Qimiao Si Rice University

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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

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

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

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

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

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

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

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)

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

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)

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

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)

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

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, 14547 (2010) S. Paschen et al, Nature (2004); P. Gegenwart et al, Science (2007)

Other Approaches to Kondo Destruction T. Senthil, M. Vojta, and S. Sachdev, PRB 69, 035111 (2004) I. Paul, C. Pépin and M. R. Norman, PRL 98, 026402 (2007) L. De Leo, M. Civelli and G. Kotliar, PRB 77, 075107 (2008) P. Wölfle and E. Abrahams, PRB 84, 041101 (2011) …

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

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, 016401 (2007)

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

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, 016401 (2007)

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

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

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

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

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

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)

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

Global Phase Diagram Motivates new theoretical questions and approaches:

Global Phase Diagram Motivates new theoretical questions and approaches: Eg, Kondo effect from QNLσM + Berry Phase P. Goswami & QS, PRL 107, 126404 (’11) More generally, how to capture Kondo effect using bosonic representations of spin

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

Kondo effect and Berry phase in 1D JK<< Irkky, W QNLσM -- chiral rotation: P. Goswami + QS, PRL 107, 126404 (’11)

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, 126404 (’11)

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

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

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, 247201 (2010)

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:1108.5227

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:1108.5227

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

Superconductivity near Kondo-destroying AF QCP in CeRhIn5 T. Park et al., Nature 440, 65 (’06); G. Knebel et al., PRB74, 020501 (’06) H. Shishido, R. Settai, H. Harima, & Y. Onuki, JPSJ 74, 1103 (’05) _

Superconductivity near Kondo-destroying AF QCP in CeRhIn5 T. Park et al., Nature 440, 65 (’06); G. Knebel et al., PRB74, 020501 (’06)

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)

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)

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

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, 205106 (2010)