Non Fermi Liquids: Theory and Experiment. Challenges of understanding Critical and Normal Heavy Fermion Fluids

Beyond Quasiparticles: New Paradigms for Quantum Fluids Aspen Center for Physics 14-17 June, 2014 Non Fermi Liquids: Theory and Experiment. Challenges of understanding Critical and Normal Heavy Fermion Fluids 8.00-8.15 am Piers Coleman (Rutgers University) Challenges of Understanding Critical and Normal Heavy Fermion Fluids Show abstract 8.15-8.50 Collin Broholm (Johns Hopkins University) The magnetism of strongly correlated metals Show abstract 8.50-9.25 Y. Matsumoto (ISSP, University of Tokyo) Valence fluctuation and strange metal phase in YbAlB4 Show abstract 9.25-9.45 Coffee break 9.50 -.25 J. D. Thompson (Los Alamos National Laboratory) Non-Fermi Liquid Behaviors in CeRhIn5 and CeCoIn5 Show abstract.25-11.00 A. Yazdani (Princeton University) Visualizing the Emergence of Heavy Fermions, their Superconductivity, and Hidden Orders with STM Show abstract Piers Coleman Center for Materials Theory Rutgers, USA

Kmetko-Smith Phase Diagram Smith and Kmetko (1983)

Kmetko-Smith Phase Diagram Increasing localization Smith and Kmetko (1983)

Kmetko-Smith Phase Diagram Increasing localization Increasing localization Smith and Kmetko (1983)

Kmetko-Smith Phase Diagram Increasing localization Increasing localization Smith and Kmetko (1983) A lot of action at the brink of localization.

Heavy Fermion Primer Spin (4f,5f): basic fabric of heavy electron physics.

Heavy Fermion Primer 2j+1 Spin (4f,5f): basic fabric of heavy electron physics.

Heavy Fermion Primer 2j+1 Curie Spin (4f,5f): basic fabric of heavy electron physics.

Heavy Fermion Primer Electron sea 2j+1 Curie Spin (4f,5f): basic fabric of heavy electron physics. H = X k k c k c k + J ~ S ~ (0)

Heavy Fermion Primer Electron sea 2j+1 Curie Spin (4f,5f): basic fabric of heavy electron physics. H = X k k c k c k + J ~ S ~ (0) Weak Coupling FIXED POINT 0 1 AFM J>0 J(T) T>>TK TK T<<TK Strong Coupling FIXED POINT

Heavy Fermion Primer Electron sea 2j+1 Curie Spin screened by conduction electrons: entangled H = X k k c k c k + J ~ S ~ (0) Weak Coupling FIXED POINT 0 1 AFM J>0 J(T) T>>TK TK T<<TK Strong Coupling FIXED POINT

Heavy Fermion Primer Electron sea 2j+1 Curie Spin screened by conduction electrons: entangled " # #" H = X k k c k c k + J ~ S ~ (0) Weak Coupling FIXED POINT 0 1 AFM J>0 J(T) T>>TK TK T<<TK Strong Coupling FIXED POINT

Heavy Fermion Primer Electron sea T K De 1 2J Kondo temperature Pauli 2j+1 Curie Spin screened by conduction electrons: entangled " # #" H = X k k c k c k + J ~ S ~ (0) Weak Coupling FIXED POINT 0 1 AFM J>0 J(T) T>>TK TK T<<TK Strong Coupling FIXED POINT

Heavy Fermion Primer

Heavy Fermion Primer Kondo Lattice

Kondo Insulators Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order.

Kondo Insulators 1968 Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. Kondo Insulators SmB6 B6 Sm 2.7+

Kondo Insulators 1968 Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. Kondo Insulators Mott Phil Mag, 30,403,1974 SmB6 Sm2.7+ B6

Kondo Insulators 1968 PH 74, NUMBER 9 VOLUME 1 1 $P -24 Persistent conduc-vity Plateauof temperatures ' :(b) bar. kba3r YSICAL REVIEW LETTERS Cooleyet al (1995) 33 kb Kondo Lattice E body state of EntangledClo many spins and electrons gives rise to many new kinds of order. 53 kb Kondo Insulators 60 kbar 66 kbar,i T(K) 0 0.0 0.2 0.4 1/T(K) 1. The electrical resistivity p as a function of temfig.mag, Mott Phil 30,403,1974 perature (a) and inverse temperature (b). (b) Q = 1 bar, = 33 kbar, A = 45 kbar, and = 25 kbar, Q = 24 kbar, A = 53 kbar. The solid lines in (b) are fits by the function [p(t)] ' = [po(p)] ' + (p,(p) exp[a(p)/k&t]) ', described in the text. over which simple linear becomes increasingly limited define with increased pressure. In co resistor formulation provides uniformly SmB6 range, and consequently pressure Sm2.7+ yie determination of A. Since there is no evidence in SmB6 B6 at or below 60 kbar structural change appearance of 5 suggests that it is not tion gap, for in that case the insulat occurs by band crossing and the gap tinuously to zero. A valence instabilit discounted, as high pressure x-ray a ments [] find that the Sm valence from +2.6 to +2.75 between 1 bar and We have used Hall effect measurem evolution of the camers in the vicinit constant RH is plotted as a function o pressures ranging from 1 bar to 66 k T bet RH is negative for temperatures and at all pressures, as well as indepe

Kondo Insulators Broken Kondo Singlets 1968 PH 74, NUMBER 9 VOLUME 1 1 $P -24. kba3r Cooleyet al (1995) 33 kb Kondo Lattice E body state of EntangledClo many spins and electrons gives rise to many new kinds of order. 53 kb Topological Kondo Insulators 60 kbar (Dzero,Sun,PC,Galitski (20) Wolgast et al (2013). Persistent conduc-vity Plateauof temperatures ' :(b) bar YSICAL REVIEW LETTERS 66 kbar,i T(K) 0 0.0 0.2 0.4 1/T(K) 1. The electrical resistivity p as a function of temfig.mag, Mott Phil 30,403,1974 perature (a) and inverse temperature (b). (b) Q = 1 bar, = 33 kbar, A = 45 kbar, and = 25 kbar, Q = 24 kbar, A = 53 kbar. The solid lines in (b) are fits by the function [p(t)] ' = [po(p)] ' + (p,(p) exp[a(p)/k&t]) ', described in the text. over which simple linear becomes increasingly limited define with increased pressure. In co resistor formulation provides uniformly SmB6 range, and consequently pressure Sm2.7+ yie determination of A. Since there is no evidence in SmB6 B6 at or below 60 kbar structural change appearance of 5 suggests that it is not tion gap, for in that case the insulat occurs by band crossing and the gap tinuously to zero. A valence instabilit discounted, as high pressure x-ray a ments [] find that the Sm valence from +2.6 to +2.75 between 1 bar and We have used Hall effect measurem evolution of the camers in the vicinit constant RH is plotted as a function o pressures ranging from 1 bar to 66 k T bet RH is negative for temperatures and at all pressures, as well as indepe

Kondo Insulators Broken Kondo Singlets Neupane, arxiv: 1306.4634 Nature(2013). 1968 VOLUME PH 74, NUMBER 9 YSICAL REVIEW LETTERS Persistent conduc-vity Plateauof temperatures ' over which simple 1 bar.:(b) Cooleyet al (1995) linear becomes increasingly limited -24 kba3r P $ define with increased pressure. In co resistor formulation provides uniformly 33 kb SmB6 range, and consequently pressure Sm2.7+ yie Kondo Lattice determination of A. E o body state of EntangledCl many Since there is no evidence in SmB6 B6 at or below 60 kbar structural change spins and electrons gives rise to appearance of 5 suggests that it is not many new kinds of order. tion gap, for in that case the insulat 53 kb Topological Kondo Insulators occurs by band crossing and the gap 60 kbar (Dzero,Sun,PC,Galitski (20) tinuously to zero. A valence instabilit 66 kbar Wolgast et al (2013). discounted, as high pressure x-ray a 0 0.0 0.2 0.4 ments [] find that the Sm valence T(K) 1/T(K) from +2.6 to +2.75 between 1 bar and tem1. FIG. The electrical resistivity p as a function of We have used Hall effect measurem perature (a) and inverse temperature (b). (b) Q = 1 bar, evolution of the camers in the vicinit = 33 kbar, A = 45 kbar, and = 25 kbar, Q = 24 kbar, Fermi and dispersion of SmB (a) Ferm constant maps A = 53 kbar. The solid FIG. as6.a function o lines in3: (b) are fitssurface RH is plotted by the function ' + ' = [p(t)] [po(p)] (p,(p) exp[a(p)/k&t]) ', described pressures ranging from 1 bar to 66 k measured by 7 ev LASER source at temperature of 7 K. A small pock in the text. T bet RH is negative for temperatures and atcircular all pressures, well dash as indepe are observed. A big elliptical and a small shaped as black lines 1,I

Kondo Insulators Broken Kondo Singlets Neupane, arxiv: 1306.4634 Nature(2013). 1968 VOLUME PH 74, NUMBER 9 YSICAL REVIEW LETTERS Persistent conduc-vity Plateauof temperatures ' over which simple 1 bar.:(b) Cooleyet al (1995) linear becomes increasingly limited -24 kba3r P $ define with increased pressure. In co resistor formulation provides uniformly 33 kb SmB6 range, and consequently pressure Sm2.7+ yie Kondo Lattice determination of A. E o body state of EntangledCl many Since there is no evidence in SmB6 B6 at or below 60 kbar structural change spins and electrons gives rise to appearance of 5 suggests that it is not many new kinds of order. tion gap, for in that case the insulat 53 kb Topological Kondo Insulators occurs by band crossing and the gap 60 kbar (Dzero,Sun,PC,Galitski (20) tinuously to zero. A valence instabilit 66 kbar Wolgast et al (2013). discounted, as high pressure x-ray a 0 0.0 0.2 0.4 ments [] find that the Sm valence T(K) 1/T(K) from +2.6 to +2.75 between 1 bar and tem1. FIG. The electrical resistivity p as a function of We have used Hall effect measurem and inverse perature (a) temperature Collin Broholm: what happens to the (b).correlations (b) Q = 1 bar, between d- and! evolution of the camers in the vicinit = 33 kbar, A = 45 kbar, and = 24 kbar, = 25 kbar, Q anddevelops? dispersion of SmB (a) Ferm f-electrons topological insulator constant maps A = 53 kbar.asthe as6.a function o lines in3: Kondo solid FIG. are fitssurface RH is plotted (b)fermi by the function ' + ' = [p(t)] [po(p)] (p,(p) exp[a(p)/k&t]) ', described pressures ranging from 1 bar to 66 k measured by 7 ev LASER source at temperature of 7 K. A small pock in the text. T bet RH is negative for temperatures and atcircular all pressures, well dash as indepe are observed. A big elliptical and a small shaped as black lines 1,I

Kondo Insulators Broken Kondo Singlets Neupane, arxiv: 1306.4634 Nature(2013). 1968 VOLUME PH 74, NUMBER 9 YSICAL REVIEW LETTERS Persistent conduc-vity Plateauof temperatures ' over which simple 1 bar.:(b) Cooleyet al (1995) linear becomes increasingly limited -24 kba3r P $ define with increased pressure. In co resistor formulation provides uniformly 33 kb SmB6 range, and consequently pressure Sm2.7+ yie Kondo Lattice determination of A. E o body state of EntangledCl many Since there is no evidence in SmB6 B6 at or below 60 kbar structural change spins and electrons gives rise to appearance of 5 suggests that it is not many new kinds of order. tion gap, for in that case the insulat 53 kb Topological Kondo Insulators occurs by band crossing and the gap 60 kbar (Dzero,Sun,PC,Galitski (20) tinuously to zero. A valence instabilit 66 kbar Wolgast et al (2013). discounted, as high pressure x-ray a 0 0.0 0.2 0.4 ments [] find that the Sm valence T(K) 1/T(K) from +2.6 to +2.75 between 1 bar and tem1. FIG. The electrical resistivity p as a function of We have used Hall effect measurem and inverse perature (a) temperature Collin Broholm: what happens to the (b).correlations (b) Q = 1 bar, between d- and! evolution of the camers in the vicinit = 33 kbar, A = 45 kbar, and = 24 kbar, = 25 kbar, Q anddevelops? dispersion of SmB (a) Ferm f-electrons topological insulator constant maps A = 53 kbar.asthe as6.a function o lines in3: Kondo solid FIG. are fitssurface RH is plotted (b)fermi by the function ' + ' = [p(t)] [po(p)] (p,(p) exp[a(p)/k&t]) ', described pressures ranging from 1 bar to 66 k measured by 7 ev LASER source at temperature of 7 K. A small pock in the text. is negative for temperatures T bet RHthe Collin Broholm: what collective excitations result from excitonic Kondo lattic and atcircular all pressures, well dash as indepe are observed. A big elliptical and a small shaped as black lines 1,I

Heavy Fermion Metals Ott et al (1976) Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. TopologicalKondo Insulators (Dzero,Sun,PC,Galitski (20) Wolgast et al (2013). Heavy Fermion Metals:

Heavy Fermion Metals Coherent HFs~Hole doped KIs ~TK Ott et al (1976) Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. TopologicalKondo Insulators (Dzero,Sun,PC,Galitski (20) Wolgast et al (2013). Heavy Fermion Metals:

Heavy Fermion Metals Coherent HFs~Hole doped KIs ~TK (T )= 0 + AT 2 Ott et al (1976) Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. TopologicalKondo Insulators (Dzero,Sun,PC,Galitski (20) Wolgast et al (2013). Heavy Fermion Metals:

Heavy Fermion Metals Coherent HFs~Hole doped KIs Ali Yazdani: spectroscopically! image the composite HF? ~TK Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. TopologicalKondo Insulators (Dzero,Sun,PC,Galitski (20) Wolgast et al (2013). Heavy Fermion Metals: (T )= 0 + AT 2 Ott et al (1976) J N c j S V j f j Composite Fermion Singlet formation Energy [mev] 60 40 20 0-20 -40-60 0.15 0.25 0.35 0.45 0.55 0.65 q [2π/a,0]

Heavy Fermion Metals Coherent HFs~Hole doped KIs Ali Yazdani: spectroscopically! image the composite HF? ~TK (T )= 0 + AT 2 Ott et al (1976) Energy [mev] 60 40 20 0-20 Kondo Lattice Entangled many body state of spins and electrons gives rise to many new kinds of order. TopologicalKondo Insulators (Dzero,Sun,PC,Galitski (20) Wolgast et al (2013). Heavy Fermion Metals: J N c j S V j f j Composite Fermion Singlet formation -40-60 0.15 0.25 0.35 0.45 0.55 0.65 q [2π/a,0] Ali Yazdani: and what happens to them in a HF SC?

Quantum Criticality & SC RKKY Interaction Mott 1974, Doniach, 1977 T K = D exp[ 1/2J ] >

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Strange Metals. Yosuke Matsumoto -YbAlB 4

Strange Metals. Yosuke Matsumoto Y. Matsumoto et al, Science (2011) Bc < 0.1mT Critical field, if it exists, is no bigger than the earth s magnetic field (0.06mT) -YbAlB 4

Strange Metals. Yosuke Matsumoto Y. Matsumoto et al, Science (2011) Bc < 0.1mT Critical field, if it exists, is no bigger than the earth s magnetic field (0.06mT) -YbAlB 4 Matsumoto: Strange metal phase or QCP?

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Matsumoto: Strange metal phase or quantum critical point? Matsumoto: Can Topology play a role in strange metals?

Matsumoto: Strange metal phase or quantum critical point? Matsumoto: Can Topology play a role in strange metals? Broholm: what collective excitations result from the excitonic Kondo lattice? Broholm: what happens to the correlations between d- and! f-electrons as topological Kondo insulator develops? Thompson: Linear Resistance due to magnetic quantum Criticality? Thompson: How does a local moment time-share between SC and antiferromagnetism?