Bad Metal Behavior and Mott Quantum Criticality

Transcription

1 Bad Metal Behavior and Mott Quantum Criticality Vladimir Dobrosavljevic Florida State University Collaborators: Jaksa Vucicevic (Belgrade, Serbia) Hanna Terletska (FSU, Ames Lab) Darko Tanaskovic (Belgrade, Serbia) Marcelo Rozenberg (Orsay) Funding: Abrahams, Chakravarty, Kotliar, Haule, Miranda, Pankov,... NSF grants: DMR

2 From Metals to Insulators: universality at ``high temperatures carrier density: Wigner-Mott 2DEG pressure: Mott organics Si-MOSFET TF ~ 10K

3 MIT Quantum Cri4cality? T Can t decide (quantum critical region) Insulator Metal QCP Fermi energy

4 2D- MIT: Duality Scaling??? T o dn nz mirror symmetry S. Kravchenko, D. Popovic 1997

5 Scaling Theory Redux b T (g)= d lng d lnt 1 nz lng strong coupling - dominated by insulator? g(t ) g o exp{dn(t o /T ) 1/nz } znbt g (dn,t = 1/g ( dn,t ) Experiment: D. Popovic, 1997 s/s c

6 How to tackle Phase Transitions? Standard critical points: Spontaneous symmetry breaking Order parameter, Landau-Ginzburg Renormalization group, field theory Metal-Insulator Transitions: NO symmetry breaking! Order parameter???

7 Maximally Frustrated Hubbard Model Infinite-range model Suppress all orders: pure Mott Local self-energy: DMFT solution Kondo physics forms Fermi liquid

8 Finite temperature transport: the Mott transition at half-filling (also J. Vučičevic, et al., Phys. Rev. B, 88, (2013)) Experiment: organic Mott system Jerome, PRL 2003 Theory (DMFT) Early work: Kotliar, Rozenberg 1992, etc. Tc ~2%TF Fermi liquid Mott insulator

9 Crossover - quantum Widom line! Recent work: Sordi, Tramblay, 2012, etc. DMFT theory around Widom line Mott insulator kfl << 1 impossible Fermi liquid Tc ~2%TF kfl = 1 MOSFET: Tc ~2%TF ~ 200mK

10 Crossover line: eigenvalue analysis Curvature - eigenvalue Free energy landscape (actual quantitative results!) T >Tc l(u) l(u)=l min l(u) > l min T =Tc l = 0 U*(T) U T <Tc du = U U (T ) On crossover line Away from crossover line du(t )=0 du(t ) 6= 0

11 Scaling r(du,t )/r c (T )= f (T /T o (du)) du > 0 mirror symmetry! du < 0

12 Mott organics: universal high-t scaling K. Kanoda et al., Nature Physics (2015) Weaker frustration: AFM at low T Strong frustration: spin liquid at low T

13 Mott organics: universal high-t scaling K. Kanoda et al., Nature Physics (2015) zν = 0.60 and c = 25.3 for κ-cu2(cn)3 zν = 0.55 and c = 65.8 for κ-cl zν = 0.65 and c = 18.9 for EtMe3Sb-dmit mirror symmetry! stretched exponential

14 Doped Mott insulators: Bad Metals vs. Quantum Criticality?? Mott-Ioffe-Regel limit: kfl > 1 kfl = 1 Experiment: H. Takagi, 1992

15 Tc = 0.03 Tc = 0.003

16 TINY coexistence dome Tc = Doped Mott: DMFT vs. QCP? J. Vučičevic, D.Tanaskovic, M. Rozenberg, and V. D., 2014

17 Doped Mott:QC Scaling J. Vučičevic, D.Tanaskovic, M. Rozenberg, and V. D., 2014 kfl = 1 New feature: Quantum Widom Line - MIR limit mirror symmetry: defines QC region stretched exponential

18 Doped Mott: Quantum Critical Region? J. Vučičevic, D.Tanaskovic, M. Rozenberg, and V. D., 2014 (Kotliar, 2014) Key Results: kfl = 1 Bad Metal (linear resistivity ~ MIR limit) = Mott QC region QC Scaling - (semi) analytical formula for linear-t resistivity

19 Doped Mott: Theory vs. Experiment J. Vučičevic, D.Tanaskovic, M. Rozenberg, and V. D., 2014 Mott QC region: universal behavior at high temperatures

20 Moral of the story - using words anyone can understand - Bad Liquid: AdS-CFT?? Viscous (quantum) liquid is not a gas (Landau quasiparticles)

21 To learn more: (just Google Bad Metals ) Book: Oxford University Press, 2012 ISBN

22 Really, but really bad metals: resistivity maxima (experiments) MOSFETs And now... something completely different V2O3 22

23 Phenomenological scaling (experiments) MOSFETs theory All curves!

24 Evaporating the Fermi liquid Darko Tanaskovich Low Fermi liquid coherence scale T FL ZT F T F /m Thermal death of quasi-particles?

25 DMFT theory Theory theory Experiment

26 Approaching the transition - trends DMFT Theory Experiments