Post on 01-Sep-2020
Emergence of the Hidden Order State from the Fano Lattice Electronic Structure of the Heavy-Fermion Material URu2Si2
J.C. Séamus Davis
1 5.7(meV)
εf
Mohammad HamidianCornell / BNL
Dr. Andy SchmidtCornell / BNL
Prof. Graeme LukeMcMaster
Dr. Peter WahlCornell/MPI Stuttgart
Cornell/McMaster URu2Si2 Team
Kondo Lattice & Heavy Fermions
Kondo Effect
Kondo Wilson
Heavy Fermion Effects in f-electron Lattices
Interactions bring f level close to E=0 and result in a d-f hybridization and a sharp DOS(E) resonance
Kondo Impurity & Kondo Lattice
High temperature Low temperature
Heavy Fermion Effects in Kondo Lattices
( )
( ) 22
22
||4
)(2)sgn(1
14)(
2||4
V
mD
V
f
ff
kkf
kkf
kk
εεεε
πε
εεεεε
−−+=
++±+=±
Visualize d-f hybridization and heavy electron formation ?
•Many-body resonance εf just above E=0
• Hybridization energy region Γ surrounding εf
• Light d-band beyond Γ from εf
• High DOS and heavy f-band within Γ from εf
Challenge: atomically resolved image of d-f electron hybridization and heavy band formation ?
Heavy Fermion Spectroscopic Imaging STM
0
280
ÅSpectroscopic Imaging STM
-30 -20 -10 0 10 20 30
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Cond
ucta
nce(
ns)
Underground Concrete Vibration Isolation Vault
Remote ControlRoom
Internal Acoustic Isolation Chamber
concreteinertial block
sound room #2: IAC
six air springspump box
lead-filledtable
threeair springs
lead-filledlegs
sound room #1: lab lined with Sonex
vacuumlines
30 Ton
Ultra low vibration cryostat.Ultra low vibration lab.
6 m
Rev. Sci. Inst. 70, 1459 (1999).Spectroscopic Imaging STM Systems
Ultra low vibration cryostat.
to Pumps
Load Lock
LeadFilledLegs
High-field SC Magnet
Lead Filled Table
Turbo Pump
Air Springs
Fridge
Cleaver
L4He -270O
Rev. Sci. Inst. 70, 1459 (1999).Spectroscopic Imaging STM Systems
Rev. Sci. Inst. 70, 1459 (1999).Spectroscopic Imaging STM Systems
10 mK / 9 Tesla / SI-STM
0
280
Å
),(g ErSpectroscopic Image1% Ti atoms on Ru sites
Nature Physics 5, 800 (2009)
Heavy Fermion QPI Example: Sr3Ru2O7
0
280
Å
),(g ErSpectroscopic Image1% Ti atoms on Ru sites
Nature Physics 5, 800 (2009)
Heavy Fermion QPI Example: Sr3Ru2O7
-0.8nS
-1.4nS
-0.05 a. u.
-0.24 a. u.
Nature Physics 5, 800 (2009)
Heavy Fermion QPI Example: Sr3Ru2O7
QPI identification of heavy d-electron (α2) band
Nature Physics 5, 800 (2009)
Visualize d-f hybridization and heavy electron formation ?Can we explore Kondo-Lattice Heavy Fermions similarly?
Single Adatom Kondo Effect
M. Plihal und J.W. Gadzuk, Phys. Rev. B 63, 085404 (2001)O. Újsághy, J. Kroha, L. Szunyogh und A. Zawadowski, Phys. Rev. Lett. 85, 2557 (2000)
r
zd
Substrate
Tip
Adatom
Single Magnetic Adatom Kondo Resonance
Co on Au(111)
V. Madhavan et al, Science 280, 567 (1998)
Single Magnetic Adatom Kondo Resonance
V. Madhavan et al, Science 280, 567 (1998)H. Manoharan et al Nature 403, 512-515 (2000).N. Knorr, et al. Phys. Rev. Lett. 88, 096804 (2002).
‘Fano Spectrum’ of Kondo Resonance
M. Plihal und J.W. Gadzuk, Phys. Rev. B 63, 085404 (2001)
α)(
0)(rd
etrt−
=)(Im)()(Re)(
rGrtrGrq +=
-6 -4 -2 0 2 4 60
5
10
q=0
q=1
q=2
q=3
ε
Fano resonance:
q
Γ
0ε energy of many-body state screening spin
width of resonance (simple Kondo 2kBTk)
Ratio of matrix elements linking tip state to resonance and to continuum
Physical Significance of Fano Signature
( )2/
)(';1''),( 02
2
Γ−
=+
+∝
εEEE
EqErg
Kondo Lattice system: Perhaps one might expect a ‘Fano Lattice’?
-6 -4 -2 0 2 4 60
5
10
q=0
q=1
q=2
q=3
ε
Fig 2
‘Fano Lattice’ Theories
Haule K. & Kotliar G, Nature Phys. 5, 796 (2009).
Maltseva, M., Dzero, M. & Coleman P. Phys. Rev. Lett. 10, 206402 (2009)
URu2Si2
URu2Si2
(same as CeCu2Si2 with U and Ru instead of Ce and Cu);
a=4.124Å; c=9.582Å (PRL65-3189)
4.12Å
Step height: 4.79Åa0/√2=2.91Å
out-of-plane U-U distance: 5.61Å
U
Ru
Si
γ=100 mJ/mol K2 m*/me ~ 25
URu2Si2 is a modestly heavy fermion system
URu2Si2URu2Si2 is a modestly heavy fermion system T*~55K
with an additional ‘Hidden Order’ phase transition at 17.5K
URu2Si2‘Hidden Order’
Transition
URu2Si2 is a modestly heavy fermion system T*~55Kwith an additional ‘Hidden Order’ phase transition at 17.5K
URu2Si2Why URu2Si2 ?
• Heavy fermion system• Perfect cleave surface• Lattice of f-atoms at surface• Scattering interference
4.12Å
Step height: 4.79Åa0/√2=2.91Å
out-of-plane U-U distance: 5.61Å
U
Ru
Si
γ=100 mJ/mol K2 m*/me ~ 25
40nm x 40nm Si surface topography(70619)
Si-layer termination
40nm x 40nm topography
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.080.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Energy (eV)
Fano-like spectrum at every Si atom
A.R. Schmidt et al (2009)
M. Plihal und J.W. Gadzuk, Phys. Rev. B 63, 085404 (2001)
α)(
0)(rd
etrt−
=)(Im)()(Re)(
rGrtrGrq +=
-6 -4 -2 0 2 4 60
5
10
q=0
q=1
q=2
q=3
ε
Fano resonance:
q
Γ
0ε energy of many-body state screening spin
width of resonance (simple Kondo 2kBTk)
Ratio matrix elements linking tip state to resonance and continuum
Fano Signature Analysis
A.R. Schmidt et al (2009)
( )2/
)(';1''),( 02
2
Γ−
=+
+∝
εEEE
EqErg
A.R. Schmidt et al (2009)
‘Fano Lattice’ Electronic Structure (T>TO )
URu2Si2 ‘Hidden Order’ State
URu2Si2‘Hidden Order’
Transition
‘Hidden Order’ Transition To=17.5K
• Heavy fermion material • Superconductor below Tc~1.5K• Energy-gap ~10+-2 mV (Photo, INS, Cp)
‘Hidden Order’ Transition To=17.5K
• Palstra, T.T.M., Menovsky, A.A., & Mydosh, J.A. Superconducting and magnetic transitions in the heavy-fermion system URu2Si2. Phys. Rev. Lett. 55, 2727-2730 (1985).
•[Broholm, C. et al. Magnetic excitations and order in the heavy-electron superconductor URu2Si2. Phys. Rev. Lett. 58, 1467-1470 (1987).
• Bonn, D.A. et al. Far-infrared properties of URu2Si2. Phys. Rev. Lett. 61, 1305-1308 (1988).
• Wiebe, C.R. et al. Gapped Itinerant spin excitations account for missing entropy in the hidden order state of URu2Si2. Nature Phys. 3, 96-99 (2007).
•] Santander-Syro, A.F. et al. Fermi-surface instability at the ‘hidden-order’ transition of URu2Si2. Nature Phys. 5, 637-641 (2009).
‘Hidden Order’ Transition To=17.5K
Broholm, C. et al. Magnetic excitations in the heavy-fermion superconductor URu2Si2. Phys. Rev. B. 43, 809-822 (1991).
Ikeda, H. & Ohashi, Y. Theory of unconventional spin density wave: a possible mechanism U-based heavy fermion compounds. Phys. Rev. Lett. 81, 3723-3726 (1998).
Chandra, P. et al. Hidden orbital order in the heavy fermion metal URu2Si2. Nature 417, 831-834 (2002).
Varma, C.M. & Lijun, Z. Helicity order: Hidden order parameter in URu2Si2. Phys. Rev. Lett. 96, 036405-1-036405-4 (2006).
Balatsky, A.V. et al. Incommensurate spin resonance in URu2Si2. Phys. Rev. B. 79, 214413 (2009).
Santini, P. Crystal field model of the mag properties of URu2Si2. Phys. Rev. Lett. 73, 1027-1030 (1994).
Barzykin, V. & Gor’kov, L.P. Singlet magnetism in heavy fermions. Phys. Rev. Lett. 74, 4301-4304 (1995).
Haule K. & Kotliar G. Arrested Kondo effect and hidden order in URu2Si2. Nature Phys. 5, 796-799 (2009).
Haule K. & Kotliar G. Complex Landau Ginzburg theory of the hidden order of URu2Si2. Preprint available arXiv:0907.3892.
‘Conventional’ Density Wave ‘Altered’ Kondo Effect
Emergence of ‘Hidden Order’ DOS(E) from the Heavy Fermion Fano Spectrum
Alterations in Fano signature at HO Transition
A.R. Schmidt et al (2009)
U-terminated
Si-terminated
Rotated to overlap with 4.2K map
2012
4
Si-layer Quasiparticle Interference Imaging
Rotated to overlap with 4.2K map
2012
4
QPI inversion to identify bands was unachievable
Th0.01U0.99Ru2Si2 40nm x 40nm Topography
(70619)
U-layer termination
U0.99Th0.01Ru2Si2
A.R. Schmidt et al (2009)
Signature of HO near E=0 on dI/dV spectrum at U-layer
2 Å
T
A.R. Schmidt et al (2009)
T=1.9K
A.R. Schmidt et al (2009)
T=1.9K • Extremely rapid k(E) – heavy fermions
• Within range of hidden-order gap only
• Highly anisotropic QPI & gap structure
• Completely different E0
• No static Q* (density wave) at any energy
A.R. Schmidt et al (2009)
T=1.9KT dependence
q
A.R. Schmidt et al (2009)
T=1.9KExtremely rapid T-dependence of band structure
q
q q
‘Hidden Order’ splits light band into two heavy bands
A.R. Schmidt et al (2009)
Conclusions
-6 -4 -2 0 2 4 60
5
10
q=0
q=1
q=2
q=3
ε
Challenge: atomically resolved image of d-f electron hybridization and heavy band formation in Kondo lattice?
‘Fano Lattice’ Imaging: New approach to heavy fermion physics
A.R. Schmidt et al (2009)
URu2Si2‘Hidden Order’
Transition
‘Hidden Order’ Transition To=17.5K
HO transition in LDOS emerges from ‘Fano Lattice’ signature
A.R. Schmidt et al (2009)
1.9K
Light d-band splits rapidly into two heavy bands below To
A.R. Schmidt et al (2009)
• Conventional density wave, non-dispersive modulations at Q* should appear in the gap-edge states both above and below EF.. But the high-DOS gap-edge states of ‘hidden order’ state are at a completely different k-space locations
• Instead, light band crossing EF near k = 0.3(π/a0) above To which undergoes rapid temperature changes below To.
• The result is its splitting into two far heavier bands widely separated in k-space and with quite different anisotropies
• The k-space hybridization gap and the DOS(E) changes detected in r-space occur within the same narrow energy range (consistent with the energy ranges deduced from thermodynamics and other spectroscopies),
1.9K
A.R. Schmidt et al (2009)
‘Hidden order’ transition is caused primarily by a sudden alteration of the many-body state centered upon each U atom, with associated
alterations to the r-space /k-space hybridization processes
‘Hidden Order’ State - Change in Kondo Effect at U atoms
Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Spectroscopic Imaging STM Systems Spectroscopic Imaging STM Systems Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26URu2Si2URu2Si2URu2Si2URu2Si2Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35URu2Si2Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52URu2Si2Slide Number 54Slide Number 55Slide Number 56