qimiao si rice university

Qimiao Si

Rice University

Local Quantum Criticality

and Emergent Phases

Workshop on Heavy Fermion Physics: Perspective and Outlook,

Institute of Physics, CAS, Jan 8, 2012

S. Friedemann C. Krellner Y. Tokiwa P. Gegenwart S. Paschen S. WirthN. Oeschler T. Westerkamp R. KüchlerT. Lühmann T. Cichorek K. NeumaierO. Tegus O. Trovarelli C. GeibelF. SteglichP. Coleman E. Abrahams

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.)

Heavy fermions Kasahara et alO. Stockert et al

TN

Linearresistivity

Superconductivity at the Border of Magnetism

Cuprates OrganicsBroun

Faltermeier et al

Iron pnictides

YbRh2Si2

H. v. Löhneysen et al

J. Custers et al

CePd2Si2

N. Mathur et al

TN

Linearresistivity

Heavy fermion metals as prototype quantum critical points

CeCu6-xAux

“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 resonanceNo symmetry breaking, but macroscopic order

Critical Kondo destruction (f-elec. localization)at the T=0 onset of antiferromagnetism

Critical Kondo Destruction

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

• Extended-DMFT:

collapsing Eloc* from paramagnetic side

From the paramagnetic heavy Fermi liquid side:

• Kondo effect:

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

= 0.72

= 0.83

= 0.78

J-X Zhu, D. Grempel and QS, PRL (2003)

J-X Zhu, S. Kirchner, R. Bulla, and QS, PRL (2007)

M. Glossop & K. Ingersent, PRL (2007)

EDMFT: collapsing Eloc* from paramagnetic side

Dynamical Scaling of Local Quantum Critical Point

= 0.72

= 0.83

= 0.78

J-X Zhu, D. Grempel and QS, PRL (2003)

J-X Zhu, S. Kirchner, R. Bulla, and QS, PRL (2007)

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

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)

T *

Other Approachesto 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

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)

Heisenberg model + coherent spin path integral QNLM

Quantum non-linear Sigma Model Representation

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)

•JK EXACTLY MARGINAL;

•AFs “small” Fermi surface stable

JK

G

AFS

PL

AFL

I

II

Global Phase Diagram

SDW of PLQS, Physica B 378, 23 (2006)

S. Yamamoto & QS, PRL 2007

G: frustration, reduced dimensionaltiy, …

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

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)

Effect of dimensionality – the case of Ce3Pd20Si6

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 fromQNLσM + Berry Phase

P. Goswami & QS, PRL 107, 126404 (’11)

More generally, how to capture Kondo effect using bosonic representations of spin

Heisenberg model + coherent spin path integral QNLM

Role of Berry Phase term in QNLσM Approach

JK<< Irkky, W

QNLσM-- chiral rotation:

Kondo effect and Berry phase in 1D

P. Goswami + QS, PRL 107,

126404 (’11)

JK<< Irkky, W

QNLσM-- chiral rotation: (Tanaka & Machida)

Kondo effect and Berry phase in 1D

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

J. Pixley, S. Kirchner, K. Ingersent and QS, arXiv:1108.5227

Charge excitations part of the quantum-critical spectrum

spin susceptibility charge susceptibility

Kondo destruction and valence fluctuations in pseudogapped asymmetric anderson model

J. Pixley, S. Kirchner, K. Ingersentand QS, arXiv:1108.5227

• Temperature dependence of valence

• Field/temperature scaling

SOME ISSUES AND QUESTIONS

– Materials basis: diversity and universality

– Berry phase and Kondo effects

– Kondo destruction and valence fluctuations

– Implications for superconductivity

T. Park et al., Nature 440, 65 (’06);

G. Knebel et al., PRB74, 020501 (’06) _

Superconductivity near Kondo-destroying AF QCP in CeRhIn5

H. Shishido, R. Settai, H. Harima,

& Y. Onuki, JPSJ 74, 1103 (’05)

T. Park et al., Nature 440, 65 (’06);

G. Knebel et al., PRB74, 020501 (’06)

Superconductivity near Kondo-destroying AF QCP in CeRhIn5

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

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

SUMMARY

• AF QCPs in heavy fermion metals– 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

S. Yamamoto & QS, PRB 81, 205106 (2010)

All directions scalesOnly 1 direction scales (Shankar)