1. Qimiao Si Rice University
Local Quantum Criticality
and Emergent Phases
Qimiao Si
Rice University
Workshop on Heavy Fermion Physics: Perspective and Outlook,
Institute of Physics, CAS, Jan 8, 2012

2. Jed Pixley, Jianda Wu,
Rong Yu (Rice University)
Pallab Goswami, Seiji Yamamoto (NHMFL, FSU)
Stefan Kirchner (MPI-PKS,CPfS)
Lijun Zhu (UC Riverside)
Jian-Xin Zhu (Los Alamos)
Kevin Ingersent (U. of Florida)
Jianhui Dai (Zhejiang U.)
S. Friedemann C. Krellner Y. Tokiwa P. Gegenwart S. Paschen S. Wirth N. Oeschler T. Westerkamp R. Küchler T. Lühmann T. Cichorek K. Neumaier O. Tegus O. Trovarelli C. Geibel F. Steglich P. Coleman E. Abrahams

3. Superconductivity at the Border of Magnetism
Heavy fermions
Iron pnictides
Kasahara et al
O. Stockert et al
Cuprates
Organics
Faltermeier et al
Linear
resistivity
Broun TN

4. Heavy fermion metals as prototype quantum critical points
CePd2Si2
CeCu6-xAux
H. v. Löhneysen et al
N. Mathur et al
Linear
resistivity TN
YbRh2Si2
J. Custers et al

5. “Beyond-Landau” Quantum Criticality
Inherent quantum modes, beyond order-parameter fluctuations:
-- need to identify the additional critical modes.

6. Local Kondo-destruction QCP Global phase diagram
Some issues and questions:
Diversity and universality of QCPs
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

7. Kondo lattices: heavy Fermi liquid: Kondo singlet Kondo resonance
No symmetry breaking, but macroscopic order

8. Critical Kondo Destruction
Critical Kondo destruction (f-elec. localization)
at the T=0 onset of antiferromagnetism
QS, S. Rabello, K. Ingersent & J. L. Smith, Nature 413, 804 (’01); PRB (’03)
P. Coleman et al, JPCM 13, R723 (’01)

9. Critical Kondo Destruction
From the paramagnetic heavy Fermi liquid side:
Kondo effect:
Extended-DMFT:
collapsing Eloc* from paramagnetic side

10. Fermi Surface Reconstruction and Energy Scales
Kondo-destruction energy scale
Sudden reconstruction of Fermi surface
/T scaling in χ(q,ω,T) and G(k,ω,T)

11. Dynamical Scaling of Local Quantum Critical Point
J-X Zhu, D. Grempel and QS, PRL (2003)
a = 0.83
J-X Zhu, S. Kirchner, R. Bulla, and QS, PRL (2007)
a = 0.78
M. Glossop & K. Ingersent, PRL (2007)
EDMFT: collapsing Eloc* from paramagnetic side

12. Dynamical Scaling of Local Quantum Critical Point
J-X Zhu, D. Grempel and QS, PRL (2003)
a = 0.83
J-X Zhu, S. Kirchner, R. Bulla, and QS, PRL (2007)
a = 0.78
M. Glossop & K. Ingersent, PRL (2007)
EDMFT: collapsing Eloc* from paramagnetic side
Cf. neutron scattering expts: A. Schröder et al., Nature(’00);
O. Stockert et al, PRL (’98); M. Aronson et al, PRL (’95)

13. Kondo-destroying AF QCP in CeRhIn5
H. Shishido, R. Settai, H. Harima,
& Y. Onuki, JPSJ 74, 1103 (’05) _

14. Fermi Surface and Energy Scales in YbRh2Si2
T *
S. Friedemann, N. Oeschler, S. Wirth, C. Krellner, C. Geibel, F. Steglich,
S. Paschen, S. Kirchner, and QS, PNAS 107, (2010)
S. Paschen et al, Nature (2004); P. Gegenwart et al, Science (2007)

15. Other Approaches to Kondo Destruction
T. Senthil, M. Vojta, and S. Sachdev, PRB 69, (2004)
I. Paul, C. Pépin and M. R. Norman, PRL 98, (2007)
L. De Leo, M. Civelli and G. Kotliar, PRB 77, (2008)
P. Wölfle and E. Abrahams, PRB 84, (2011) …

16. Local Kondo-destruction QCP Global phase diagram
Some issues and questions:
Diversity and universality of QCPs
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

17. JK<< Irkky << W
Kondo lattice
JK<< Irkky << W
JK=0 as the reference point of expansion:
f- local moments: AF, QNLσM
conduction electrons: Fermi volume “x”
S. Yamamoto & QS,
PRL 99, (2007)

18. Quantum non-linear Sigma
Model Representation
Heisenberg model + coherent spin path integral QNLM

19. JK<< Irkky << W
Kondo lattice
JK<< Irkky << W
JK=0 as the reference point of expansion:
f- local moments: AF, QNLσM
conduction electrons: Fermi volume “x”
JK EXACTLY MARGINAL;
AFs “small” Fermi surface stable
S. Yamamoto & QS,
PRL 99, (2007)

20. G: frustration, reduced dimensionaltiy, …
Global Phase Diagram G
G: frustration, reduced dimensionaltiy, … I PL II
AFS
AFL JK
QS, Physica B 378, 23 (2006)
S. Yamamoto & QS, PRL 2007
SDW of PL

21. Global Phase Diagram Q. Si, Phys. Status Solidi B247, 476 (2010)
P. Coleman & A. Nevidomskyy, JLTP 161, 182 (2010)

22. Global Phase Diagram Pure and doped YbRh2Si2 S. Friedemann et al,
Nat. Phys. 5, 465 (’09)

23. SOME ISSUES AND QUESTIONS
Materials basis: diversity and universality
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

24. Global Phase Diagram Diversity and universality of QCPs:
materials basis –
YbRh2Si2
CeCu6-xAux
CeRhIn5
CeIn3
β-YbAlB4
Ce3Pd20Si6
Yb2Pt2Pb
YbAgGe …

25. Global Phase Diagram Effect of dimensionality – the case of Ce3Pd20Si6
J. Custers, K.-A. Lorenzer, M. Müller, A. Prokofiev, A. Sidorenko,
H. Winkler, A.M. Strydom, Y. Shimura, T. Sakakibara, R. Yu, QS,
and S.Paschen, Nature Materials (Jan. 8, 2012)

26. SOME ISSUES AND QUESTIONS
Materials basis: diversity and universality
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

27. Global Phase Diagram
Motivates new theoretical questions and approaches:

28. Global Phase Diagram
Motivates new theoretical questions and approaches:
Eg, Kondo effect from
QNLσM + Berry Phase
P. Goswami & QS, PRL 107, (’11)
More generally, how to capture Kondo effect using bosonic representations of spin

29. Role of Berry Phase term
in QNLσM Approach
Heisenberg model + coherent spin path integral QNLM

30. Kondo effect and Berry phase in 1D
JK<< Irkky, W
QNLσM
-- chiral rotation:
P. Goswami + QS, PRL 107,
(’11)

31. Kondo effect and Berry phase in 1D
JK<< Irkky, W
QNLσM
-- chiral rotation:
(Tanaka & Machida)
Kondo vs spin-Peierls:
large vs small FS
in paramagnets
P. Goswami + QS, PRL 107,
(’11)

32. SOME ISSUES AND QUESTIONS
Materials basis: diversity and universality
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

33. Kondo destruction
(kicking one electron/site
out of the Fermi surface)
What happens beyond the Kondo limit, w/ mixed-valency?

34. Kondo destruction
(kicking one electron/site
out of the Fermi surface)
What happens beyond the Kondo limit, w/ mixed-valency?
β-YbAlB4
-- H/T scaling  interacting
Y. Matsumoto et al, Science 331, 316 (2011)
-- Mixed valency
M. Okawa et al, PRL 104, (2010)

35. Kondo destruction and valence fluctuations in pseudogapped asymmetric anderson model
spin susceptibility
charge susceptibility
Charge excitations part of the quantum-critical spectrum
J. Pixley, S. Kirchner, K. Ingersent and QS, arXiv:

36. Kondo destruction and valence fluctuations in pseudogapped asymmetric anderson model
Field/temperature scaling
Temperature dependence of valence
J. Pixley, S. Kirchner, K. Ingersent
and QS, arXiv:

37. SOME ISSUES AND QUESTIONS
Materials basis: diversity and universality
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

38. Superconductivity near Kondo-destroying
AF QCP in CeRhIn5
T. Park et al., Nature 440, 65 (’06);
G. Knebel et al., PRB74, (’06)
H. Shishido, R. Settai, H. Harima,
& Y. Onuki, JPSJ 74, 1103 (’05) _

39. Superconductivity near Kondo-destroying
AF QCP in CeRhIn5
T. Park et al., Nature 440, 65 (’06);
G. Knebel et al., PRB74, (’06)

40. Superconductivity in CeCu2Si2
Exchange energy saving
≈ 20 times of SC condensation energy
 large kinetic energy loss
O.Stockert, J.Arndt, E.Faulhaber, C.Geibel, H.S. Jeevan, S.Kirchner,
M.Loewenhaupt, K.Schmalzl, W.Schmidt, QS, & F.Steglich, Nat. Phys. 7, 119 (2011)

41. Superconductivity in CeCu2Si2
Exchange energy saving
≈ 20 times of SC condensation energy
 large kinetic energy loss
due to transfer of spectral weight to higher energies
O.Stockert, J.Arndt, E.Faulhaber, C.Geibel, H.S. Jeevan, S.Kirchner,
M.Loewenhaupt, K.Schmalzl, W.Schmidt, QS, & F.Steglich, Nat. Phys. 7, 119 (2011)

42. SUMMARY AF QCPs in heavy fermion metals Emergent phases:
SDW type: Order-parameter fluctuations
Local quantum criticality: Electronic localization
in the form of Kondo destruction
Emergent phases:
Global phase diagram
Discussions and outlook:
Diversity and universality of QCPs
Berry phase and Kondo effects
Kondo destruction and valence fluctuations
Implications for superconductivity

43. RG for mixed Bosons and Fermions with a Fermi Surface
All directions scales
Only 1 direction
scales (Shankar)
We need to consider both a bosonic vector field and fermionic fields, which requires that we combine the two methods. This is something we can do, and we are somewhat lucky in our case, basically because zf=zb=1.
The first step in RG is the tree level analysis, which is basically power counting. To do this we need the scaling dimension of the fields. We find [\psi]=-3/2 from the free electron part of the action, and the dimension of the boson field from the non-linear sigma model. When we plug it all end we find that lo-and-behold, the coupling is marginal! The next question is whether this is marginally relevant, or marginally irrelevant. This requires that we go to 1-loop.
S. Yamamoto & QS, PRB 81, (2010)