FERMI LIQUID BEHAVIOUR IN STRONGLY CORRELATED METALSf1web.ijs.si/~zitko/conference.ngsces.org/2015/wp-content/uploads/… · NGSCES 2015 — Trogir September 2015 Damien Stricker

FERMI LIQUID BEHAVIOUR IN STRONGLY CORRELATED METALS

NGSCES 2015 — TrogirSeptember 2015

Damien StrickerDirk van der Marel

Jernej MravljeAntoine Georges Christophe Berthod Rosalba Fittipaldi

Antonio Vecchione

Traditional signature of Fermi liquids

⇢ =m

ne2⌧= ⇢0 +AT 2

Transport

Andres et al. PRL 35, 1779 (1975)

CeAl3

Specific heat

CV =⇡2N(0)

3kBT

m*/m~300CeAl3

MnSi

SrTiO3 UPd2Al3

Silicides

Titanates Heavy Fermions

CupratesHgBa2CuO4+d

One example among dozen

1. What are the Fermi-Liquid fingerprints in optics ?

Sr2RuO4 as an example

2. Can we understand the non-Fermi-liquid behavior above ~ 0.1 eV ?

Compare with DFT+DMFTResilient quasiparticles

3. What does it teach us about Sr2RuO4 ?

A simple model : from Tc to 1300 K !

Outline* * *

Local Fermi-liquid regimes in optics

ω

Tlo

g σ/σ D

C

ħω = 2π

kBT

ReIm

Dru

de

log(ω)

Thermal

DrudeDrude (classical)

Thermal (interacting electrons)

The

rmal

• Non Drude « foot » of the optical conductivity

• Scaling of the optical scattering rate• Universal scaling factor p = 2

Gurzhi et al. JETP 35(8), 673 (1959)Berthod et al. PRB 87, 115109 (2013)Götze & Wölfle PRB 6, 1226 (1972)

⌧�1

opt

/ [!2 + (p⇡kB

T )2]

Strangely enough, this precise form (including factor 2) was not experimentally demonstrated from optics until now !

�(!) =!2p/4⇡

⌧�1 � i!

�(!) =!2

p/4⇡

⌧�1

opt

(!)� i![1 + �opt

(!)]

Fermi liquid regimes in optics

ω

Tlo

g σ/σ D

C

ħω = 2π

kBT

ReIm

Dru

de

log(ω)

Thermal

DrudeDrude (classical)

Thermal (interacting electrons)

The

rmal

• Non Drude « foot » of the optical conductivity

• Scaling of the optical scattering rate• Universal scaling factor p = 2

Gurzhi et al. JETP 35(8), 673 (1959)Berthod et al. PRB 87, 115109 (2013)Götze & Wölfle PRB 6, 1226 (1972)

⌧�1

opt

/ [!2 + (p⇡kB

T )2]

Strangely enough, this precise form (including factor 2) was not experimentally demonstrated from optics until now !

�(!) =!2p/4⇡

⌧�1 � i!

�(!) =!2

p/4⇡

⌧�1

opt

(!)� i![1 + �opt

(!)]

Compound Material Tmax ωmax p ref

Heavy Fermions

UPt3 1 1 <1Sulewski, Phys. Rev. 38(8), 5338 (1998)

CePd3 1.14

URu2Si2 2 10 1.0 Nagel, PNAS 109, 47 (2012)

TitanatesCe0.95Ca0.05TiO3.04 24 100 1.31 Katsufuji, PRB 60 7673 (1999)

Nd0.95TiO3 24 50 1.05 Yang, PRB 73 195125 (2006)

Transition metals

Cr 28 370 1.6 Basov, PRB 65 054516 (2002)

Organics κ-(BEDT-TTF)2 4 70 2.38 Dressel, J. Phys.Cond.Mat. 23, 293201 (2011)

Cuprates HgBa2CuO4.1 19 100 1.5 Mirzaei & Stricker, PNAS 110 5774 (2013)

Magnetic moments

Resonant level 1-∞ Maslov, PRB 86 155137 (2012)

Sr2RuO4 the archetypal Landau-Fermi-liquid

1. Known Fermi-Liquid TFL ~25 KTransportHussey, PRB 57 5505 (1998)

Quantum oscillation Jaudet, PhD Thesis (2009)

ARPES Bergemann, Adv. Phys. 52, 7 (2003)

2. Solid-state analogue of 3Hep-wave symmetry of the SC phase Kallin et al., Rep. Prog. Phys. 75, 042501 (2012)

3. Low TcFermi-liquid properties not hidden by SCMackenzie et al., PRL 80, 161 (1998)

0 1 2 3Residual resistivity (µ⌦ cm)

0

0.5

1

1.5

T c(K

)

FitMackenzie et al.Sr2RuO4 Tc134

Pre

ssure

Temperature

Tc

3He-B

Fermi-liquid

3He-A

Solid

So why Sr2RuO4 ?

Some questions about 1/τopt(ω,T)

1. 1/τ∝Tµ ?

What is the value of µ ?

2. 1/τopt∝ωη ?

What is the value of η ?3. 1/τopt(ω,T)∝ω2+(pπkBT)2 ?

What is the value of p ?

Stricker et al. unpublished (2015)

0 10 20 30

40

50

Temperature (K)

0

5

10

15

⇢ab

(µ⌦

cm

)

Fit (1.8 K T 8 K)Experimental data

⇢(T ) = aTµ +⇢0

0 10 20 30 40 50

Temperature (K)

1.4

1.6

1.8

2

µ(T)

Fit for 1.8 K T 0 T

0 10 20 30

40

50 60

Temperature (K)

0

5

10

15

⇢c

(m⌦

cm

)

Fit (3K T 0 7K)

0 10 20 30 40 50 60

Temperature (K)

1.4

1.6

1.8

2

µ(T)

Fit for 3K T 0 T

Transport : What is the value of µ ?

µ = 2

RRR = 6930K300K RRR = 1220K

150K

Crystals from R. Fittipaldi and A. Vecchione, Salerno, Italy


1. 1/τ∝Tµ ?

µ = 2

2. 1/τopt∝ωη ?

What is the value of η ?3. 1/τopt(ω,T)∝ω2 + (pπkBT)2 ?


✓

IsampleIgold

R(!) =Isample

(!)

Ireference

(!)

Ireference�mirror

(!)

Isample�mirror

(!)R(!) =R(!) =

Isample(!)R(!) =Isample(!)

Ireference(!)

Reflectivity (3 meV - 3 eV)

R(!) =1�

p✏(!)

1 +p

✏(!)Ellipsometry(0.47 eV - 6.2 eV)

Optical Spectroscopy

Crystals from R. Fittipaldi and A. Vecchione, Salerno, Italy

Sr2RuO4 Optical spectroscopy

0 1 2 3

4

5 6

Photon energy (eV)

0

0.2

0.4

0.6

0.8

1

Refl

ectivity

(a)

0 20

40

60

80

Photon energy (meV)

0.92

0.94

0.96

0.98

Refl

ectivity

(1)

(2)

(3)

(b)

0 0.5 1 1.5

Photon energy (eV)

0

0.2

0.4

0.6

0.8

1

Refl

ectivity

9 K

50 K

100 K

150 K

200 K

250 K

290 K

(c)

0 20 40 60 80

Photon energy (meV)

0

0.2

0.4

0.6

0.8

Refl

ectivity

(1)

(2)

(3)

(d)

Plasma frequency ωp = 3.3 eVNo interband below 1 eV

Stricker et al. PRL 113, 087404 (2014)

10�2 10�1 100

Photon energy (eV)

103

104

�1(!)

(Scm�1

) 9 K50 K100 K150 K200 K250 K290 K

(c)

0 50 100 150 200 250

Temperature (K)

0

30

60

90

⇢(µ⌦

cm)

Hagen-Rubensdc transport

(a)

10�2 10�1 100

Photon energy (eV)

101

102

�1 (!)

(Scm�

1)

(d)

0 50 100 150 200 250

Temperature (K)

0

10

20 ⇢(m⌦

cm)

(b)Drude-Lorentz fitHagen-Rubens

Kramers-Kronig

10�2 10�1 100

Photon energy (eV)

103

104

�1(!)

(Scm�1

) 9 K50 K100 K150 K200 K250 K290 K

(c)

0 50 100 150 200 250

Temperature (K)

0

30

60

90⇢

(µ⌦

cm)

Hagen-Rubensdc transport

(a)

10�2 10�1 100

Photon energy (eV)

101

102

�1 (!)

(Scm�

1)

(d)

0 50 100 150 200 250

Temperature (K)

0

10

20 ⇢(m⌦

cm)

(b)Drude-Lorentz fitHagen-Rubens

Very good agreement with dc conductivity

Lee et al., PRL 89, 257402 (2002)

0 50 100 150 200

Photon energy (meV)

0

50

100

150

~h!�

opt

(m

eV

)

(a)

0 50 100 150 200

Photon energy (meV)

0

50

100

150

200

250

300

~h/⌧

opt

(m

eV

)

290 K

275 K

250 K

200 K

150 K

100 K

50 K

9 K

(b)

!2

p

4⇡i�(!, T )= ![1 + �

opt

(!)] +i

⌧opt

(!)

0 10 20 30 40~h! (meV)

0

10

20

30

40

5043 K, ⌘ = 1.936 K, ⌘ = 2.329 K, ⌘ = 1.722 K, ⌘ = 1.915 K, ⌘ = 1.29 K, ⌘ = 1.8


Sr2RuO4 Mass renormalization and relaxation rate

η ≈ 2

m*(ω)/m ~ ħωFermi Liquid : ~ ħω2


1. 1/τ∝Tµ ?

µ = 2

2. 1/τopt∝ωη ?

η ≈ 2

3. 1/τopt(ω,T)∝ω2+(pπkBT)2 ?


✓

✓

0 10 20 30 40~h! (meV)

0

10

20

30

40

5043 K, ⌘ = 1.936 K, ⌘ = 2.329 K, ⌘ = 1.722 K, ⌘ = 1.915 K, ⌘ = 1.29 K, ⌘ = 1.8


1. 1/τ∝Tµ ?

µ = 2

2. 1/τopt∝ωη ?

η ≈ 2



✓

✓ω

1/τ

(ω)

0 10 20 30 40~h! (meV)

0

10

20

30

40

5043 K, ⌘ = 1.936 K, ⌘ = 2.329 K, ⌘ = 1.722 K, ⌘ = 1.915 K, ⌘ = 1.29 K, ⌘ = 1.8


1. 1/τ∝Tµ ?

µ = 2

2. 1/τopt∝ωη ?

η ≈ 2



✓

✓ω2

1/τ

(ω)

0 10 20 30 40~h! (meV)

0

10

20

30

40

5043 K, ⌘ = 1.936 K, ⌘ = 2.329 K, ⌘ = 1.722 K, ⌘ = 1.915 K, ⌘ = 1.29 K, ⌘ = 1.8

0 1000 2000 3000 4000 5000 6000

(ħhω)2 (meV2)

0

20

40

60

80

100

120

140

160

180

200ħh/τ

(meV

)

20 30 40 50 60 70

(ħhω) (meV)Tem

peraturephonons

0 500 1000 1500

⇠2

p (meV

2

)

0

10

20

30

40

50

~h/⌧

opt

(!,T)

(m

eV

)

p = 2

Tmax

= 40K

T=

9K T=

40

K

Sr2RuO4 Scaling collapse in the thermal regime


rescaling the energy axis by ξp2 = (ħω)2 + (pπkBT)2

Statistics with 9 K < T < Tmax and 3 meV < ħω < 36 meV

50 70 90Tmax

1.5

2p

Sr2RuO4 is a perfect Fermi liquid

1. 1/τ∝Tµ ?

µ = 2

2. 1/τopt∝ωη ?

η ≈ 2


p = 2 first experimental proof

✓

✓

✓

Optics + DMFT calculationsRe σ + i Im σ o DFT + LDA and DMFT— Experiment--- Universal Fermi liquid form


10

�1

10

0

10

1

10

2

~h!/(2⇡kB

T )

Con

du

ctivity

(kS

cm

�1) T = 19 K

0.01 0.1

1

Photon energy (eV)

10

�1

10

0

10

1

10

2

~h!/(2⇡kB

T )

10

0

10

1

10

2

T = 29 K

0.01 0.1

1

Photon energy (eV)

10

�2

10

�1

10

0

10

1

~h!/(2⇡kB

T )

Con

du

ctivity

(kS

cm

�1) T = 116 K

0.001 0.01 0.1

1

Photon energy (eV)

10

�2

10

�1

10

0

10

1

~h!/(2⇡kB

T )

10

0

10

1

T = 290 K

0.01 0.1

1

Photon energy (eV)

Beautiful agreement at low temperature and energy

No e-phonon/impurity scatteringNo scale adjustmentThermal shoulder confirmed

Signature of FL is a deviation from Drude

Very good fit below 40 KFrequency dependence of 1/τopt

Clear deviations from FL above ~ 0.1 eV.

Very well described by DMFT !

Mravlje, Georges et al., PRL 106, 096401 (2011)Deng, Georges et al., PRL 110, 086401 (2012)Berthod et al. PRB 87, 115109 (2013)

Stricker et al. PRL 113, 087404 (2014)Mravlje, Georges et al. PRL 106, 096401 (2011) Deng, Georges et al. PRL 110, 086401 (2012)DMFT QP scattering

Well above TFL well-defined single-particle excitations or resilient quasiparticles continue to exist which

1. Are broad but with 1/τ not exceeding ~ πkBT2. Do not obey Landau’s T2

3. Stronger dispersion than LDA one in sharp contrast to the low-energy effective mass in the FL regime.

0 50 100 150 200

Photon energy (meV)

0

50

100

150

~h!�

opt

(m

eV

)

(a)

0 50 100 150 200

Photon energy (meV)

0

50

100

150

200

250

300

~h/⌧

opt

(m

eV

)

290 K

275 K

250 K

200 K

150 K

100 K

50 K

9 K

(b)

�0.5 �0.25 0 0.25 0.5" (eV)

0

0.1

0.2

0.3

0.4

0.51/⌧

qp(e

V)

LDA+DMFT – x y

LDA+DMFT – xz

FL – x y

FL – xz

ω

ℏτqp-1

QP

RQP

ℏτqp~ω

2

ℏτ qp~ω

-1

τ-1< E < kBT

� (100)(110) � (101) Z � (111)(011) ��2.5

�2

�1.5

�1

�0.5

0

0.5

1

Ener

gy(e

V)

0

2

4

6

8

10

K-resolved spectral function

Stricker & Mravlje et al. PRL 113, 087404 (2014)


1. Non-Drude ≢ non-Fermi-liquid

2. First experiment indicating accurately the FL behavior (p = 2) !

3. The FL regime provides the reference to characterize without ambiguity the deviations from FL theory

4. First optical proof of Resilient Quasiparticles with non-FL lifetime.

5. Question : Why is it the only Fermi-liquid with p = 2 ?

Intermediate conclusions

Mackenzie & Maeno, Rev. Mod. Phys. 75 2 (2003)

firm the basic electronic structure of Oguchi. In the ab-sence of experimental data, the calculated electronicstructure would undoubtedly have been useful in analyz-ing subsequent experiments. However, the failure ofband-structure calculations to account for some key fea-tures of cuprate physics might have led to some skepti-cism about trusting calculation details on isostructuralSr2RuO4 . Fortunately, it has proved to be possible toobtain detailed information about the Fermi surface andquasiparticle spectrum of Sr2RuO4 experimentally, byobserving quantum oscillations (see Sec. II.B).

3. Anisotropic electrical conductivity

The anisotropic dc resistivity (!) of single-crystalSr2RuO4 was first reported by Lichtenberg and collabo-rators (1992), two years before the discovery of the su-perconductivity. Their basic results are in agreementwith those shown in Fig. 5, which are from a later paper(Hussey et al., 1998). The resistivity is strongly aniso-tropic, with low-temperature ratios varying between 400and 4000 reported by several groups.16 At high tempera-tures, !c (the interplane resistivity) decreases with in-creasing temperature, characteristic of an incoherentconduction mechanism. Similar behavior is seen in manycuprate materials (see, e.g., Clarke and Strong, 1997,and references therein). As the temperature is lowered,however, !c goes through a broad maximum at approxi-mately 130 K and then follows a metallic temperaturedependence down to Tc . The in-plane resistivity, !ab , ismetallic from 300 K to low temperatures, and below ap-proximately 20 K, both !ab and !c have an approximateT2 dependence, as shown in the inset. This T2 depen-dence of ! at low temperatures is consistent with thepredictions of the Fermi-liquid theory of metals, inwhich a quadratic temperature dependence of the

quasiparticle-quasiparticle scattering rate is imposed byphase-space restrictions on the scattering process (see,e.g., Schofield, 1999). A particularly notable feature isthe very low residual resistivity of less than 1 "# cm,which gives evidence of the high sample purity.

Another important aspect of the dc transport shownin Fig. 5 is the temperature-independent resistive anisot-ropy below 20 K, which strongly suggests that a standardanisotropic effective-mass approach is valid for under-standing the conduction. This implies highly anisotropic,but basically three-dimensional, conduction at low tem-peratures, with coherent band formation in the c direc-tion. Although the temperature dependence of !c in thecuprates shows considerable variation with material anddoping level, the key feature of the temperature-independent anisotropy has never been observed in acuprate. The idea of coherent transport in all directionsat low temperatures in Sr2RuO4 is consistent with astudy of ac conductivity by Katsufuji et al. (1996), whosemain results are summarized in Fig. 6. Below 30 K, aDrude peak is seen with the electric field applied bothparallel and perpendicular to the RuO2 planes. Bulkelectrical transport data, then, are consistent with theexistence of a Fermi liquid at low temperatures inSr2RuO4 (Maeno et al., 1997). The mechanism of con-duction at higher temperatures is an interesting issue,which is mentioned again in Appendix A, along with adiscussion of the effects of high pressure on the normal-state transport.

16See Lichtenberg et al. (1992); Maeno et al. (1994, 1997);Yoshida (1997); Tyler et al. (1998); Ohmichi et al. (2000).

FIG. 5. Anisotropic resistivity in Sr2RuO4 , from Hussey et al.(1998). The dotted line in the inset, showing the low-temperature T2 dependence expected of a Fermi liquid, is forcomparison with the data.

FIG. 6. Optical conductivity data for Sr2RuO4 showing that aDrude peak for transport perpendicular to the Ru-O planesonly develops at low temperatures (a), while the one for in-plane transport exists up to room temperature (b). The inset to(a) is a comparison between optical and dc transport perpen-dicular to the planes. From Katsufuji et al. (1996).

664 A. P. Mackenzie and Y. Maeno: Superconductivity of Sr2RuO4 and the physics of spin-triplet pairing

Rev. Mod. Phys., Vol. 75, No. 2, April 2003

Kidd, PRL 94107003 (2005)

Orbital Dependence of the Fermi Liquid State in Sr2RuO4

T. E. Kidd, T. Valla, A. V. Fedorov,* and P. D. JohnsonPhysics Department, Brookhaven National Laboratory, Upton, New York 11973, USA

R. J. Cava and M. K. HaasDepartment of Chemistry and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08540, USA

(Received 24 November 2004; published 16 March 2005)

We have used angle-resolved photoemission spectroscopy to determine the bulk electronic structure ofSr2RuO4 above and below the Fermi liquid crossover near 25 K. Our measurements indicate that theproperties of the system are highly orbital dependent. The quasi-2D ! band displays Fermi liquid behaviorwhile the remaining low energy bands show exotic properties consistent with quasi-1D behavior. In theFermi liquid state below 25 K, the ! band dominates the electronic properties, while at highertemperatures the quasi-1D " and # bands become more important.

DOI: 10.1103/PhysRevLett.94.107003 PACS numbers: 74.70.Pq, 71.10.Ay, 79.60.-i

The physics of low dimensional systems is determinedby their electronic structure near the Fermi level. The lowenergy excitations in these states can give rise to exoticphenomena such as Mott insulators [1], charge and spindensity waves [2], and high temperature superconductivity[3]. Sr2RuO4, known for being the only perovskite super-conductor without Cu-O planes [4], is a particularly inter-esting example. Unlike the cuprates, which at optimal dop-ing enter the superconducting phase from a non-Fermiliquid state, strontium ruthenate is known to show Fermiliquid properties well above the superconducting transi-tion. The electronic structure in this material is actuallyquite complex, with three bands that are either quasi-one- or two-dimensional depending on their orbital sym-metry [5].

The normal state transport in Sr2RuO4 is defined by twodistinct phases. Below 25 K, the system acts like a simpleanisotropic metal, although with strong electron correla-tions. The T2 dependent resistivity [6] and linear specificheat [7] are well described by Fermi liquid theory. It is veryunusual to witness these Fermi liquid properties in trans-port, as in simple metals these excitations are overwhelmedby electron-phonon interactions. As the temperature israised, the system undergoes a broad crossover, and thesystem shows distinct non-Fermi liquid behavior. A tem-perature dependent anisotropy between the c axis and in-plane transport properties is developed, resulting in a fully2D material with a peak in the c-axis resistivity near 130 Kand an in-plane resistivity with a linear T dependence withno signs of saturation at the highest temperatures [8]. Thistransformation from a highly anisotropic Fermi liquid to abad metal much like the normal state seen in the high-TCcuprates indicates that the scattering mechanisms are verydifferent between the high and low temperature phases.

While dimensional crossovers of this sort are wellknown in low dimensional materials [9], Sr2RuO4 is asomewhat unique case owing to the nature of its electronicstructure. The carriers in the system arise from three Ru t2g

states, forming the Fermi surface shown in Fig. 1(a). Thedxz and dyz orbitals make up the highly 1D bands " and #,while the 2D ! band arises from the dxy orbital [5,10].Because the interactions between the 1D and 2D bands arevery weak, there are several aspects of the system that arisefrom either one or the other subset, such as the nature of thesuperconducting ground state [11], ferromagnetic excita-tions from ! [12], and antiferromagnetic excitations due tonesting between # and " [10,13].

Γ M

X

γ

βα

k|| (Å-1

)

0.50 0.60 0.70 0.80

Inte

nsity

(ar

b. u

nits

) InitialAfter Cycling

γβ

γβ

γβ Sβ Sγ

(a) (b)

(c) (d)

-0.05

0.00

0.05

0.10

0.15

0.20

Bin

ding

Ene

rgy

(eV

)

-0.05

0.00

0.05

0.10

0.15

0.20

Bin

ding

Ene

rgy

(eV

)

FIG. 1. (a) Schematic Fermi surface of Sr2RuO4.(b) Photoemission spectra taken along the !-M direction fromthe freshly cleaved sample. Both surface (S" and S!) and bulk "and ! contributions can be seen. (c) MDC’s taken at the Fermilevel (after the suppression of the surface state) at the beginningand end of the experiment. (d) Spectra taken after aging processwith only bulk contributions remaining.

PRL 94, 107003 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending18 MARCH 2005

0031-9007=05=94(10)=107003(4)$23.00 107003-1 © 2005 The American Physical Society

Two decade of transport measurement …

0 100 200

Temperature (K)

0

30

60

90

120

⇢ab

(µ⌦

cm

)

Fit (1.6 K to 8 K)

Experimental data

T ?

2A1T

2A2T+ B2T

0 100 200

Temperature (K)

0

0.2

0.4

d⇢

ab

/dT

(µ⌦

cm

K

�1)

Exp. data

Fit

(b)Tmax

0 100 200 300

Temperature (K)

0

10

20

30

⇢c

(m⌦

cm

)

(d)TfFL

Tfimax

0 100 200 300

Temperature (K)

0

0.1

0.2

0.3

0.4

d⇢

c

/dT

(m⌦

cm

K

�1)

What is the « glue » of electrons in Sr2RuO4

ρ

T

Susceptibility

Susceptibility of correlations

⌃(!) =1

⇡

Z 1

�1d⌦ I2�00(⌦)

Z 1

�1d"N(")

f(�") + b(⌦)

! � ⌦� "+ i0+

core functionscatteredelectron

incomingelectron I

I�00

ω

χ’’(ω

)

3D Fe

rmi-liq

uid

I2�00 = ↵2F (!) + ��00charge + ��00

spin

slope

= I*n(EF)

ρ

T

Susceptibility

Susceptibility of correlations

⌃(!) =1

⇡

Z 1

�1d⌦ I2�00(⌦)

Z 1

�1d"N(")

f(�") + b(⌦)

! � ⌦� "+ i0+

core functionscatteredelectron

incomingelectron I

I�00

ω

χ’’(ω

)I2�00 = ↵2F (!) + ��00

charge + ��00spin

slope

= I*n(EF)

ω★

kBω★

2πTFL=

0 100 200

Temperature (K)

0

30

60

90

120

⇢ab

(µ⌦

cm

)

Fit (1.6 K to 8 K)

Experimental data

T ?

2A1T

2A2T+ B2T

0 100 200

Temperature (K)

0

0.2

0.4

d⇢

ab

/dT

(µ⌦

cm

K

�1)

Exp. data

Fit

(b)Tmax

0 100 200 300

Temperature (K)

0

10

20

30

⇢c

(m⌦

cm

)

(d)TfFL

Tfimax

0 100 200 300

Temperature (K)

0

0.1

0.2

0.3

0.4

d⇢

c

/dT

(m⌦

cm

K

�1)

What is the « glue » of electrons in Sr2RuO4

0 0.02 0.04 0.06 0.08 0.1

Photon energy (eV)

0

0.02

0.04

0.06

0.08

0.1

I2

�00 (!) ω★ = 13.8 meV

(a)

0 500 1000Temperature (K)

0

0.3

0.6

0.9

1.2

1.5⇢

ab(m⌦

cm)

Tyler et al.Fit

(b)

0 500 1000Temperature (K)

0

0.5

1

1.5

d⇢ab/d

T(µ⌦

cmK�1

)

Tyler et al. PRB 58 R10107 (1998)

0 0.02 0.04 0.06 0.08 0.1

Photon energy (eV)

0

0.02

0.04

0.06

0.08

0.1

I2

�00 (!) ω1★ = 13.8 meV

ω2★ = 0.5 eV

Case n°1 : 3D Fermi liquid ?

α, β, γ bands

Van Hove Singularity

Case n°2 : Resilient Quasiparticles ?

Case n°3 : collective modes ?

2D paramagnon

2D phonon

any modes with lineardispersion in 2D…

Case n°4 : Dimensional crossover ?

Transition too sharp ?�2 �1.5 �1 �0.5 0 0.5 1" (eV)

0

0.5

1

1.5 �(")/�(0)N(")/N(0)

0 0.02 0.04 0.06 0.08 0.1

Photon energy (eV)

0

0.02

0.04

0.06

0.08

0.1

I2

�00 (!) ω1★ = 13.8 meV

ω2★ = 0.5 eV

Open question

K. Chen, PRB 84 245107 (2011)

Fischer & Sigrist EPL 85 2 (2009)


Stricker et al. in prep (2015)

…

1. Sr2RuO4 the archetypal Fermi-liquid

Correct scaling with p = 2

Low-frequency « Drude Foot »

Q : Why is it the only one ?

2. Sr2RuO4 the not so simple Fermi-liquid

Resilient quasiparticles

Two different mechanism link the electron together

Q : The origin of TFL ?

Thank you

FERMI LIQUID BEHAVIOUR IN STRONGLY CORRELATED METALSf1web.ijs.si/~zitko/conference.ngsces.org/2015/wp-content/uploads/… · NGSCES 2015 — Trogir September 2015 Damien Stricker

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