Residual Meissner effect and other pre-pairing phenomena in the cuprate superconductors. T. Domański

Transcription

1 Wrocław, 2 Oct Residual Meissner effect and other pre-pairing phenomena in the cuprate superconductors T. Domański M. Curie-Skłodowska University, Lublin, Poland

2 Outline

3 Outline Preliminaries / pairing vs coherence /

4 Outline Preliminaries / pairing vs coherence / Pre-pairing / experimental evidence /

5 Outline Preliminaries / pairing vs coherence / Pre-pairing / experimental evidence / Selected results

6 Outline Preliminaries / pairing vs coherence / Pre-pairing / experimental evidence / Selected results Bogoliubov quasiparticles above T c

7 Outline Preliminaries / pairing vs coherence / Pre-pairing / experimental evidence / Selected results - Bogoliubov quasiparticles above T c Diamagnetism above T c

8 Outline Preliminaries / pairing vs coherence / Pre-pairing / experimental evidence / Selected results - Bogoliubov quasiparticles above T c - Diamagnetism above T c Summary

9 1. Preliminaries

10 Superconducting state properties

11 Superconducting state properties ideal d.c. conductance

12 Superconducting state properties ideal d.c. conductance Normal conductors: resistance R = ρ l S where ρ 1/σ and σ = ne2 τ m τ(t) relaxation time

13 Superconducting state properties ideal d.c. conductance a.c. conductance Drude conductance σ(ω) = ne2 τ m 1 1 iωτ obeys the f-sum rule ne2 Re σ(ω) = π m σ N Re σ(ω) ωτ 3 4 5

14 Superconducting state properties ideal d.c. conductance a.c. conductance This f-sum rule ne2 Re σ(ω) = π m must be obeyed also below T c, where n = n n + n s n s superfluid density

15 Superconducting state properties (continued)

16 Superconducting state properties (continued) ideal diamagnetism /perfect screening of d.c. magnetic field/ T > T c T < T c

17 Superconducting state properties (continued) ideal diamagnetism /perfect screening of d.c. magnetic field/ Meissner effect is described by the Londons equation T > T c T < T c j = e2 n s (T) mc 2 A where the coefficient e 2 n s (T) mc 2 ρ s (T) = 1 λ 2 ρ s (T) superfluid stiffness λ(t) penetration depth B(x) = B 0 e x/λ x

18 Superconducting state basic concepts

19 Superconducting state basic concepts ideal d.c. conductance

20 Superconducting state basic concepts ideal d.c. conductance ideal diamagnetism (Meissner effect)

21 Superconducting state basic concepts ideal d.c. conductance ideal diamagnetism (Meissner effect) can be regarded as two sides of the same coin.

22 Superconducting state basic concepts ideal d.c. conductance ideal diamagnetism (Meissner effect) can be regarded as two sides of the same coin. Both effects are caused by the superfluid fraction n s (T)

23 Such superfluid fraction marks the coherence between paired electrons.

24 Such superfluid fraction marks the coherence between paired electrons. Pairing mechanisms can be driven for instance by:

25 Such superfluid fraction marks the coherence between paired electrons. Pairing mechanisms can be driven for instance by: 1. exchange of phonons / classical superconductors, MgB 2,... /

26 Such superfluid fraction marks the coherence between paired electrons. Pairing mechanisms can be driven for instance by: 1. exchange of phonons / classical superconductors, MgB 2,... / 2. exchange of magnons / heavy fermion compounds /

27 Such superfluid fraction marks the coherence between paired electrons. Pairing mechanisms can be driven for instance by: 1. exchange of phonons / classical superconductors, MgB 2,... / 2. exchange of magnons / heavy fermion compounds / 3. strong correlations / exchange coupling 2t2 ij U in the high T c superconductors /

28 Such superfluid fraction marks the coherence between paired electrons. Pairing mechanisms can be driven for instance by: 1. exchange of phonons / classical superconductors, MgB 2,... / 2. exchange of magnons / heavy fermion compounds / 3. strong correlations / exchange coupling 2t2 ij U in the high T c superconductors /.. other exotic processes / ultracold atoms, nuclei, gluon-quark plasma /

29 Such superfluid fraction marks the coherence between paired electrons. Pairing mechanisms can be driven for instance by: 1. exchange of phonons / classical superconductors, MgB 2,... / 2. exchange of magnons / heavy fermion compounds / 3. strong correlations / exchange coupling 2t2 ij U in the high T c superconductors /.. other exotic processes / ultracold atoms, nuclei, gluon-quark plasma / Onset of the fermion pairing often goes hand in hand with appearance of the superconductivity/superfluidity but it doesn t have to be a rule.

30 Formal issues generalities

31 Formal issues generalities The order parameter χ ĉ ( r i )ĉ ( r j )

32 Formal issues generalities The order parameter χ ĉ ( r i )ĉ ( r j ) is a complex quantity χ = χ e iθ

33 Formal issues generalities The order parameter χ ĉ ( r i )ĉ ( r j ) is a complex quantity χ = χ e iθ It has the following physical implications:

34 Formal issues generalities The order parameter χ ĉ ( r i )ĉ ( r j ) is a complex quantity χ = χ e iθ It has the following physical implications: χ 0 amplitude causes the energy gap

35 Formal issues generalities The order parameter χ ĉ ( r i )ĉ ( r j ) is a complex quantity χ = χ e iθ It has the following physical implications: χ 0 amplitude causes the energy gap θ 0 phase slippage induces supercurrents

36 Critical temperature classification

37 Critical temperature classification The complex order parameter χ = χ e iθ

38 Critical temperature classification The complex order parameter χ = χ e iθ can vanish at T T c by:

39 Critical temperature classification The complex order parameter χ = χ e iθ can vanish at T T c by: 1. closing the gap [conventional BCS superconductors ] lim T Tc χ = 0

40 Critical temperature classification The complex order parameter χ = χ e iθ can vanish at T T c by: 1. closing the gap [conventional BCS superconductors ] lim T Tc χ = 0 2. disordering the phase [ HTSC compounds, URh 2 Si 2 (?) ] lim T Tc θ = 0

41 Amplitude vs phase driven transition scenario # 1

42 Amplitude vs phase driven transition scenario # 1 amplitude transition / classical superconductors / k B T c (0) 1.76

43 Amplitude vs phase driven transition scenario # 1 amplitude transition / classical superconductors / k B T c (0) 1.76 (0) (T) Electrons pairing is responsible for the energy gap (T) in a single particle spectrum 0 Temperature T c (T c ) = 0 Appearance of the electron pairs is simultaneous with onset of their coherence

44 Amplitude vs phase driven transition scenario # 2

45 Amplitude vs phase driven transition scenario # 2 phase-driven transition / high T c cuprate oxides / T c / (0)

46 Amplitude vs phase driven transition scenario # 2 phase-driven transition / high T c cuprate oxides / T c / (0) Early experiments using the muon-spin relaxation indicated that in HTSC T c ρ s (0) / Uemura scaling / The superfluid stiffness ρ s (T) is here defined by ρ s (T) 1 λ 2 (T) = 4πe2 m c 2 n s (T) Y.J. Uemura et al, Phys. Rev. Lett. 62, 2317 (1989).

47 Amplitude vs phase driven transition scenario # 2 phase-driven transition / high T c cuprate oxides / T c / (0) Recently such scaling has been updated from transport measurements 1 8 ρ s = 4.4σ dc T c / Homes scaling / This new relation is valid for all samples ranging from the underdoped to overdoped region. C.C. Homes, Phys. Rev. B 80, (R) (2009). / ab - plane /

48 Amplitude vs phase driven transition scenario # 2 phase-driven transition / high T c cuprate oxides / T c / (0) Recently such scaling has been updated from transport measurements 1 8 ρ s = 4.4σ dc T c / Homes scaling / This new relation is valid for all samples ranging from the underdoped to overdoped region. C.C. Homes, Phys. Rev. B 80, (R) (2009). / c - axis /

49 2. Pre-pairing /experimental evidence/

50 Incoherent pairs above T c experimental fact # 1

51 Incoherent pairs above T c experimental fact # La 2-x Sr x CuO 4 T (K) T onset 20 T c Sr content x Phase slippage detected in the large Nernst effect. Y. Wang et al, Science 299, 86 (2003).

52 Incoherent pairs above T c experimental fact # La 2-x Sr x CuO 4 T (K) T onset 20 T c Sr content x Phase slippage detected in the large Nernst effect. Y. Wang et al, Science 299, 86 (2003).

53 Incoherent pairs above T c experimental fact # 2

54 Incoherent pairs above T c experimental fact # 2 M d (10 3 A/m ) K Bi2201 La:0.44 T c = 30 K M d (10 3 A/m ) Van Vleck background (A + BT)H is subracted -0.2 (A) H ( T ) (B) 29 K H ( T ) -0.3 T c = 30K Enhanced diamagnetic response revealed above T c by the high precission torque magnetometry. L. Li,... and N.P. Ong, Phys. Rev. B 81, (2010). / Princeton University /

55 Incoherent pairs above T c experimental fact # 1 + 2

56 Incoherent pairs above T c experimental fact # ( A ) La 2-x Sr x CuO 4 ( B ) Bi 2 Sr 2-y La y CuO T ν onset T onset, T C ( K ) T M onset T M onset T ν onset T onset, T C ( K ) T c T c Sr content x La content y 0 T ν T M onset of the Nernst effect onset of the diamagnetism L. Li,... and N.P. Ong, Phys. Rev. B 81, (2010).

57 Incoherent pairs above T c experimental fact # G. Yu et al, arxiv:// v1 (preprint). T c T c onset of the sc fluctuations onset of the superconductivity

58 Incoherent pairs above T c experimental fact # 3

59 Incoherent pairs above T c experimental fact # 3 G. Drachuck et al, Phys. Rev. B 85, (2012). / Technion Group / Magnetization measurements for the needle shape La 2 x Sr x CuO 4 single crystals.

60 Incoherent pairs above T c experimental fact # 3 G. Drachuck et al, Phys. Rev. B 85, (2012). / Technion Group / Magnetization measurements for the needle shape La 2 x Sr x CuO 4 single crystals.

61 Incoherent pairs above T c experimental fact # 4

62 Incoherent pairs above T c experimental fact # 4 Transfer of the spectral weight in the single particle spectrum. T. Kondo, R. Khasanov, T. Takeuchi, J. Schmalian & A. Kamiński, Nature 457, 296 (2009).

63 Incoherent pairs above T c experimental fact # 4 A. Kamiński, T. Kondo, T. Takeuchi, and G. Gu, arxiv:// (2014) preprint.

64 Incoherent pairs above T c experimental fact # 5

65 Incoherent pairs above T c experimental fact # 5 Josephson current in YBaCuO - LaSrCuO - YBaCuO junction with LaSrCuO being in the pseudogap state well above T c T. Kirzhner and G. Koren, Scientific Reports 4, 6244 (2014).

66 Incoherent pairs above T c experimental fact # 5 Phase diagram for the coherence length ξ(t, x) appearing in the empirical law I c exp [ d/ξ] for Josephson current I c. T. Kirzhner and G. Koren, Scientific Reports 4, 6244 (2014).

67 Incoherent pairs above T c experimental fact # 6

68 Incoherent pairs above T c experimental fact # 6 a) STM tip thin normal metal 20 b) 90 nm LSCO x=0.10 SrTiO 3 R (Ω) 10 Au/0.08 Au/0.10 Au/ T (K) Pseudogap induced well above T c in ultrathin metallic slab deposited on La 2 x Sr x CuO 4. c) 600 nm O. Yuli et al, Phys. Rev. Lett. 103, (2009).

69 Incoherent pairs above T c experimental fact # 6 Measured DOS a) 8 K x = K Proximity induced pseudogap observed di/dv 0.0 b) 4 K x = 0.10 far above T c K 1.0 c) 8 K x = O. Yuli et al, PRL 103, (2009) K Sample Bias (mv)

70 Incoherent pairs above T c experimental fact # 7

71 Incoherent pairs above T c experimental fact # 7 S.J. Moon et al, Phys. Rev. B 90, (2014). Schematic view of the optical conductance in the pseudogap state of YBaCuO superconductor compared with conventional BCS materials.

72 Incoherent pairs above T c experimental fact # 7 A. Dubroka et al, Phys. Rev. Lett. 106, (2011). Onset of the superfulid fraction observed in the c-axis optical measurements Reσ c (ω).

73 Incoherent pairs above T c... continued

74 Incoherent pairs above T c... continued Josephson-like features seen above T c in the tunneling N. Bergeal et al, Nature Phys. 4, 608 (2008).

75 Incoherent pairs above T c... continued Josephson-like features seen above T c in the tunneling N. Bergeal et al, Nature Phys. 4, 608 (2008). Bogoliubov quasiparticles detected above T c in ARPES measurements for YBaCuO and LaSrCuO compounds Argonne (2008), Villigen (2009).

76 Incoherent pairs above T c... continued Josephson-like features seen above T c in the tunneling N. Bergeal et al, Nature Phys. 4, 608 (2008). Bogoliubov quasiparticles detected above T c in ARPES measurements for YBaCuO and LaSrCuO compounds Argonne (2008), Villigen (2009). Bogoliubov-type interference patterns in pseudogap state as the fingerprint of phase incoherent d-wave superconductivity preserved up to 1.5 T c J. Lee,... and J.C. Davis, Science 325, 1099 (2009).

77 3. Selected results / below and above T c /

78 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l

79 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l R l = ( r i + r j )/2

80 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l R l = ( r i + r j )/2 This Hamiltonian describes a two-component system consisting of:

81 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l R l = ( r i + r j )/2 This Hamiltonian describes a two-component system consisting of: ĉ ( ) iσ itinerant fermions (e.g. holes near the Mott insulator)

82 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l R l = ( r i + r j )/2 This Hamiltonian describes a two-component system consisting of: ĉ ( ) iσ itinerant fermions (e.g. holes near the Mott insulator) ˆb( ) l immobile local pairs (RVB defines them on the bonds)

83 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l R l = ( r i + r j )/2 This Hamiltonian describes a two-component system consisting of: ĉ ( ) iσ itinerant fermions (e.g. holes near the Mott insulator) ˆb( ) l immobile local pairs (RVB defines them on the bonds) interacting via:

84 Boson and fermion degrees of freedom [ spatial representation ] Ĥ = (t ij µ δ i,j ) ĉ iσĉjσ + i,j,σ l + ] g ij [ˆb l ĉi, ĉ j, + h.c. i,j ( E (B) l 2µ )ˆb lˆb l R l = ( r i + r j )/2 This Hamiltonian describes a two-component system consisting of: ĉ ( ) iσ itinerant fermions (e.g. holes near the Mott insulator) ˆb( ) l immobile local pairs (RVB defines them on the bonds) interacting via: ˆb l ĉi, ĉ j, + h.c (the Andreev-type scattering)

85 Phenomenological arguments supporting BF scenario

86 Phenomenological arguments supporting BF scenario 3 paired & unpaired carriers V.G. Geshkenbein, L.B. Ioffe, A.I. Larkin, Phys. Rev. B 55, 3173 (1997).

87 Phenomenological arguments supporting BF scenario 3 paired & unpaired carriers V.G. Geshkenbein, L.B. Ioffe, A.I. Larkin, Phys. Rev. B 55, 3173 (1997).

88 Phenomenological arguments supporting BF scenario K.-Y. Yang, E. Kozik, X. Wang, and M. Troyer, Phys. Rev. B 83, (2011). cooperons & holes

89 Phenomenological arguments supporting BF scenario nodal antinodal dichotomy T. Kondo, R. Khasanov, T. Takeuchi, J. Schmalian & A. Kamiński, Nature 457, 296 (2009).

90 Bogoliubov quasiparticles below and above T c

91 BCS physics The BCS ground state:

92 BCS physics The BCS ground state: BCS = Π k ( uk + v k e iθk ĉ k ĉ k ) vac

93 BCS physics The BCS ground state: BCS = Π k ( uk + v k e iθk ĉ k ĉ k ) vac v k, u k θ k coherence factors, phase

94 BCS physics The BCS ground state: BCS = Π k ( uk + v k e iθk ĉ k ĉ k ) vac v k, u k θ k where coherence factors, phase v k e iθ k 2 = 1 2 [ 1 ] ε k µ (εk µ) = 1 u k 2

95 BCS excitation spectrum

96 BCS excitation spectrum The effective (Bogoliubov) quasiparticles : ˆγ k = u k ĉ k + v k ĉ k ˆγ k = v k ĉ k + u k ĉ k

97 BCS excitation spectrum The effective (Bogoliubov) quasiparticles : ˆγ k = u k ĉ k + v k ĉ k ˆγ k = v k ĉ k + u k ĉ k represent a coherent superposition of the particles and holes

98 BCS excitation spectrum The effective (Bogoliubov) quasiparticles : ˆγ k = u k ĉ k + v k ĉ k ˆγ k = v k ĉ k + u k ĉ k represent a coherent superposition of the particles and holes A(k, ω) = u k 2 δ(ω E k ) + v k 2 δ(ω + E k )

99 BCS excitation spectrum The effective (Bogoliubov) quasiparticles : ˆγ k = u k ĉ k + v k ĉ k ˆγ k = v k ĉ k + u k ĉ k represent a coherent superposition of the particles and holes A(k, ω) = u k 2 δ(ω E k ) + v k 2 δ(ω + E k ) Occupancy of the momentum k is given by n k = u k 2 f F D (E k ) + v k 2 f F D ( E k ) }{{} 1 f F D (E k )

100 (a) Energy T c < T Intensity E F k F Wave vector ε k Intensity (b) v k 2 u k 2 E F Energy T <T c k F Wave vector -E k 2 E k Single particle spectrum of conventional superconductors consists of two Bogoliubov branches gaped around E F (no fluctuation effects are here taken into account).

101 Experimental data for cuprates below T c H. Matsui, T. Sato, and T. Takahashi et al, Phys. Rev. Lett. 90, (2003).

102 Beyond the BCS approximation

103 Beyond the BCS approximation We have generalized the Bogoliubov ansatz taking into account the non-condensed (preformed) pairs

104 Beyond the BCS approximation We have generalized the Bogoliubov ansatz taking into account the non-condensed (preformed) pairs ĉ k (l) = u k (l) ĉ k + v k (l) ĉ k + 1 [ ] uk,q (l) ˆb qĉ q+k + v k,q (l) ˆb q ĉ q k, N q 0 ĉ k (l) = v k (l) ĉ k + u k (l) ĉ k 1 [ ] v k,q (l) ˆb qĉ q+k + u k,q (l) ˆb q ĉ q k, N q 0 (1) (2)

105 Beyond the BCS approximation We have generalized the Bogoliubov ansatz taking into account the non-condensed (preformed) pairs ĉ k (l) = u k (l) ĉ k + v k (l) ĉ k + 1 [ ] uk,q (l) ˆb qĉ q+k + v k,q (l) ˆb q ĉ q k, N q 0 ĉ k (l) = v k (l) ĉ k + u k (l) ĉ k 1 [ ] v k,q (l) ˆb qĉ q+k + u k,q (l) ˆb q ĉ q k, N q 0 (1) (2) with the boundary conditions u k (0)=1 and v k (0)=v k,q (0)=u k,q (l)=0

106 Beyond the BCS approximation We have generalized the Bogoliubov ansatz taking into account the non-condensed (preformed) pairs ĉ k (l) = u k (l) ĉ k + v k (l) ĉ k + 1 [ ] uk,q (l) ˆb qĉ q+k + v k,q (l) ˆb q ĉ q k, N q 0 ĉ k (l) = v k (l) ĉ k + u k (l) ĉ k 1 [ ] v k,q (l) ˆb qĉ q+k + u k,q (l) ˆb q ĉ q k, N q 0 (1) (2) with the boundary conditions u k (0)=1 and v k (0)=v k,q (0)=u k,q (l)=0 and we determined the fixed point values lim l u k (l) ũ k etc from the coupled set of flow equations l u k(l), l v k(l), l u k,q(l), l v k,q(l).

107 Effective spectrum above T c T c < T < T A(k,ω) k - k F ω 0.05 T. Domański and J. Ranninger, Phys. Rev. Lett. 91, (2003).

108 Evidence for Bogoliubov QPs above Tc

109 Evidence for Bogoliubov QPs above T c J. Campuzano group (Chicago, USA) Results for: Bi 2 Sr 2 CaCu 2 O 8 A. Kanigel et al, Phys. Rev. Lett. 101, (2008).

110 Evidence for Bogoliubov QPs above T c PSI group (Villigen, Switzerland) Max Energy [ev] Cut 1 Cut 1 Intensity [arb. units] Energy [mev] Cut 2 Cut 2 Min Energy [ev] Energy [ev] k - k F [ /a] Results for: La Sr CuO 4 M. Shi et al, Eur. Phys. Lett. 88, (2009).

111 Evidence for Bogoliubov QPs above T c D. Jin group (Boulder, USA) T/Tc = 0.74 T/Tc = 1.24 Spectral Weight (arb.) k = T/Tc = 1.47 T/Tc = Single-Particle Energy (E S/E F) Results for: ultracold 40 K atoms J.P. Gaebler et al, Nature Phys. 6, 569 (2010).

112 Bogoliubov QPs above Tc

113 Bogoliubov QPs above T c Reproducing experimental line-shapes of the ultra-cold fermion atoms A(k,ω) T = 0.76 T c k / k F ω / T. Domański, Phys. Rev. A 84, (2011).

114 Bogoliubov QPs above T c Reproducing experimental line-shapes of the ultra-cold fermion atoms A(k,ω) T = 1.24 T c k / k F ω / T. Domański, Phys. Rev. A 84, (2011).

115 Bogoliubov QPs above T c Reproducing experimental line-shapes of the ultra-cold fermion atoms A(k,ω) T = 1.47 T c k / k F ω / T. Domański, Phys. Rev. A 84, (2011).

116 Bogoliubov QPs above T c Reproducing experimental line-shapes of the ultra-cold fermion atoms A(k,ω) T = 2.06 T c k / k F ω / T. Domański, Phys. Rev. A 84, (2011).

117 Diamagnetism its origin above T c

118 Diamagnetic response above Tc

119 Diamagnetic response above T c The anomalous contributions k - q k + q q 1 q 1 q 1 + k q 1 - k

120 Diamagnetic response above T c The anomalous contributions k - q k + q q 1 q 1 q 1 + k q 1 - k resemble the Aslamasov-Larkin diagram

121 Diamagnetic response above T c The anomalous contributions k - q k + q q 1 q 1 q 1 + k q 1 - k resemble the Aslamasov-Larkin diagram enhancing the conductance/diamagnetism above T c.

122 Onset of diamagnetism above Tc

123 Onset of diamagnetism above T c Onset of the diamagnetism coincides with appearance of the collective features in the fermion/boson spectrum.

124 Onset of diamagnetism above T c Onset of the diamagnetism coincides with appearance of the collective features in the fermion/boson spectrum k B T / D = ~ E q / D k B T / D = k B T / D = q x a Qulitative changes of the preformed pairs spectrum.

125 Onset of diamagnetism above T c Onset of the diamagnetism coincides with appearance of the collective features in the fermion/boson spectrum. m B / m 0 F T c g = 0.2 D T * k B T / D Effective mass m B of the preformed pairs M. Zapalska and T. Domański, Phys. Rev. B 84, (2011).

126 Onset of diamagnetism above T c Onset of the diamagnetism coincides with appearance of the collective features in the fermion/boson spectrum. M. Zapalska and T. Domański (2014) theory expt M d (T) T * M (A/m) T / D T/T c K.-Y. Yang,... and M. Troyer, Phys. Rev. B 83, (2011).

127 Onset of diamagnetism above T c Onset of the diamagnetism coincides with appearance of the collective features in the fermion/boson spectrum. n s (T) / n fluctations T * T c k B T / D J x (q 0, 0) = e2 n s (T) m A x(q 0, 0) M. Zapalska and T. Domański, Phys. Rev. B 84, (2011). G. Drachuck et al, Phys. Rev. B 85, (2012).

128 Diamagnetic response above Tc

129 Diamagnetic response above T c Residual diamagnetism originates from collective behavior of the pre-formed pairs. Pair susceptibility is enhanced at T sc and it ultimately diverges at some lower T c.

130 Diamagnetic response above T c Residual diamagnetism originates from collective behavior of the pre-formed pairs. Pair susceptibility is enhanced at T sc and it ultimately diverges at some lower T c. Cartoon illustrating the vortex liquid above T c.

131 Summary

132 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c

133 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c residual diamagnetism / torque magnetometry, magnetization of needle samples /

134 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c residual diamagnetism / torque magnetometry, magnetization of needle samples / Bogoliubov quasiparticles / ARPES, Josephson effect, FT-STM /

135 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c residual diamagnetism / torque magnetometry, magnetization of needle samples / Bogoliubov quasiparticles / ARPES, Josephson effect, FT-STM / Short-range superconducting correlations

136 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c residual diamagnetism / torque magnetometry, magnetization of needle samples / Bogoliubov quasiparticles / ARPES, Josephson effect, FT-STM / Short-range superconducting correlations are responsible for the sc-like features

137 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c residual diamagnetism / torque magnetometry, magnetization of needle samples / Bogoliubov quasiparticles / ARPES, Josephson effect, FT-STM / Short-range superconducting correlations are responsible for the sc-like features even though ODLRO is absent above T c

138 Summary A number of experimental data provide a clear evidence for the pre-existing pairs above T c residual diamagnetism / torque magnetometry, magnetization of needle samples / Bogoliubov quasiparticles / ARPES, Josephson effect, FT-STM / Short-range superconducting correlations are responsible for the sc-like features even though ODLRO is absent above T c T h a n k y o u