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Lecture schedule October 3 – 7, 2011. #1 Kondo effect #2 Spin glasses #3 Giant magnetoresistance #4 Magnetoelectrics and multiferroics #5 High temperature superconductivity #6 Applications of superconductivity #7 Heavy fermions #8 Hidden order in URu 2 Si 2

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Lecture schedule October 3 – 7, 2011

  • #1 Kondo effect
  • #2 Spin glasses
  • #3 Giant magnetoresistance
  • #4 Magnetoelectrics and multiferroics
  • #5 High temperature superconductivity
  • #6 Applications of superconductivity
  • #7 Heavy fermions
  • #8 Hidden order in URu2Si2
  • #9 Modern experimental methods in correlated electron systems
  • #10 Quantum phase transitions

Present basic experimental phenomena of the above topics

some spectroscopy studies of the ho state of uru 2 si 2

Some Spectroscopy Studies of the HO State of URu2Si2


Inelastic neutron scattering (spin)

Optical conductivity (charge)

Ultrasonic velocity (thermo.) [and attenuation (transp.)]

ARPES (charge)

STM/STS (charge and spin)

[But not PCS,  & QO]

J. A. Mydosh

Kamerlingh Onnes Laboratory, Leiden University, The Netherlands

what is hidden order ho
What is “Hidden Order” (HO)?

[See, e.g. N. Shah, P. Chandra, P. Coleman and JAM, PRB 6I, 564(2000).]

Now quite common usage of HO. Or as some theorists call it “Dark Quantum Matter” or as others call it “Novel Forms of Order” and “Novel Phases” {Reserve for high-field phases} or ‘‘Dark Order’’.

A clear, from bulk thermodynamic and transport measurements, phase transition at T0 where the order parameter (OP) and elementary excitations (EE) are unknown, i.e., cannot be determined from microscopic experiments.

Ψ is primary, unknown OP; m is antiferromagnetic, secondary OP

key unsolved problems questions of ho in uru 2 si 2
Key Unsolved Problems/Questions of HO in URu2Si2
  • Local, dual or itinerant?
  • OP’s primary / secondary?
  • Mediator of phase transition?
  • INS resonance mode causing HO: Q0 or Q1 ?
  • How to probe OP experimental?
  • Relation of HO to LMAF (Adiabatic Continuity)?
  • Symmetry breaking in HO vs. LMAF?
  • Spin – charge duality?
  • HF Liq.(hybridization) or Kondo Liq. at coherence T*?
  • Kondo effect in (Th1-xUx)Ru2Si2?
  • Generic  HO in other materials? Or is URu2Si2 unique?
  • Missing link experiments?(Hall effect under pressure, etc.)
  • Many theories/models -- which one is solution to HO?
spin inelastic neutron scattering resonances at q o 1 0 0 and q 1 1 4 0 0
Spin:Inelastic neutron scattering - “resonances” at Qo=(1,0,0) and Q1=(1.4,0,0)
  • Broholm et al. PRL & PRB(1987 – 1991)
  • Wiebe et al. NP(2007)
  • Bourdarot et al. JPSJ(2010) ?(2011)?
  • Niklowitz et al. to be published(2011)
excitation spectrum of uru 2 si 2 at 1 5k along h 0 0
Excitation spectrum of URu2Si2 at 1.5K along (H,0,0)


Cones of excitations persist to higher T>To and E~10meV. Well-correlated itinerant-like spin excitations at Q1(incomm). Strongly coupled spin and charge degrees of freedom.

resonance at e 0 for magnetic response at q o
Resonance at E0 for magnetic response at Qo

Longitudinal mode at 1.5K with continuum of Q-E scattering persisting to higher energies.

resonance at e 1 for magnetic response at q 1
Resonance at E1 for magnetic response at Q1

Longitudinal mode at 1.5K with continuum of Q-E scattering persisting to higher energies.

t dependence of q o resonance
T-dependence of Qo resonance

Growth of intensity below To = 17.8K with Q-E continuum

t dependence of resonance gap e 0 at q o
T-dependence of resonance gap E0 at Qo

E0 represents a long lifetime (small decreasing half-width) collective mode rapidly reaching its final value 1.7 meV.

integrated intensity of dynamical spin susceptibility what about at q 1 incommensurate resonance
Integrated intensity of dynamical spin susceptibilityWhat about at Q1 incommensurate resonance?

Red line is a BCS-type gap fit giving T-dependence of HO-OP. No divergence of static spin susceptibility, i.e, HO non-magnetic.

low energy excitations scanned through ho transition niklowitz et al unpublished 2011
Low energy excitations scanned through HO transition Niklowitz et al.(unpublished,2011)

Note peak at To for commensurate mode and step for incommen. mode

pressure temperature phase diagram
Pressure – temperature phase diagram


Collection of results by Niklowitz et al. PRL(2010).

pressure dependences of e 0 e 1 and bulk gap vaules
Pressure dependences of E0, E1 and bulk gap vaules


LMAF Bragg peaks

E0 disappears in LMAF phase, others persist. Note similar energy scales comparable to theoretical models.

charge optical conductivity
Charge: Optical Conductivity
  • Bonn et al. PRL(1988)
  • van der Marel et al. unpublished(2010 - 2011)
  • Lobo et al. unpublished(2010)
  • Timusk et al. cond-mat.(2011)

HO-gap in URu2Si2 measured through optical conductivity, D. A. Bonn et al. PRL (1988).

Preliminary data in a – a plane, gapping(~45cm-1) into HO phase. Strong phonons. Missing Drude peak and correlation gap

reflectivity to optical conductivity along a and c
Reflectivity to optical conductivity along a and c

Clear but slow crossover (opening) of hybridization gap at 44K, persisting into HO gapping regime (not seen here).

extracting of scattering rate 1 as function of t via extended drude model
Extracting of scattering rate -1 as function of T & ωvia extended Drude model

Note decrease of -1 into hyb. gap

optical conductivity along a and c axes
Optical conductivity along a and c-axes

Opening of correlation gap ~15meV(125cm-1), clearer along a. Note low energy Drude peak and phonon modes.

optical conductivity 20 70k in hybridization gap region extrapolated to 0 via drude peak analysis
Optical conductivity 20 – 70K in hybridization gap region extrapolated to ω 0 via Drude peak analysis

W(ω) is loss of spectra weight accumulation

Note opening of hydridization gap below 50K

relaxation rate governing the frequency dependent scattering in hybribization gap region
Relaxation rate governing the frequency dependent scattering in hybribization gap region

As T increases scattering becomes incoherent

lower frequency e optical conductivity above t o labo et al private communication 2010
Lower frequency (E) optical conductivity above To Labo et al., private communication, 2010.

Clear onset of hybridization gapping(~15 meV) below 50K. Drude peak forming at 2 meV(15 cm-1). Note phonons.

low t low e optical conductivity probing ho
Low T, low E optical conductivity probing HO

HO gapping ~5meV with transfer of spectral wt. to just above gap and shifting of Drude peak to smaller E. Need lower E & T!

some conclusions
Some conclusions
  • Drude peak narrows below coherent T*(≈ 70K) crossover into hybridization gapping (≈ 15meV)
  • Reflection peak (HO – gap) observed at lowest frequencies, (ω < 30cm-1 ). Need conversion into optical conductivity. New low ω technique/apparatus is necessary.
              • Gap (5meV) in the charge channel develops at the HO transition
      • Difference between a & c axes – gap anisotropy
      • Missing low frequency spectral suggests that a very narrow Drude peak exists
              • 47 meV phonon coupled to carriers plays (role in the scattering of the incoherent phase?)
t e dependences of optical conductivity
T – E dependences of optical conductivity

Note lack of intensity(conductivity) above To – correlation gap. No clear sign of HO gap. Need lower T and E.

Thermodynamics: Ultrasonics velocity (attenuation as transport prop.) Determination of elastic constants, cij
  • Lüthi et al. JLTP (1994)
  • Kuwahara et al. JPSJ (1997)
elastic constants c v 2 c 11 c 33 c 44 c 66
Elastic constants (c = ρv2 ): c11, c33, c44; c66

Note c11 only longitudinal mode showing softening for T < 80K, min. 30K and HO shoulder.

analysis of elastic constant c ij behavior of uru 2 si 2
Analysis of elastic constant cij behavior of URu2Si2

Need new interpretation here: softening due to slow opening of hybridization gap. No CDW?

charge arpes
Charge: ARPES
  • J. Denlinger et al. JES&RP(2001)
  • A. Santander-Syro et al. NP(2009)
  • R. Yoshida et al. PRB(2010)
  • Kawasaki et al. PRB(2011)
  • G. Dakovski et al. PRB(to be published, 2011)
  • XXX et al. ??? (2012)

Among the many difficulties of ARPES: URu2Si2 is 3D thus depending upon the energy tuning one scans an arc through the BZ (or changing detector angle).

Note in bct the high symmetry directions Γ, Z; X

denlinger et al 2001 pioneering work
Denlinger et al.(2001) – pioneering work
  • Synchrotron scans  14 - 230 eV with ΔE > 50 meV at T > 20K.
  • Good resolution and DFT comparisons of 4d (Ru); 5d (U) lower bands. Poor agreement with “old” LDA bands near EF.
  • But Fermi surface mapping.
  • Insufficient resolution for near FS and qp studies.
  • Surface states/bands difficulties!
  • X hole pocket observed in FS, not confirmed!!!
  • Local 5f2 model!
  • Awaiting new results at SCES-2011.

Comparisons ARPES vs (old) LDA

Fermi energy intensity maps off(85ev) / on(112eV)-resonance, 5f enhancement

X-point descrepancy: distinct hole pocket; LDA : small elec. pocket, also

 pts. vs large contours

DFT-LDA calculations bold=hole; fine=electron

santander syro et al 2009 t dependences
Santander Syro et al. (2009) – T dependences
  • Temperature scan into HO state
  • He lamp low energy (21 eV), high resolution ARPES
  • Surface states, poor vacuum
  • Two k space directions: [100] and [110]
  • Band of heavy quasi-particles drops below EFupon entering the HO state
  • Large restructuring of FS in HO
  • Many difficulties with data and analyses
  • Reproducible?

Integrated photoemission spectra along <110>Note quasiparticle peak that moves below To: Dispersing band of heavy QP, new electron pocket in HO state

Surface state

Surface state

heavy qp band hybridized with light hole conduction band along 110 at 13 k
Heavy qp band hybridized with light hole conduction band along <110> at 13 K

ARPES intensity


Averging of 2nd derivatives along E and k


heavy qp band hybridized with light hole conduction band along 100 at 15 k
Heavy qp band hybridized with light hole conduction band along <100> at 15 K

ARPES intensity


yoshida et al 2010 laser arpes
Yoshida et al.(2010) – Laser Arpes
  • Low energy (7 eV) Laser ARPES, high resolution (2 meV), good vacuum technique
  • Narrow, dispersive band in HO only, few meV from FS
  • Yet non-FS crossing
  • Destroyed with Rh doping on Ru sites
  • Another hole-like dispersive crossing band and surface states at ~35 meV
  • “Periodicity modification“: HO doubling of unit-cell, band backfolding, predicted by Oppeneer et al.
  • Low energy ARPES is only sensitive to d-bands, cannot detect 5f-U bands. Seeing broad (partially hybridized) 4d-Ru bands which appear in HO state
laser arpes intensity at 7k for 110 and 100
Laser ARPES intensity at 7K for [110] and [100]

Hole-like dispersion

Surface state

kawasaki et al 2011 soft x ray arpes
Kawasaki et al.(2011) Soft X-ray ARPES
  • Energy 760 eV with resolution 140 meV
  • Vary energy or detector angle to scan BZ
  • Spanning vast k-space, all of high symmetry BZ
  • Bands below 0.6 eV are Ru-4d states, agreeing with previous ARPES
  • Band above 0.6 eV to EF disagree with previous ARPES, e.g.,surface band at  not observed here. No hole band at X.
  • All U-based 5f bands are itinerant!!!
  • Quasiparticle bands clearly observed at Z(large hole FS and at (large electron FS) with some nesting
  • APRES bands consistent with LDA of Oppeneer et al.
bz with orange and blue scanning planes spectral image comparison with lda band structure
BZ with orange and blue scanning planes. Spectral image comparison with LDA band structure

Measured spectral weight along hi-sym.

Bands 4, 5; 6 cross EF

Calculated BS Agreement with LDA of Oppeneer

photoemission intensity with fs crossings and lda comparison
Photoemission intensity with FS crossings and LDA comparison

Intensity around EF

Indicated band crossings

Calculated band crossings: 6, 5; 4 with C, B; A, and 4; 5 with D; E

fermi surface images compared with lda
Fermi surface images compared with LDA

Estimated Fermi surfaces

with nesting vectors

Integrated intensity

Band structure FS’’s

dakovski et al 2011 time resolved arpes
Dakovski et al.(2011) Time Resolved ARPES
  • Pump (1.55 eV)– Probe (29.5 eV) method. First for SCES
  • Tune ARPES on URu2Si2 to focus on “hot spots” (maximium gap) in k-space, i.e., below Z in <110> plane as determined from band structure
  • Excite quasiparticles via pump, probe their fs decay
  • Measurements above To rapid fs decay within hybridization gap
  • Measurements below To qp excited above HO gap have longer fs decay times
  • Momentum (k) dependent interactions at hot spots causing HO gapping
  • Energy resolution: tr-ARPES ≈100meV; ARPES ≈10meV
comparison spectral intensity above and below t o note q 110 0 56 separating two hot spots in 110
Comparison spectral intensity above and below To Note q <110> = 0.56 separating two hot spots in <110>

ARPES (34eV,

12K) at Z. Note flat band above EF and agree-ment with Kawasaki for lower bands.

cartoon model for t evolution of hybrid and ho gaps
Cartoon model for T evolution of hybrid. and HO gaps

Hot Spots

3D FS with hot spots

See Oppeneer et al. PRB(2010)

conclusions drawn from arpes
Conclusions drawn from ARPES
  • Cleaving problem solved, requires ultra high vacuum
  • Surface states – solved?
  • Need better resolution at higher E-scans for FS mapping
  • Inconsistencies among measurements
  • Present data pushed too far
  • Yet striving towards efficacious solution of this difficult technique (note 1990’s ARPES in HTS)
  • HO gapping not clearly found or hybridization gap seen
  • First tr-ARPES on heavy fermion material

Stop Thanks


Charge and Spin: Visualizing the HO in URu2Si2

Aynajian, Yazadani et al. PNAS(2010)

Pegor Aynajian, Eduardo H. da Silva Neto, Colin V. Parker

Department of Physics, Princeton University

Yingkai Huang

van der Walls-Zeeman Institute, University of Amsterdam

Abhay Pasupathy

Department of Physics, Columbia University, New York

John Mydosh

Kamerlingh Onnes Laboratory, Leiden University

Ali Yazdani

Department of Physics, Princeton University

Supported by


Kondo-Fanoresonance in URu2Si2

q=1.3±0.3 ; Eo=5±2meV


Fano Lineshape

Reminiscent of Fano lineshape in single Kondoimpurities

q : Ratio of tunneling probability to the descrete level and the continuum.



D(V) = (V – V0 –iγ) / [(V –V0 –iγ)2 – Δ2]1/2 withγ ~ 1.5 mV


Some Conclusions

  • Recent theoretical work:
  • K. Haule and G. Kotliar, Nature Phys. (2009)
  • M. Maltseva, M. Dzero, and P. Coleman, PRL (2009)
  • Y-f. Yang, PRB(RC) (2009)
  • J. Figgins and D. Morr,PRL (2010)
  • Kondo resonance with Fano lineshape.
  • Mean field-like T dependence of DHO.
  • - DHO asymmetric around EF.
  • DHO strongest between the surface atoms where the Kondo resonance is enhanced.

TheHidden Order in URu2Si2

Interplay of the U’s f electrons with the spd electrons and with each other, results in a rich variety of electronic phases.

Palstra et. al, PRL (1985)

Palstra et. al, PRL (1986)


Variable Temperature STM

Operates between 6K – 180K

Gomes et al. Nature (2007), Pasupathy et al. Science (2008), Pushp et al. Science (2009), Parker et al. PRL (2010)


STM topography on URu2Si2




Atomically ordered lattice:

a~4.2Å corresponding to U or Si



STM spectroscopy on URu2Si2

Averaged electronic density of states:

Above THO=17.5K

Below THO=17.5K





















Entering thehidden order in URu2Si2










A gap in the DOS develops below THO


Entering thehidden order in URu2Si2

DHO turns on with a mean field-like temperature dependece.

Asymmetric gap around EF.

Palstra et al. PRL (1985)

Maple et al. PRL (1986)

Bonn et al. PRL (1998)

Wiebe et al. Nature Physics (2009)


Kondolattice in URu2Si2 ?


q map


Conductance at 6mV








  • Atomic scale modulations.
  • q anti-correlated with topography.
  • - In single Kondo impurity limit, large q indicates higher tunneling probability to the Kondo resonance.