Quantum Criticality,
Emergent Phases and
Strongly Correlated Electrons
Qimiao Si
Rice University
Center for Quantum Materials
QCM14, Quantum Critical Matter
– from Atoms to Bulk,
Obergurgl, Austria, Aug. 20, 2014
Jed Pixley, Jianda Wu,
Emil Nica, Ang Cai, Wenxin Ding
Pallab Goswami
Rong Yu
Stefan Kirchner
Lijun Zhu
Jian-Xin Zhu
Kevin Ingersent
(Rice University)
(NHMFL, FSU)
(Renmin U.)
(MPI-PKS)
(UC Riverside)
(Los Alamos)
(U. of Florida)
S. Friedemann
C. Geibel
S. Wirth
Erwin Schuberth
O. Stockert
F. Steglich
J. Custers
T. Sakakibara
K.-A. Lorenzer
S. Paschen
A.M. Strydom
K. Grube
H. v. Löhneysen
H. Yuan
J. Singleton
J. D. Thompson
Quantum Criticality
Quantum scaling:
ξτ ~ ξ
z
Tr e
-(/kT)H/
τ ~  / kTorder
Torder
TN
Linear
resistivity
!∞
@QCP
Thermodynamics near QCP
Quantum scaling:
ξτ ~ ξ
=>Grüneisen ratio
Linear
divergent at
QCP:
resistivity
TN
L. Zhu, M. Garst, A. Rosch, & QS, PRL (2003)
z
Entropy Accumulation near QCP
TN
L. Zhu, M. Garst, A. Rosch, & QS, PRL (2003);
J. Wu, L. Zhu & QS, JPCS (2011)
Quantum critical points
enhanced
entropy
unusual excitations;
emergent phases
J. Custers et al
Linear
resistivity
TN
CeRhIn5
SC
T. Park et al
N. Mathur et al
H. v. Löhneysen et al
Quantum Critical Points
of Antiferromagnetic Heavy Fermions
Quantum Criticality
Beyond-Landau Quantum Criticality
Inherent quantum modes,
beyond order-parameter
fluctuations
Antiferromagnetic QCP
Paramag. metal AF metal QCP δ Point of departure:
•  Spin fluctuations + fermions
•  Fate of local moments & Kondo effect
• Kondo lattices:
Heavy Fermi liquid:
• Kondo entanglement
No symmetry breaking,
but macroscopic order
Critical Kondo Destruction
--Local Quantum Critical Point
Critical Destruction of Kondo Entanglement at the onset
of antiferromagnetic order
QS, S. Rabello, K. Ingersent, & J. L. Smith, Nature 413, 804 (2001)
P. Coleman et al, JPCM 13, R723 (2001)
Kondo Destruction and Local Quantum
Criticality: Dynamical Scaling
•  ω/T scaling in χ(q,ω,T)
EDMFT -- collapsing Eloc*
from paramagnetic side
Kondo Destruction and Local Quantum
Criticality: Dynamical Scaling
Exponent α = 0.72-0.78
J-X Zhu, S. Kirchner et al PRL (2007)
Glossop & Ingersent, PRL (2007)
J-X Zhu, D Grempel & QS, PRL (2003)
Cf. neutron scattering expts: A. Schröder et al., Nature (’00);
M. Aronson et al, PRL
Kondo Destruction and Local Quantum
Criticality: Fermi Surface Reconstruction
•  Kondo-destruction energy scale
•  ω/T scaling in χ(q,ω,T)
•  Sudden reconstruction of Fermi surface
Fermi Surface Jump and
Kondo-Destruction Energy Scale in YbRh2Si2
Crossover:
isothermal
Hall coeff.
T*
Crossover
width
vs. T
2nd order transition across Bc
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)
Fermi Surface Jump and
Kondo-Destruction Energy Scale in YbRh2Si2
Crossover: Isothermal magnetostricton and magnetization
P. Gegenwart, T. Westerkamp, C. Krellner, Y. Tokiwa, S. Paschen, C. Geibel,
F. Steglich, E. Abrahams, and QS, Science 315, 969 (2007)
S. Paschen et al, Nature (2004); S. Friedemann et al., PNAS (2010)
Fermi Surface Jump and
Kondo-Destruction Energy Scale in YbRh2Si2
Crossover: Isothermal magnetostricton and magnetization
P. Gegenwart, T. Westerkamp, C. Krellner, Y. Tokiwa, S. Paschen, C. Geibel,
F. Steglich, E. Abrahams, and QS, Science 315, 969 (2007)
S. Paschen et al, Nature (2004); S. Friedemann et al., PNAS (2010)
Jump of Fermi-surface
– dHvA Measurements in CeRhIn5
2nd order transition
across Pc
P1
Pc
Fermi surface jumps across Pc
P1
Pc
Mass tends to diverge at Pc
H. Shishido, R. Settai, H. Harima, & Y. Onuki, JPSJ 74, 1103 (’05)
Dynamical Kondo Effect
Quasiparticle weight à 0
as the QCP is approached
from both sides
J-X Zhu, D. Grempel, QS, PRL (2003)
QS & S. Paschen, Phys. Status Solidi (2013)
Dynamical Kondo Effect
P. Gegeneart et al., PRL (2002)
Kondo Destruction in a Pnictide
CeNiAsO
Y. Luo, L. Pourovskii, S. Rowley, Y. Li, C. Feng, A. Georges, J. Dai,
G. H. Cao, Z. A. Xu, QS, & N. P. Ong, Nat. Mater. 13, 777 (2014)
Global Phase Diagram
Opposite limit –
when RKKY dominates over
Kondo coupling
what
JK << I δ = JK / I Opposite limit –
when RKKY dominates over
Kondo coupling
JK << I • JK=0 as the reference point of expansion:
• f- local moments: AF, QNLσM
• conduction electrons: Fermi volume “x”
Quantum non-linear Sigma
Model Representation
Heisenberg model + coherent spin path integral
QNLσM
SBerry not important
deep inside
ordered phase
When RKKY
dominates:
inside AF order
JK << I • 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
• Kondo destruction -- AFS phase
Global Phase Diagram
G: frustration, reduced dimensionaltiy, …
In contrast to:
single boundary
a la Landau
Q. Si, Physica B 378, 23 (2006); Phys. Status Solidi B247, 476 (2010)
also, P. Coleman & A. Nevidomskyy, JLTP 161, 182 (2010)
Global Phase Diagram
J. Custers, R. Yu et al., Nat. Mater. (2012)
E. D. Mun et al., PRB 87, 075120 (2013)
Co & Ir-doped YbRh2Si2 (S. Friedemann et al, Nat Phys 2009)
Shastry-Sutherland Lattice Yb2Pt2Pb (Kim & Aronson, PRL 2013)
Kagome lattice CePdAl (V. Fritsch et al, PRB 2014)
Mini-review:
QS & S. Paschen, Phys. Status Solidi
B250, 425 (2013)
Global Phase Diagram
G=J2/J1
J1
J2
filling x=0.5
Shastry-Sutherland lattice
J. Pixley, R. Yu & QS, arXiv:1309.0581 (2013)
Role of Berry Phase term
in QNLσM Approach
P. Goswami + QS, PRL 107, 126404 (2011) – One dimension;
PRB 89, 045124 (2014) – 2D honeycomb lattice
Role of Berry Phase term
in QNLσM Approach
Berry phase of local moments:
è Singlet phases (Spin Peierls, …)
Cond. electron spins locked to local moments:
è Cancellation of Berry phase
è Kondo singlet
è Competition w/ spin peierls
P. Goswami + QS, PRL 107, 126404 (2011) – One dimension;
PRB 89, 045124 (2014) – 2D honeycomb lattice
Superconductivity
driven by
Quantum Criticality
Enhanced Pairing Correlation
near Kondo-destruction QCP
J. Pixley
J. Pixley, L. Deng, K. Ingersent & QS, to be published (2014);
J. Pixley, L. Deng, K. Ingersent & QS, arXiv:1308.0839
Superconductivity out of
Fluctuating Fermi Surfaces
P1
Pc
SC
Superconductivity near a Kondo-destruction QCP,
with reconstructing and fluctuating Fermi surfaces
Further Contexts
Quantum Criticality in Iron Pnictides
Proposal:
QCP via
P-substitution
for As
J. Dai, QS, J-X Zhu & E. Abrahams, PNAS 106, 4118 (’09)
Quantum Criticality in Iron Pnictides
K. Hashimoto et al, Science (’12)
S. Kasahara et al, PRB 81, 184519 (’10)
J. G. Analytis et al, Nat. Phys. (2014)
BaFe2(As1-xPx)2
SUMMARY
•  Quantum criticality in heavy fermions
–  Kondo destruction
•  Emergent phases:
–  Global phase diagram
–  Superconductivity near Kondo-destruction QCP

Download Report