵0,�0 =X
V sdw↵��0↵0hf†
p0↵cp�i
How many components does the order parameter have?
S++
⇡T↵0,�0 =
XV ⇡↵��0↵0hf†
�k�q↵c†k�i S+�
Karki,Mandal,Kiselev 2015
Kopaev JETP1971
Aronov,Sonin JETP1973
Karki,Mandal,Kiselev 2015
Landau theory: triplet component includedF (�,m,⇡T ) = ↵�|�|2 + ↵mM2 + ↵⇡(⇡
T )2 +A|�|4 +BM4 + C(⇡T )4+
2D1|�|2M2 + 2D2|�|2(⇡T )2 + 2D3M2(⇡T )2
|�|2 = �↵�(BC �D23) + ↵m(D2D3 � CD1) + ↵⇡(D1D3 �BD2)
2(ABC + 2D1D2D3 �BD22 �AD2
3 � CD21)
M2 = �↵�(D2D3 � CD1) + ↵m(AC �D22) + ↵⇡(D1D2 �AD3)
2(ABC + 2D1D2D3 �BD22 �AD2
3 � CD21)
@F
@�⇤ = 0,@F
@M= 0,
@F
@(⇡T )⇤= 0.
(⇡T )2 = �↵�(D1D3 �BD2) + ↵m(D1D2 �AD3) + ↵⇡(AB �D21)
2(ABC + 2D1D2D3 �BD22 �AD2
3 � CD21)
Universalsuppressionofmagneticorder
Ph.Materne etal,PRB2015
Ca1�x
Nax
Fe2As2
Ginzburg- Landau theory
FromLandautoGinzburg - Landautheory
F = FN +
Zd~r
1
2ms|(r� 2ie
cA) |2 + ↵| |2 + �
2| |4 + |B|2
8⇡
�
@(F � FN )
@ ⇤ = 0 1st GL equation
@(F � FN )
@ ~A= 0 2nd GL equation
Ginzburg - Landautheoryinexternalmagneticfield
FO � FN = FM + FL + Fs + FB
FM =
Zd~r
am2
M2 +bm4M4 + �µBM ·B
�
FL =
Zd~r
al2L2 +
bl4L4 + cl(rL)2
�
Fs =
Zd~r
as2| |2 + bs
4| |4 + cs|(r� 2ie
cA) |2
�
Fmix
=
Zd~r
⇥↵1
L2| |2 + ↵2
L2M2 + ↵3
M2| |2⇤
FB =
Zd~r
B2
8⇡ Karki,Mandal,Kiselev 2015
GLequationsandsupercurrent
@(F � FN )
@ ⇤ = 0 1st GL equation
@(F � FN )
@ ~A= 0 2nd GL equation
@(F � FN )
@~L= 0 3rd GL equation
Karki,Mandal,Kiselev 2015
Openquestionsandperspectives
• spintexturesinthevortexcore
• influenceofmagneticimpuritiesonTc andTn
• influenceofresonanceimpuritiesTc andTn
• supercurrent incoexistentphase
• influenceofpi-tripletphaseonmagneticmomentsuppression
• coexistentphasesinexternalmagneticfield
• influenceofpi-tripletonnematic phase
• magnetizationdynamicsinthepresenceofstrongsuperconductingfluctuations
• etc
Coupledmultiple-modetheoryfors± pairing
mechanisminiron-basedsuperconductors
MIKHAIL KISELEV (ICTP,Trieste)IN COLLABORATION WITH:
DMITRY EFREMOV (IFWDresden)JEROEN VAN DEN BRINK (IFWDRESDEN)
STEFAN-LUDWIG DRECHSLER (IFWDRESDEN)KONSTANTIN KIKOIN
MK,D.V.Efremov,S.L.Drechsler,Jeroen vandenBrinkandK.Kikoin.Sci.Rep.6,37508(2016)
G
Nesting vector responsible for SDW correlations betweentwo pockets of FS
S+ - pairing: two nodeless gaps with opposite sign due to phase difference. These gaps see each other via repulsiveSDW-mediated interaction [χ (ω) with q ~ G]q
SC pairing mechanism
(Aronov, Sonin '72; Mazin et al '08; Kuroku et al '08)
EF
43
G
EF
Competingmodes:twobandmodel
SCchannel
SDWchannel
Competingmodes
IntheregionIandIII
= +
+Гsdw
= +Г = u + uПГ
Bosonicmodes.here we consider the two-band model with 6 vertices..
Bethe – Salpeter equation for the anomalous vertex Г3
=Г3
+ +..
.
u3
u3 Couplingofthemagnetic
Fluctuationsandthesuperconductingmodes
Ginzburg-Landaufunctional
Staticlimit See,Vavilov andChubukovSchmalian etal….
ThemagneticfluctuatingmodeiscoupledtoΔ±superconductingmode
ℒ(() = ∫ 𝑑𝑥 Δ./𝐿±/1Δ/ + 𝑚𝐷5/1𝑚 + 1(𝐴 Δ/ 7 + 𝐵𝑚7 + (𝐶1 − 𝐶() Δ/ (𝑚(
𝐿±/1=1
𝑢= + 𝑢>− Π= 𝑞, 𝑖ΩD, 𝑇 → 𝜈(−
𝑖Ω𝛾IJ
+ 𝜏= + 𝑐=𝑞()
𝐷5/1 =1
𝑢1 + 𝑢>− Π1 𝑞, 𝑖ΩD, 𝑇 → 𝜈(−
𝑖Ω𝛾IMN
+ 𝜏IMN + 𝑐IMN𝑞()
Vavilov andChubukov ,2011
ThemagneticfluctuatingmodeiscoupledtoΔ±superconductingmode
ℒ(() = ∫ 𝑑𝑥 Δ./𝐿±/1Δ/ + 𝑚𝐷5/1𝑚 + 1(𝐴 Δ/ 7 + 𝐵𝑚7 + (𝐶1 − 𝐶() Δ/ (𝑚(
A=Δ/ Δ/
Δ/ Δ/
~m ~m
~m ~m
B=+(𝑒 ↔ ℎ)
C1=mm
Δ/ Δ/+(𝑒 ↔ ℎ) +(𝑒 ↔ ℎ)C1=
mm
Δ/
Δ/
See,Vavilov andChubukovSchmalian etal….
FluctuationcorrectiontoTC.• Tocalculatethecorrectiontothecriticaltemperatureconsider:
where
ℒ(() = ∫ 𝑑𝑥Δ./𝐿±STT/1 Δ/ + 𝐴U Δ/ 7
𝑇V = 𝑇VW 1 − 𝜈/1(|𝐾1| − |𝐾(|)
𝐿Z±STT/1 → 𝐿±/1 + 𝐾1 + 𝐾(
Δ/ Δ/𝐾1 =
Δ/ Δ/𝐾( =
+(𝑒 ↔ ℎ)
+(𝑒 ↔ ℎ)Itleadstothecorrectionsto𝑇V
Here𝐾1 > 0, while𝐾( < 0
FluctuationcorrectiontoTS.• Tocalculatethecorrectiontothecriticaltemperatureconsider:
where
ℒ5STT(() = ∫ 𝑑𝑥𝑚�̂�5/1𝑚 + 𝐵 𝑚 7
𝑇= = 𝑇=W 1 − 𝜈(�̂�1 + �̂�()
𝐿Z5/1 → 𝐿5/1 + �̂�1 + �̂�(
�̂�1 =
�̂�( =
+(𝑒 ↔ ℎ)
+(𝑒 ↔ ℎ)~m ~m
~m ~m
Itleadstothecorrectionsto𝑇=
Here�̂�1 > 0, while�̂�( < 0
ThemagneticfluctuatingmodeiscoupledtotwosuperconductingmodeΔ_ andΔS
• ℒ` = ∫ 𝑑𝑥 Δ.SΔ._𝐿S/1 𝐾(𝐾( 𝐿_/1
ΔaΔb
+𝐴c |Δa|7 + Δ_ 7
• ℒ5 = ∫ 𝑑𝑥 𝑚𝐷5/1𝑚 + 𝐵𝑚7
• ℒdDe = ∫ 𝑑𝑥 𝐶1 |ΔS |( + |Δ_ |( 𝑚( + 𝐶( Δ.SΔb + Δ._ΔS 𝑚(
Magneticfluctuationsfirstbreak𝑈 1 ×𝑈 1 → 𝑈(1)
FluctuationcorrectionstoTC andTS.
• Tocalculatethecorrectiontothecriticaltemperatureconsider:
where
𝑇V = 𝑇VW 1 − 𝜈(𝐾1 + 𝐾()
ℒ` = ∫ 𝑑𝑥 Δ.SΔ._𝐿S/1 𝐾(𝐾( 𝐿_/1
ΔaΔb
+𝐴c |Δa h7+ Δ_ 7
�e �̄e𝐾1 =
�e �̄h𝐾( =Here𝐾1 > 0, while𝐾( < 0
Correctionsto𝑇VaresimilartotheΔ/𝑐𝑎𝑠𝑒
+(𝑒 ↔ ℎ)
+(𝑒 ↔ ℎ)
FluctuationcorrectionstoTS.
• Tocalculatethecorrectiontothecriticaltemperatureconsider:
where
ℒ5STT(() = ∫ 𝑑𝑥𝑚�̂�5/1𝑚 + 𝐵 𝑚 7
𝑇= = 𝑇=W 1 − 𝜈(2�̂�1)
𝐿Z5/1 = 𝐿5/1 + 2�̂�1
�̂�1 = +(𝑒 ↔ ℎ)~m ~m
Itleadstothecorrectionsto𝑇=
Itisquitedifferentfromthecaseofinteractionofthemagneticfluctuatingmodewithsinglesuperconductingmode
Forparticle-holesymmetry
𝑇V − 𝑇= = 𝑇W𝜈/1( 𝐾1 + |𝐾(|)
Estimateoftheintegrals
• InOrnstein–Zernikeapproximation:𝐿S 𝑞, 𝜔, 𝑇 ∼ 1
VnopqD=3
rs/rtru
∼ 𝜈/1𝐾1,( ∼1
vruwtx∼ 𝐺𝑖 >� ∼ ru
{|
(
D=2->logdivergencers/rtru
∼ 𝜈/1𝐾1,( ∼1
vruwolog Vw
�o
qs∼ 𝐺𝑖 ( ln𝐺𝑖(() ∼ ru
{|log {|
ru
Taking𝐺𝑖(() = 0.1 oneobtainsrs/rtru
∼ 0.25
SDW
SCtempe
rature
concentration
Summary
MK,D.V.Efremov,S.L.Drechsler,Jeroen vandenBrinkandK.Kikoin.Sci.Rep.6,37508(2016)
Take home message
Conclusions
• Interactionofthemagneticfluctuatingmodewithasinglesuperconductingmodechangesthetetracritical pointinthesecondorderofperturbationtheorynegligibly
• Interactionofthemagneticfluctuatingmodewithtwosuperconductingmodeschangesthetetracritical pointconsiderably,suppressingthe𝑇=.
Thankyou!