STM Study of Unconventional Superconductivity
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1 STM Study of Unconventional Superconductivity
2 1. Introduction to conventional superconductivity 2. Introduction to scanning tunneling microscopy (STM) 3. High Tc Superconductor : Cuprates 4. High T c Superconductor : Fe-based Compounds
3 FeSC Family X.H. Chen et al., National Science Review 1: (2014)
4 FeSC Family Glide plane : Good for STM/ARPES measurements X.H. Chen et al., National Science Review 1: (2014)
5 FeSC : Complex Band Structure SC layer with SDW ground state g a 1,2 b 1,2 F. Wang et al., Science 332, 200 (2011) P. J. Hirschfeld et al., Rep.Prog.Phys.74, (2011)
6 FeSC Phase Diagram FeSC D.N. Basov et al., NPhys 7, 272 (2011)
7 FeSC vs Cuprates : Phase Diagram Many common electronic characteristics! Both have antiferromagnetic parent states. Cuprates FeSC D.N. Basov et al., NPhys 7, 272 (2011)
8 FeSC Phase Diagram FeSC D.N. Basov et al., NPhys 7, 272 (2011)
9 Temperature Liquid Crystal Phases Liquid (Isotropic) Liquid crystal Nematic Smectic M. W. Davidson, FSU. Crystal F. Reinitzer, doi: /bf (1888)
10 Liquid Crystal Phases : Nematic Vs. Smectic Nematic LC breaks rotational symmetry only Smectic LC breaks rotational & translational symmetry
11 Strong Electron Correlation : Electronic Liquid Crystal Phases Temperature Liquid Liquid (Isotropic) (isotropic) Nematic Nematic Smectic Smectic (stripe) Crystal Crystal (insulating) F. Reinitzer, doi: /bf (1888) S. A. Kivelson et al., Nature 393, 550 (1998)
12 Electronic Liquid Crystal Phases in Cuprates Liquid (isotropic) Nematic J. Zaanen et al.,prb 40, 7391 (1989). S. A. Kivelson et al., Nature 393, 550 (1998). V. J. Emery et al., PNAS 96, 8814 (1999). S. R. White et al., PRL 91, (2003) S. Sachdev, RMP 75, 913 (2003). J. M Tranquada et al., Nature 429, 534 (2004) Smectic (stripe) Crystal (insulating) S. A. Kivelson et al., Nature 393, 550 (1998)
13 Electronic Nematicity in Underdoped Ca(Fe 0.97 Co 0.03 ) 2 As 2 Tien-Ming Chuang Topograph 1x2 reconstruction Milan Allan b 71nm Ca Fe or Co As (Top) As (Bottom) a T.-M. Chuang et al., Science 327, 181 (2010)
14 Electronic Nematicity in Underdoped Ca(Fe 0.97 Co 0.03 ) 2 As 2 Static I(Ԧr, E=50meV) Delocalized State, LDOS( Ԧq, E) -45pA -29pA b a No long range order! ~8a Fe-Fe T.-M. Chuang et al., Science 327, 181 (2010)
15 Electronic Nematicity in Underdoped Ca(Fe 0.97 Co 0.03 ) 2 As 2 Delocalized State, LDOS( Ԧq, E) b a T.-M. Chuang et al., Science 327, 181 (2010)
16 Nematic Electronic Structure at Twin Domain Boundary Surface reconstruction doesn t affect the nematic electronic structure. Nematic electronic structure correlates to the crystal symmetry. Topograph I (r,e=50mev) 96nm Twin boundary T.-M. Chuang et al., Science 327, 181 (2010) ~8a Fe-Fe
17 Electronic Nematicity in Detwinned Ba(Fe 1-x Co x ) 2 As 2 ρ a < ρ b DC electric transport: J.H. Chu et al. Science 329, (2010). M.A. Tanatar et al. PRB 81, (2010). S. Ishida et al. PRB 84, (2010). E.C. Blomberg et al. PRB 83, (2011). H.H. Kuo et al. PRB 84, (2011). J.J. Ying et al. PRL 107, (2011). J.H. Chu et al. Science 337, 710 (2012). A.F. Wang et al. New J. Phys (2013). b a AC electric transport: A. Dusza et al. EPL 93, (2011). M. Nakajima et al. PNAS 108, (2011). M. Nakajima et al. PRL 109, (2012) ARPES: Q. Wang, et al. arxiv: (2010). M. Yi et al., PNAS 108, 6878 (2011). I.R. Fisher et al., Rep. Prog. Phys (2011) Magnetic torque: S. Kasahara et al. Nature 486, 382 (2012). STM: C.L. Song et al., Science 332, 1410 (2011). X. Zhou et al. PRL. 106, (2011).
18 In-plane Resistivity Anisotropy in Detwinned Ba(Fe 1-x Co x ) 2 As 2 Crystalline anisotropy monotonically decreases with doping but nematicity does not! J.-H. Chu et al., Science 329, 824 (2010) M. A. Tanatar et al., PRB 81, (2010)
19 Doping Dependence of Transport Anisotropy? Proposal by I.R. Fisher: High mobility isotropic pocket short-circuits the aniostropic section of FS H.-H. Kuo et al., PRB 84, (2011) Dirac pocket at Λ=(0.75π,0) P. Richard et al., PRL104, (2010) K.K. Huynh et al., PRL106, (2011)
20 Alternative?
21 Theorectical Proposal : Impurity States Impurity-induced nematic state from orbital fluctuation: Y. Inoue et al., PRB 85, (2012) Ising nematic state from the scattering interference between impurities and spin fluctuation. R.M. Fernandes et al., PRL 107, (2011) Impurity states determined by reconstructed nesting wavevector. Jian Kang & Zlatko Tesanovic, PRB85, (2012)
22 Diminishing Resistivity Anisotropy by Annealing Defects and impurities play any role in transport anisotropy? RRR improved a factor of 10. M. Nakajima et al. PNAS 108, (2011) M. Nakajima et al. PRL 109, (2012)
23 Doping Dependence of Electronic Structure in Ca(Fe 1-x Co x ) 2 As 2 Co atoms induce nanoscale C 2 -symmetric electronic structure. Topography I(r, E=-36meV) X=0 21pA 9pA X=3.0% 109pA 25nm 52pA T.-M. Chuang et al., Science 327, 181 (2010) M.P. Allan et al., Nature Phys. 9, 220 (2013)
24 Our Proposal : Anisotropic Impurity State Anisotropic electronic impurity state Separated by 8a Fe-Fe, aligned with AFM a-axis Distributed randomly ~8a Fe-Fe ~8a Fe-Fe M.P. Allan et al., Nature Phys. 9, 220 (2013)
25 Static Nematic Electronic Structure vs Simulation Data, g(r, E=-37meV) Simulation, 1000 impurities ~ 3% doping 48nm Consistent with real-space electronic structure. M.P. Allan et al., Nature Phys. 9, 220 (2013)
26 Where Are Cobalt Dopant Atoms? What Role Do They Play?
27 Atom-projected DOS for Co Dopants A. F. Kemper et al., PRB 80, (2009)
28 Possible Identification of Co Dopants g( r, 150mV) 48nS 61.3nm 31nS T.-M. Chuang et al., Science 327, 181 (2010) M.P. Allan et al., Nature Phys. 9, 220 (2013)
29 Correlation between Co and Static Electronic Structure I( r, 50mV )+ Co Dopants -45pA b a Normalized cross-correlation=0.22 T.-M. Chuang et al., Science 327, 181 (2010) M.P. Allan et al., Nature Phys. 9, 220 (2013) -29pA
30 Anisotropic Impurity States Induced or Pinned by Co Atoms Autocorrelation of I-map Averaged I-map around Co Averaged I-map away from Co ~8a Fe-Fe ~8a Fe-Fe M.P. Allan et al., Nature Phys. 9, 220 (2013)
31 Reconcile QPI and ARPES QPI from a2 band at Additional symmetry breaking? M.P. Allan et al., Nature Phys. 9, 220 (2013)
32 0meV -7.5meV -15meV Impact of Anisotropic Impurity State on QPI Calculation QPI Data Power spectral density in differential conductance modulation Bare QPI q b Structure Factor : FFT of r-space scattering potential q a M.P. Allan et al., Nature Phys. 9, 220 (2013) Capriotti et al., PRB 68, (2003)
33 0meV -7.5meV -15meV Impact of Anisotropic Impurity State on QPI Calculation QPI Data Power spectral density in differential conductance modulation Bare QPI q b Structure Factor : FFT of r-space scattering potential q a M.P. Allan et al., Nature Phys. 9, 220 (2013) Capriotti et al., PRB 68, (2003)
34 Reconcile with Transport Anisotropy?
35 Scattering Rate in Born Approximation Boltzman transport equation : Band structure Scattering Scattering probability ~8a Fe-Fe Scattering is anisotropic and q-dependent possible strong influence on transport. Effective scattering rates also depend on the Fermi surface M.P. Allan et al., Nature Phys. 9, 220 (2013)
36 Consistent with Recent Transport Measurements a and b show similar T dependence in the AFO phase. T-dependent component of resistivity is nearly isotropic. S. Ishida et al. PRL 110, (2013)
37 Consistent with Recent Transport Measurements The anisotropy in resistivity in AFO arises from the anisotropy in the residual component which increases in proportion to the Co concentration x. J.-H. Chu et al., Science 329, 824 (2010) S. Ishida et al. PRL 110, (2013)
38 Nematicity above T s and T c BaFe 2 (As 1-x P x ) 2 NaFeAs : T s =52K, T N =41K S. Kasahara et al., Nature 486, 382 (2012) E. P. Rosenthal et al., NatPhys 10, 225 (2014) What drives the large nematic susceptibility?
39 Nematicity Relevant to High Tc FeSC? R. M. Fernandes et al., Nature Phys. 10, 97 (2014)
40 Nematicity Relevant to High T c Superconductivity? YBCO Pseudogap S. Kasahara et al., Nature 486, 382 (2012) N. Doiron-Leyraud et. al., Nature 447, 565 (2007)
41 FeSC vs Cuprates : Superconducting Layer Both have antiferromagnetic parent states. Cooper pairing mediated by AF? d 2 x y 2 5 d-orbitals A. Cho, Science 320, 870 (2008)
42 FeSC: Unconventional Superconductivity 1. The electron-phonon coupling is too weak to account for such high T C. L. Boeri et al., PRL 101, (2008) 2. Isotope effect on some materials shown to be negligible. P.M. Shirage et al., PRL 105, (2010) 3. Everything seems to work doping / pressure / different structures Possible pairing symmetries
43 FeSC: Candidates for Pairing Mechanism SDW suppression leads to SC AF Spin Fluctuation Exchange. S± OP symmetry I. I. Mazin et al., PRL 101, (2008) K. Kuroki et al., PRL 101, (2008) K. Seo et al., PRL 101, (2008). Orbital Fluctuation S++ OP symmetry H. Kontani et al., PRL 104, (2010) Gap symmetry? Phase sensitive measurements required!
44 STM on an iron chalcogenide Fe (Se,Te) T c = 13~14.5 K T ~ 1.5 K 2 /T c ~ 3.5 Tetsuo Hanaguri V mod = 0.1 mv RIKEN 19 nm 19 nm, -20 mv/0.1 na SC gap FULLY cf. F. Massee opens et al., PRB all 80, over (R) the (2009), FS pockets. T. Kato al., PRB 80, (R) (2009).
45 How will it work in iron-based SC? q 1 (2p,2p) Disconnected pockets q 3 E ~ (p,p) q 1 q 2 q 2 q 3 M k space D. J. Singh and M.-H. Du, PRL 100, (2008). q space Inter-pocket scattering Relationship between the pockets
46 QPI in an iron chalcogenide Fe(Se,Te) T ~ 1.5 K di/dv +E /di/dv -E T c ~ 13 K 1.0 mv T. Hanaguri et al., Science 328, 474 (2010). FT-Z map 1.0 mev Topo. q 1 q 3 q 1 q 2 M q 3 q 2 34 nm 34 nm, -20 mv/0.1 na Inter-pocket scatterings are detected.
47 How to determine the phase? q 1 (2p,2p) E ~ (p,p) q 3 q 1 q 2 M q 2 q 3 s d ± k space I. I. Mazin et al., PRL 101, (2008). K. Kuroki et al., PRL 101, (2008). q space Sign-preserving scattering Sign-reversing scattering cf. F. Wang, H. Zhai and D. H. Lee, EPL 85, (2009). Yan-Yang Zhang et al., PRB 80, (2009). E. Plamadeala, T. Pereg-Barnea, and G. Refael PRB 81, (2010).
48 Phase-sensitive STM on an iron chalcogenide Fe 1+x (Se,Te) T ~ 1.5 K di/dv +E /di/dv -E T c ~ 13 K 1.0 mv T. Hanaguri et al., Science 328, 474 (2010). B = = 10 T FT-Z map 1.0 mev q 1 q 1 q 2 M q 3 inc. q 3 q 2 dec. 34 nm 34 nm, -20 mv/0.1 na Vortices as magnetic scatterers Evidence Inter-pocket of s ± -wave scatterings symmetry are!! detected. Spin fluctuation plausible.
49 Summary of gap structure of iron-based SC STM suggests s ± -wave gap in an FeSC! Tunneling spectrum suggests that the superconducting gap fully opens over the Fermi surface. Inter-Fermi-pocket scatterings are identified in quasi-particle interference patterns, providing momentum-resolved information of the superconducting gap. Magnetic-field dependence of the quasi-particle interference pattern contains information on the phase of the superconducting gap function. The result on Fe(Se,Te) suggests s ± -wave superconductivity where the gap changes its sign between hole and electron pockets.
50 FeSC: SC Energy Gap Functions Spin Fluctuation S± OP symmetry Orbital Fluctuation S++ OP symmetry Gaps show different anisotropy at different pockets! P. J. Hirschfeld et al., Rep.Prog.Phys.74, (2011) H. Kontani et al., PRL 104, (2010)
51 Our Samples : LiFeAs Charge neutral cleaved surface :No surface states. Ideal for STM / ARPES! Large field of view necessary for intra-band QPI measurements! Milan Allan Andreas Rost T=1.2K 710Å Tien-Ming Chuang Li Fe As c b a 87Å M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
52 Spectroscopic Imaging, LDOS(r,E) T= 1.2K 880Å M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
53 Quasiparticle Interference, LDOS(q,E) Fourier Transform of LDOS(r,E) LDOS(q, E) T= 1.2K T= 1.2K 880Å M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
54 Band Identification by QPI above SC gap Identification based on comparison with ARPES and LDA results. γ band 10meV I.R. Shein et al., Solid State Comm.150, 152 (2010) S.V. Borisenko et al., PRL 105, (2010) 5meV -π/a 0 0 π/a 0 M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
55 Three hole-like bands: γ, a 2, a 1 γ a 1 a 2 E=+7.68meV E=-6.60meV M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
56 Quasiparticle Interference, g(q,e) around SC Gap Some QPI signals are suppressed. The SC gap at this Fermi sheet is anisotropic! +2.00meV +7.68meV T= 1.2K T= 1.2K M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
57 Determination of Superconducting Energy-Gap Structure q-space +2.00meV How to obtain i (k)? k-space γ band + anisotropic gap M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
58 Anisotropic Superconducting Energy-Gap Structure g a 1 M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
59 Two ARPES Groups Confirm Our Results STM and ARPES are consistent around. Consistent with AFSF theory. S.V. Borisenko et al., Symmetry 4, 251 (2012) K. Umezawa et al. PRL 108, (2012) P J Hirschfeld et al., Rep.Prog.Phys.74, (2011)
60 Anisotropic SC Energy Gaps in LiFeAs by ARPES STM and ARPES are consistent around. Consistent with AFSF theory. BCS gap equation at T=0 pairing interaction? S.V. Borisenko et al., Symmetry 4, 251 (2012) K. Umezawa et al. PRL 108, (2012) P J Hirschfeld et al., Rep.Prog.Phys.74, (2011)
61 Electron-Boson Interaction ReΣ(k, ω) k(ω) ImΣ k, ω τ 1 (k, ω)
62 di/dv (AU) Superconductivity by Tunneling Spectroscopy Ivar Giaever Nobel Prize 1973 Pb/MgO/Pb =1.34meV T=0.33K 1 2 I. Giaever, Phys. Rev. 126, 941 (1962)
63 di/dv (AU) a 2 ( ) F( ) d 2 I/dV 2 Electron-Phonon Interaction by Tunneling Spectroscopy William McMillan John Rowell F(ω)=phonon DOS α 2 (ω)= e-ph coupling Normalized di/dv van Hove Transverse phonon Longitudinal phonon 1 2 W.L. McMillan & J.W. Rowell, PRL 14, 108 (1965)
64 Normalized Conductance Atomic Visualization of Electron-Boson Coupling in FeSC Milan Allan Dip-hump in spectrum of FeSC Andreas Rost Momentum info? Energy (mev) M. P. Allan & A.W. Rost et al., Science 336, 563 (2012) M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
65 Energy QPI in LiFeAs q y q x M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
66 Normalized Conductance Atomic Visualization of Electron-Boson Coupling in FeSC Energy (mev) The change in dispersion occurs at the same energy as the traditional Electron-Boson coupling signature in the spectrum. M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
67 Atomic Visualization of Electron-Boson Coupling in FeSC A.E. Taylor et al., PRB 83, (2011) The change in dispersion occurs at the same energy as the traditional Electron-Boson coupling signature in the spectrum. M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
68 Atomic Visualization of Electron-Boson Coupling in FeSC The self energy due to e-b coupling is strongly anisotropic FeAs FeFe M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
69 Theoretical Calculation of E-B Couplings d-orbital fluctuations by Fe Eg-phonon Kyungmin Lee Mark Fischer Eun-Ah Kim M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
70 Theoretical Calculation of E-B Couplings d-orbital fluctuations by Fe Eg-phonon AF spin fluctuation M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
71 Theoretical Calculation of E-B Couplings d-orbital fluctuations by Fe Eg-phonon AF spin fluctuation M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015)
72 Fingerprint of Pairing Mechanism in FeSC Our experimental results support AF spin fluctuation pairing! M. P. Allan, Kyungmin Lee & A. W. Rost et al., Nature Physics 11, 177 (2015) M. P. Allan & A.W. Rost et al., Science 336, 563 (2012)
73 Single Unit-Cell FeSe Films on SrTiO3 Qikun Xue 薛其坤 Q.Y. Wang et al., CHIN. PHYS. LETT (2012)
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