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CDW PHASE SHIFT STUDY BY UHV-LT-STM

CDW PHASE SHIFT STUDY BY UHV-LT-STM. J.-C. Girard et Z.Z. Wang Laboratoire de Photonique et de Nanostructures LPN / CNRS Route de Nozay – 91460 Marcoussis , France. Outline. 1/ Introduction : Quantum Imaging by STM

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CDW PHASE SHIFT STUDY BY UHV-LT-STM

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  1. CDW PHASE SHIFT STUDY BY UHV-LT-STM J.-C. Girard et Z.Z. Wang Laboratoire de Photonique et de Nanostructures LPN / CNRS Route de Nozay – 91460 Marcoussis , France

  2. Outline 1/Introduction : Quantum Imaging by STM imaging of ground state of quantum mechanics and of many body problem 2/ CDW in TTF-TCNQ : an ideal candidate for local phase shift j(r)studying (unique?) 3/ phase shift ja(x,y) for modulation in “a” direction (perpendicular to the chain direction): the variation is trivial in real space (commensurate pining) 4/ phase shift jb(x,y) for modulation in “b”direction (chain direction): important variation presented in our measurement, phase shift “map” 5/ Conclusion: CDW complex order parameter Y = D eiF can be studied by STM

  3. measurement We soon find ourselves armed with wonderful new tools. The more we used them, the more applications we find; and the more applications we find, the more use of quantum theory we make. In no way do the advances of physics spread more widely to the community than in new and improved measuring devices. Is it true that « no elementary quantum phenomenon is a phenomenon until it is a recordedphenomenon »? John Archibald Wheeler Quantum Theory and Measurement

  4. STM measurement STM might be a unique technique to study, in real space, local electronic structure with energy resolution. - the typical tip-sample resistance (tunneling gap resistance) is of 6- 10 orders higher than the sample resistance, resulting in a less significant matrix transfer element in tunneling junction. - only an insignificant electric field built inside the sample. - tunneling current is of order of 1-100pA, one electron every 1-100ns! No question for escaping, recombination , thermalizing… Both topographic and spectroscopic measurement in nanometer scale can be performed simultaneously with a least tip-sample interaction (without destructive). Ground state in quantum mechanics is robust against the STM measurement

  5. Quantum Imaging with STM -A lot of the phenomena that are traditionally encountered in course in quantum mechanics, such as molecular orbital, harmonic oscillators, particle in a box, eigen wave function, impurity Bohr radius, Fermi’s golden rule, chemical bonding, and the electron spin can be directly visualized with the STM. -Recently, some second quantification phenomena that are introduced in many body problems of condensed matter physics are studied by STM too. Kondo effect, Friedel Oscillation, Charge Density Wave, inhomogeneity of superconducting gap are clearly observed without ambiguity.

  6. Band structure

  7. Eigenenergy and eigenstate in QD InAs(P)/nP(001)QD Height : 5.8 nm Lateral size : 42 nm e5 e4 e3 e1 e11 e10 e2 e0 e9 e7 e8 e6 LPN PRL 2009, APL 2010 e5 V = 1074 mV e6 V = 1124 mV e7 V = 1155 mV e8 V = 1182 mV e9 V = 1216 mV e10 V = 1255 mV e11 V = 1297 mV e0 V = 867 mV e1 V = 901 mV e2 V = 936 mV e3 V = 970 mV e4 V = 1024 mV

  8. Confined electronic states in different nanostructures by STS Electronics states for InAs/GaSb (QW) Electronics states steps confinement Electronics states in Ag(111) islands Suzuki et al., Technical Review NTT (2008) C. Tournier-Colletta et al., PRL 104, 016802 (2010) Burgi et al, PRL 81, 24 (1998)

  9. TTF-TCNQ crystallography S H C H N C - Monocrystal: monoclinic cell a = 1.23 nm b = 0.38 nm c = 1.58 nm b= 104.6 ° Cleavage plane ab :quadratic cell

  10. TTF+ TCNQ- TCNQ- Molecular Resolution at T = 63K on TTF-TCNQ (001) surface Corrugation: TCNQ : 2 x 0.6 Å TTF : 2 x 0.2 Å hTCNQ-hTTF= 1 Å It= 1nA , Vbias= 50mV Acquisition time : 210 s

  11. CDW at 35.6K

  12. Sequential images of CDW on TTF-TCNQ at T = 35.6 K 100 mV 1nA Time for take one Image: 210s Total time : 50 minutes Temp. shift: 0.4K

  13. T = 35.6K dimensions : 14.89 nm x 16.09 nm a x b 41.b a=1.22nm b=0.38nm y: chain dir. analysis on 12 rows X 41columns 12.a LPN PRB 2003

  14. Fourier Analysis : bi-q modulation two generating vectors for CDW at 35.6K : q1= 0.25 a* + 0.295 b* = qa. a* + qb b* q2= -0.25 a* + 0.295 b* = - qa.a* + qb b* In real space, the wave vectors are: l1= la a + lb b with la = (2p/qa) = 4 (commensurate) l2= - la a + lb b lb = (2p/qb) = 3.39 (incommensurate) (LPN PRL 2009, PRB 2008, PRB 2006, PRB2003)

  15. Phase shift j (r) • CDW is a quantum condensate state of electronic state in low-dimensional materials. It can be presented as a complex order parameter Y = D eiF • Ddetermines - the size of the electronic energy gap - the amplitude u1 of the atomic displacements - the amplitude of the electron density modulation F(r) determines the position of the CDW relative to the underlying lattice. Dr (r) = r0.cos [F (r) ] • with F (r) = qCDW. r + j (r) • j(r) represents local deformation of CDW which is related to the elastic energy

  16. j(r) No impurities r f(r) j(r) r i i i i i i i i i i i i i i Weak / Strong CDW pining and local phase shift Perfect one-dimensional lattice: f(r) is constant (superconducting state) CDW pinning : Coulomb interaction between the CDW and impurities weak pinning (Fukuyama, Lee, Rice): smooth variation in j(r)over a distance containing several impurities strong pinning: abrupt variation in f(r) at each impurity site r • Phase determination is crucial to understand the physics of a complex order parameter • - Importance in the understanding of the static and dynamic properties of the CDW state.

  17. : b unit : a unit Phase shift in modulation bi-q r(x,y) = r0 [1+Dr(x,y) ] Dr(x,y)= A1cos(q1.r + j1 ) cos(q2.r + j2 ) q1= 0.25 a* + 0.295 b* = qa. a* + qb b* q2= -0.25 a* + 0.295 b* = - qa.a* + qb b* Dr(x,y) = 2A . cos[(2p/la). x + ja] . cos[(2p/lb).y + jb] (2) the phase shift ja and jb can be calculated separately: Perpendicular to chain, in “a” direction (commensurate) y = const ; Dr(x) = 2A(y) .cos[(2p/la). x + ja] (3) For a chain , in “b” direction (incommensurate) x = const ; Dr(y) = 2A(x) .cos[(2p/lb).y + jb] (4)

  18. TTF-TCNQ: an ideal candidate to study the local phase shift j(r) • CDW phase transition (TP = 53K) • Semiconductor at low temperature (condensate state) • an ideal candidate to study the local phase shift j(r) • Quadratic unit cell in the ab plane. (a.b = 0) • - Low temperature CDW phase (T<38K): • Commensurate in the “a” direction • Incommensurate in the “b” direction • bi-q modulation • -the phase shift ja and jb can be treated as independents parameters • both ja and jb are fonction of x and y

  19. T = 35.6K dimensions : 14.89 nm x 16.09 nm a x b 41.b a=1.22nm b=0.38nm y: chain dir. analysis on 12 rows X 41columns 12.a LPN PRB 2003

  20. phase shift ja for modulation in “a” direction analysis method: 1st step: cross section profile in “a” direction (perpendicular to chain ) 2nd step: determination of the CDW maxima at the lattice position 3rd step: best fit from sinusoidal function A.cos((2p/la).x + ja) Origin’s non linear regression method : Levenberg-Marquardt algorithm (c2 minimization) ja is the only fitting parameter (jaaverage on ~ 3 CDW wavelengths)A = Max(Zi) – Min(Zi) In “a” direction (commensurate), for a TCNQ molecular row (y = const), CDW modulation Dr(x,y) = A(y)½ y cst..cos((2p/la).x + ja) (4) with (2p/la)= 2p/4 = p/2 Amplitude (nm) Distance (nm)

  21. “a” direction phase shift ja Amplitude (nm) Distance (nm) ja = - 0.76 p »- (p/2 + p/4) Agree with X-ray analysis result reported: p/4 J.P. Pouget The change of ja is trival in real space, we concentrate on the local variation of jb Commensurate pining by the lattice

  22. phase shift <jb> for modulation in “b” direction a single chain analysis In “b” direction (in commensurate), for a TCNQ chain (x = constant) CDW modulation is Dr(x,y) = A(x)½ x cst..cos((2p/lb).y+ jb) With (2p/lb)= 2p/3.39 The fitting function is Dr(x,y) = A..cos((2p/lb).y+ jb) jb is the only fitting parameter (average on ~ 12 CDW wavelengths) amplitude (nm) We find jb = -258° distance (nm)

  23. The fitting function is Dr(x,y) = A..cos((2p/lb).y + jb) jb is the only fitting parameter (average on ~ 12 CDW wavelengths) amplitude (nm) distance (nm)

  24. The phase shift <jb>on four adjacent chains

  25. As we measured ja = p/4 for the CDW commensurate a-component First chain: Dr(y,x = 0) = 2Acos(ja).cos(qb.y+ jb) = 2 A1 cos(qb.y+ jb) Second chain Dr(y,x = a) = 2Acos(p/2 + ja).cos(qb.y+ jb) = 2 A2 cos(qb.y+ jb) Third chain Dr(y, x = 2a) = 2Acos(p + ja).cos(qb.y+ jb) = 2 A1 cos(qb.y+ jb+ p) Fourth chain Dr(y,x = 3a) = 2Acos(3p/2 + ja).cos(qb.y+ jb) = 2 A2 cos(qb.y+ jb+ p)

  26. Djb(n) = 0.15 Djb(n) = 0.51 Djb(n) = 0.22 Djb(n) = -0.38 Djb(n) = 0.12 Djb(n) = -0.77 Djb(n) = -0.11 Djb(n) = -0.94 Djb(n) = -0.04 Djb(n) = -0.36 Djb(n) = 0.73 Djb(n) = -0.72 Variation on each chain of jb(n) Average <Djb(n)>= 0.45°/ b unit

  27. Variation of the phase shift jb in the “a” direction jbfor 12 chains With p correction the phase shift <jb>has a variation of 4 degrees per a unit length in the a direction.

  28. jb(30) = -252° jb(10) = -262° Local phase shift: the variation of jb(n)in the “b” direction We have previously measured the average phase shift <jb> over 12 CDW for each TCNQ chain.On a single chain, the local variation of the phase shift jb(n) can be determinedby selecting only 6 CDW wavelengths centred at y = n.b jb(10) = -262° jb(30) = -252° We measured a Djb phase shift of 0.15 degrees per b unit length along a single chain in the b direction

  29. Local phase shift jb(n)in next image in “b” direction

  30. CDW Domains Size Estimation in TTF-TCNQ In 1980’s, Fukuyama, Lee, Rice postulated the existence of domain in the CDW condensate in the weak pinning case. Inside the domain the variation of phase shift is less than p. So far, the experimental observations of domains is difficult (Steed and Fung;? Fleming; ?) We have measured variations of the phase shift jb for modulation in b direction Transverse to the chains (in a direction) D<jb>= 4 degrees / a unit length Parallel to the chains (in b direction) 0 < Djb(n)< 0.45 degrees / b unit length If we defines size domains with L^and Lúï as the lengths on which the phase shift varies by 180 degrees: L^= ( 180 / 4 )2 . a = 2470 nm »2.5 mm Lúï = ( 180 / 0.45 )2 . b = 61120 nm »60 mm

  31. Fourier Analysis Methode d’analyse d’images HR-TEM M.J. Hyttch (Ultramicriocopy 74 (1998) 131) 2p 0 Selection d’un spot dans le spectre de Fourier Transformation de Fourier inverse écart a la périodicité Phase shift map Dj < p/5 (F. Pailloux, LMP, Univ Poitiers)

  32. Summary • in “a” direction ( commensurate ), CDW is pinned by the lattice with a phase shift ja close to ~p/4 relative to the underlying lattice • in “b” direction ( incommensurate), CDW is weakly pinned by impurities as the phase shift jb varies smoothly along the chain • the existence of the jb correlation between chains and the jb vary slowly from chain to chain., however the change of jb is more important in “a” direction than in “b” direction • the size of the CDW domains in TTF-TCNQ, can be estimated as: • L^x Lúï = 2.5 mm x 60 mm • STM ability to determine both atomic structure and CDW structure • Þresolution ofcomplicated structural details of CDW • CDW complex order parameter Y = D eiF can be studied by STM

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