ICTP2012: Innovations in Strongly Correlated Electronic Systems

Wednesday, August 15th
Tom Timusk, "The normal state of URu2Si2: spectroscopic evidence for an anomalous Fermi liquid"
Blogged by Andrey Chubukov 

Tom starts  with the summary of 1988 view of URu2Si2 (the time of first ICTP workshop on correlated electrons)

He discusses  normal state properties of URuSi2: mass enhancement, scattering rate, Drude peak.

 Scattering rate has  a peak  at 20 meV.  There is a coherent Drude peak at 20K,  it becomes incoherent avove 20K.   The conclusion was that at low T/\omega the system is a Fermi liquid  with m^* =25m

In 1988 the community believed that hidden order below 18K is  spin-density-wave (SDW).  Superconductivity (SC) emerges  below 1K. Tom presented arguments for SDW which sounded reasonable back in 1988 but later were found to be in disagreement with the measurements.

20 years have passed (but ICTP workshop is still running!)

He cites STM data by S. Davis group, which show that  at 18.6K (right above  transition into hidden order phase)  the system shows  normal metallic dispersion with m^* =3m. At 5.9K  the  gap develops due to hybridization.   This gap was not detected in earlier opt conductivity data because of  too much noise .

He next describes new method – refined thermal reflectance, which allows one to  change T without moving the sample. He divides all the spectra by reflectance at 25K and argues that accuracy increases substantially (noise is reduced by 8). All  T-independent features in conductivity are lost, all T-dependent features stay.

Tom shows data for \sigma (w) down from 75K.  At T decreases, Drude peak forms.  No change in the total spectral weight  at 15 meV ->  total Drude weight is independent on T (m^* remains the same). Conclusion – heavy mass is already present at 75K.  

Second result – 1/tau  is smaller that \omega up to 30K .  The implication is that a coherent Fermi liquid forms at 30K. He shows plot of \pho (w,T)  [=Re 1/\sigma(w,T)].

 \pho (w, T) follows A (w^2 + b (pi^2 T^2))

Discussion on the value of b follows.  In a Fermi liquid, b should be =4.  He finds,  from high-frequency part, \rho (w,T) = A T^2, A = 0.3 \muOm* cm/K^2  . He next looks at DC resistivity, takes  derivative with respect to T , gets the same A.

Shows Matsuda data in a wider range of T d^2 \pho/dT^2  is almost a const up to 100K (hence T^2 form works).

Discusses the difference  between single fermion lifetime  (m \Sigma (w,T) \propto (w^2 + \pi^2 T^2) and optical lifetime  (1/tau \propto w^2 + b \pi^2 T^2) with b=4. He cites many examples of T^2 resistivity with various A

Examples of b=4?  There are none

UPt3    b<1

Nd0.9TiO3  b =1.1   Ce0.95Ca0.05TiO3   b=1.7

Tom discusses theory proposal from two Russian gringo about resonance impurity scattering.  If Im \Sigma has no T^2 term  then optical conductivity has w^2 + b \pi^2 T^2 form with  b=1

He argues that resonant impurities  are un-hybridized uranium f-electrons.

Last part – hidden order phase

Tom shows data   fitted  by Dynes formula for a dirty SC.  He finds one gap  along ab axis and two gaps along c axis (3.1 meV and 2.7 and 1.8  meV) .  Roughly the same gaps have been found from the resistivity fit and from neutrons.

Questions:  (i) about w/T range and about direct vs indirect gap, (ii) is  the two-component electronic model valid in the hidden order phase,(iii) is b=1 vs b=4 related to vertex corrections?