Workshop on Principles and Design of Strongly Correlated Electronic Systems August 2010
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1 Workshop on Principles and Design of Strongly Correlated Electronic Systems 2-13 August 2010 Imaging the Fano Lattice to "Hidden Order" Transition in URu2Si2 Mohammad HAMIDIAN J.C. Davis Group, A03 Clark Hall Cornell University Ithaca NY U.S.A.
2 Imaging the Fano Lattice to Hidden Order Transition in URu 2 Si 2 Nature 465, 570 (2010)
3 Collaboration Dr. Andy Schmidt Cornell /BNL Mohammad Hamidian Cornell/BNL Dr. Peter Wahl Cornell/ MPI Stuttgart Dr. Focko Meier Cornell/BNL Dr. A.V. Balatsky Los Alamos Prof. Graeme Luke McMaster Travis Williams McMaster Dr. J.D. Garrett (Brockhouse Institute) Prof. J.C. Davis Cornell
4 Outline Heavy Fermions, Kondo Effect / Kondo Lattice & Tunneling URu 2 Si 2 : Introduction Spectroscopic Imaging STM & Heavy Fermion QPI URu 2 Si 2 : Fano Lattice Imaging T>T 0 URu 2 Si 2 : Heavy Fermion QPI Imaging T<T 0 New Perspectives from QPI on URu 2 Si 2 Hidden Order Conclusions & Future Work
5 Heavy Fermions, Kondo Effect / Kondo Lattice & Tunneling
6 Heavy Fermions Basics Electronic density of states up to 1000 times higher than copper at low temperatures Seen in specific heat and magnetic susceptibility measurements Heavy effective mass m* - INFERRED Partially filled f-shell Matrix of localized magnetic moments immersed in a sea of conduction electrons
7 Single Impurity Kondo Effect T > T K T < T K
8 Fano Lineshape f 1 ~kt K f 2 Co on Au(111) V. Madhavan et al, Science 280, 567 (1998)
9 Fano Lineshape Tip di dv ' ' 2 2 ' (, ' 0) 1 / 2 10 ζ= 3 q=3 z d Adatom di/dv 5 q=2 ζ= 2 ζ= q=11 r Substrate 0 ζ= q= width of resonance V. Madhavan et al, Science 280, 567 (1998) ζ - coupling ratio M. Plihal und J.W. Gadzuk, Phys. Rev. B 63, (2001) O. Újsághy, J. Kroha, L. Szunyogh und A. Zawadowski, Phys. Rev. Lett. 85, 2557 (2000) Γ 0 - energy of resonant state
10 Anderson/Kondo Lattice Model High T Low T E E k 2 f k E k 2 f k 2 V k 2 1/ 2 P. Coleman in Handbook of Magnetism and Advanced Magnetic Materials (2007)
11 Path to Heaviness Ce : [Xe]4f 2 5d 0 6s 2 2 itinerant 1 local La : [Xe]5d 1 6s 2 Lieke, W. et al., J. Appl. Phys. 53, 2111 (1982).
![: [Xe]5d 1 6s 2 Lieke, W. et al.](/docs-images/58/5195222/images/page_11.jpg ", J. Appl. Phys. 53, 2111 (1982).")
12 URu 2 Si 2
13 URu 2 Si 2 Specific heat coefficient = 65mJ/mol/K² U Ru Si Effective mass m* = 25m e - 50m e HF Coherence Temperature T* ~ 55K Hidden Order transition T N = 17.5K Superconducting transition T C = 1.5K 4.12Å a=4.124å c=9.582å Palstra et. al. PRL 55, 2727 (1985) Maple et. al. PRL 56, 185 (1986) Mason et. al. PRL 65, 3189 (1990)
14 URu 2 Si 2 T 0 T* T c
15 Hidden Order in URu 2 Si 2 Energy-Gap ~11mV (optical & specific heat) Reorganization of band-structure and magnetic excitation spectrum Palstra, T.T.M., Menovsky, A.A., & Mydosh, J.A. Superconducting and magnetic transitions in the heavyfermion system URu 2 Si 2. Phys. Rev. Lett. 55, (1985). Broholm, C. et al. Magnetic excitations and order in the heavy-electron superconductor URu 2 Si 2. Phys. Rev. Lett. 58, (1987). Bonn, D.A. et al. Far-infrared properties of URu 2 Si 2. Phys. Rev. Lett. 61, (1988). Wiebe, C.R. et al. Gapped Itinerant spin excitations account for missing entropy in the hidden order state of URu 2 Si 2. Nature Phys. 3, (2007). Santander-Syro, A.F. et al. Fermi-surface instability at the hidden-order transition of URu 2 Si 2. Nature Phys. 5, (2009).
16 Hypotheses for Identity of OP Susceptibility of FL /FS Momentum Space Broholm, C. et al. Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2. Phys. Rev. B. 43, (1991). Ikeda, H. & Ohashi, Y. Theory of unconventional spin density wave: a possible mechanism U- based heavy fermion compounds. Phys. Rev. Lett. 81, (1998). Chandra, P. et al. Hidden orbital order in the heavy fermion metal URu 2 Si 2. Nature 417, (2002). Varma, C.M. & Lijun, Z. Helicity order: Hidden order parameter in URu 2 Si 2. Phys. Rev. Lett. 96, (2006). Altered Kondo Effect / Real Space Santini, P. Crystal field model of the mag properties of URu 2 Si 2. Phys. Rev. Lett. 73, (1994). Barzykin, V. & Gor kov, L.P. Singlet magnetism in heavy fermions. Phys. Rev. Lett. 74, (1995). Haule K. & Kotliar G. Arrested Kondo effect and hidden order in URu 2 Si 2. Nature Phys. 5, (2009). Harima H., Miyake K., Flouquet J. Why the hidden order in URu2Si2 is still hidden - one simple answer. arxiv: Balatsky, A.V. et al. Incommensurate spin resonance in URu 2 Si 2. Phys. Rev. B. 79, (2009).
17 Key Issues What is the relationship between the initial Kondo Lattice and the Hidden Order state? What are the alterations to real- and momentum-space electronic structure due to the onset of the Hidden Order? Can one distinguish between FS/FL susceptibility and local mechanisms?
18 Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM)
19 Our SI-STM Facilities STM1 (9T/250mK) STM3 (4K 100K) STM2(9T/10mK) Cornell Brookhaven Cornell
20 STM
21 L DOS(r,E) from di/dv(r,v) Spectra I Ce di dv z( V ) z ev 0 LDOS r, E 0 LDOS(E de ev) Point Spectrum
22 Spectroscopic Imaging di dv ( r, V) g( r, V) LDOS(r,E ev) Energy (ev) LDOS(r = r 1, E)
23 Spectroscopic Imaging di dv ( r, V) g( r, V) LDOS(r,E ev) Energy (ev) LDOS(r = r 2, E)
24 Spatially and Energy Resolved LDOS LDOS(r,1.5mV) y x LDOS(r,0.5mV) E LDOS(r,-0.5mV) LDOS(r,-1.25mV)
25 Example: Bi-2212 Topographic Image g (r,v) (r( r, E) 2 Nature doi: /nature09169 (2010)
26 QPI: Bi-2212 Topographic Image g (q,v) (r( r, E) 2 Nature doi: /nature09169 (2010)
27 Example: Ca-122 Topography Topographic Image g (r,v) (r( r, E) 2 Science 327, 181 (2010)
28 QPI: Ca-122 Topography Topographic Image g (q,v) (r( r, E) 2 Science 327, 181 (2010)
29 Example: SrRuO-327 Topographic Image g (r,v) (r( r, E) 2 Nature Physics 5, 800 (2009)
30 QPI Infrastructure Ultra low vibration lab. Underground Concrete Vibration Isolation Vault Internal Acoustic Isolation Chamber sound room #1: lab lined with Sonex sound room #2: IAC Remote Control Room lead-filled table three air springs vacuum lines lead-filled legs 30 Ton concrete inertial block pump box 6 m six air springs Rev. Sci. Inst. 70, 1459 (1999).
31 QPI Infrastructure Ultra low vibration lab. Underground Concrete Vibration Isolation Vault Internal Acoustic Isolation Chamber Ultra low vibration cryostat. sound room #1: lab lined with Sonex sound room #2: IAC Remote Control Room lead-filled table three air springs vacuum lines lead-filled legs 30 Ton concrete inertial block pump box 6 m six air springs Rev. Sci. Inst. 70, 1459 (1999).
32 How/Why Heavy Fermion QPI? Heavy Fermion many body state and bands are above E High T F Low T Heavy Fermion bands are extremely flat requiring ~100 V energy resolution or better Sub-kelvin temperatures, low vib. & EM noise, plus high electronic sensitivity
33 Dilution Fridge Spectroscopic Imaging-STM
34 URu 2 Si 2 : Fano Lattice
35 Cleave Plane 1 Si Surface Si U U Ru Si a=4.124å; c=9.582å (PRL )
36 Fano Lineshape Tip di ' ( / dv ( V ), ' 0) ' 2 1 / ζ= 3 q=3 z d Adatom di/dv 5 q=2 ζ= 2 ζ= q=11 r Substrate 0 ζ= q= width of resonance V. Madhavan et al, Science 280, 567 (1998) ζ - coupling ratio M. Plihal und J.W. Gadzuk, Phys. Rev. B 63, (2001) O. Újsághy, J. Kroha, L. Szunyogh und A. Zawadowski, Phys. Rev. Lett. 85, 2557 (2000) Γ 0 - energy of resonant state
37 di/dv Spectroscopy 19K > T HO
38 Imaging Fano Parameters 0(r) (r) (r) mev meV
39 Topography 19K > T HO
40 0(r) 19K > T HO mev
41 (r) 19K > T HO mev
42 (r) 19K > T HO
43 Visualization of a Fano Lattice 0(r) (r) (r) mev meV A. Schmidt & M. Hamidian et al. Nature 465, 570 (2010) P. Aynajian et al. PNAS 107, ( 2010)
44 URu 2 Si 2 : DOS
45 Theory (DMFT) Haule, K. & Kotliar, G. Nature Phys. 6, 769 (2009)
46 Theory (Large-N) Maltseva M. et al PRL 103, (2009)
47 Temp. dependence of Fano Spectra 19K 17.5K Hidden Order Transition 15K 10K 6K 1.7K
48 Temp. dependence of Fano Spectra 19K 17.5K Hidden Order Transition 15K 10K 6K 1.7K
49 Temp. dependence of Fano Spectra 19K 17.5K Hidden Order Transition 15K 10K 6K 1.7K Bias (mv)
50 Consistent Spectroscopic Gap Spectroscopic Gap 1.7K Thermodynamic Gap 12 mv = 129K = 11 mev Maple, B. et. al. PRL 56, 185 (1986) Bonn, D.A. et al. PRL 61, 1305 (1988).
51 Comparison: Kondo Lattice Theory 19K 17.5K 15K 10K 6K 1.7K Maltseva M. et al PRL 103, (2009)
52 Thorium doped URu 2 Si 2 : for Quasiparticle Interference Imaging
53 U 0.99 Th 0.01 Ru 2 Si 2 : U surface Th 5 nm Topography
54 U 0.99 Th 0.01 Ru 2 Si 2 : U surface 19K 16K Hidden Order Transition (drops with Th) 15K 10K 6K 1.9K Bias (mv)
55 Transition within 1K of bulk value 19K 16K Hidden Order Transition (drops with Th) 15K 10K 6K 1.9K
56 Comparison with Specific Heat Gap 4.3 mev = 50K 1.9K A. Lopez de la Torre et al Physica B 179, 208 (1992)
57 URu 2 Si 2 : Temperature Dependent Quasiparticle Interference Imaging
58 1.9K Conductance Map g(rr,e) U0.99Th0.01Ru2Si2 55nm
59 1.9K QPI Image g(q q,e) U0.99Th0.01Ru2Si2 (0,2 /a0) (0,0) (0,2 /a0)
60 HO Transition in QPI g(q,e) T>T o (19K) T<<T o (2K)
61 Tracking Heavy QPI (0,2 /a 0 ) (2 /a 0,0)
62 Heavy QPI 18.6K > T HO (0,2 /a 0 ) (0,2 /a 0 ) A. Schmidt, M. Hamidian, Nature (2010)
63 Heavy QPI 14.5K < T HO (0,2 /a 0 ) (0,2 /a 0 ) A. Schmidt, M. Hamidian, Nature (2010)
64 Heavy QPI 9.7K < T HO (0,2 /a 0 ) (0,2 /a 0 ) A. Schmidt, M. Hamidian, Nature (2010)
65 Heavy QPI 5.9K < T HO (0,2 /a 0 ) (0,2 /a 0 ) A. Schmidt, M. Hamidian, Nature (2010)
66 m* = 9m e m* = 9m e m* = 50m e m* = 17m e
67 HO: Two New Heavy Bands 5.9K 5.9K (0,2 /a 0 ) Theory (0,2 /a 0 )
68 New Perspectives from QPI on HO Thermodynamics, ARPES, SI-STM are consistent with each other in HO phase No fixed Q modulations, gap-edge state different k-space locations below and above E F, indirect gap does not cross E F,. DOS(E) emerging below T 0 looks quite like predicted gap for Kondo Lattice (!)
69 New Perspectives from QPI on HO Thermodynamics, ARPES, SI-STM are consistent with each other in HO phase No fixed Q modulations, gap-edge state different k-space locations below and above E F, indirect gap does not cross E F,. DOS(E) emerging below T 0 looks quite like predicted gap for Kondo Lattice (!) A single light band is split into two new heavy bands below T 0 These new bands appear remarkably like expectations for a Kondo Lattice (!)
70 New Perspectives from QPI on HO Thermodynamics, ARPES, SI-STM are consistent with each other in HO phase No fixed Q modulations, gap-edge state different k-space locations below and above E F, indirect gap does not cross E F,. DOS(E) emerging below T 0 looks quite like predicted gap for Kondo Lattice (!) A single light band is split into two new heavy bands below T 0 These new bands appear remarkably like expectations for a Kondo Lattice (!) BUT Mean-field-like, second order transition
71 Future
72 mk SI-STM/QPI for Heavy Fermions 0(r) (0,0) mev Nature 465, 570 (2010)
73 Future Work SI-STM and QPI opens a new window onto the heavy fermion problem Visualization Kondo Lattice formation/deformation QPI carries symmetries of the Kondo interactions and allows the intricacies of the heavy bands to be measured QPI of heavy f-electron superconductivity The symmetry of URu2Si2 hidden order within reach (?)
74 Collaboration Dr. Andy Schmidt Cornell /BNL Mohammad Hamidian Cornell/BNL Dr. Peter Wahl Cornell/ MPI Stuttgart Dr. Focko Meier Cornell/BNL Dr. A.V. Balatsky Los Alamos Prof. Graeme Luke McMaster Travis Williams McMaster Dr. J.D. Garrett (Brockhouse Institute) Prof. J.C. Davis Cornell
75 Thank You
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