2. 2D-MIT as a Wigner-Mott Transition Collaborators: John Janik (FSU) Darko Tanaskovic (FSU) Carol Aguiar (FSU, Rutgers) Eduardo Miranda (Campinas) Gabi Kotliar (Rutgers) Elihu Abrahams (Rutgers) Funding NHMFL/FSU Alfred P. Sloan Foundation NSF grant DMR-0234215 Vladimir Dobrosavljevic Department of Physics and National High Magnetic Field Laboratory Florida State University

3. 2D MIT: distinct experimental features Drastic change of behavior near n = n c ~ 10 11 cm -2 NOTE: behavior seen up to T ~ 0.25 T F ; broad density range Mass enhanced But not the g-factor Large resistivity drop! Metal destroyed by small parallel field near transition Low density: r s ~ 10 Close to Wigner crystal? T F ~ 10K

4. Experimental puzzles: A)On the metallic side: Origin of small energy scale T * ~ T F /m * ~ (n-n c ) Origin of small field scale H * ~   ~ (n-n c ) Large T-dependence of (drop) resistivity (factor 10!!), but only close to transition. NOTE: strong enhancements seen ONLY close to the critical density n c ncnc 2n c n STRONG CORRELATIONWEAK CORRELATION INSULATORSTRANGE METAL F. L. METAL

5. What does the mass enhancement ”mean“?? Lessons from THERMODYNAMIC: Assume large: m * ~ (n-n c ) -1 !1 Then coherence temperaure: T * ~ T F /m * ! 0 (Fermi liquid destroyed above T * ) Large specific heat C ~ m * T Entropy per carrier: Conclusion: MASS ENHANCEMENT = “ENTROPIC” INSULATOR??!!!

6. B) On the insulating side: Nature of the insulator: origin of magnetism? Near transition: (Sivan et al.) Susceptibility approaches FREE SPIN LIMIT!!! Local moment magnetism??? Origin of glassy behavior – disorder dependence (experiments by D. Popovic) My claim: all features: approach to Wigner-Mott glass

7. Physical picture: Wigner crystal melting as Mott transition (Analogy with He 3 ; Spivak 2001; Dolgopolov 2002) Wigner crystal ~ Mott insulator (magnet) Melting: Vacancy-Interstitial pair formation (Phillips, Ceperley; 2001) Ignore “phonons” (Giamarchi, le Doussal,...) (lattice distortions - pinned by impurities?) E gap Low density: electrons tightly bound to lattice sites (electrostatic repulsion) Model: disordered Hubbard-like (charge-transfer) model. Microscopic modelling (density-dependent parameters)?

8. Coulomb potential (side view) Interstitial orbital Lattice orbital Charge-transfer (vacancy-interstitial) model (similar model as in oxides, cuprates) Virtual process: hopping in and out of interstitial site (similar as superexchange through the oxygen p-orbital in oxides) Correlations: single-occupation (U=inf.) constraint in the lattice orbitals Remains at half-filling at any density, bands broaden: bandwith-driven Mott transition Coulomb potential (top view) Quantum Fluctuations

9. MIT – Mott transition + disorder Use DMFT !! Interstitial band Lower Hubbard band (U=inf.) Energy Density-dependent band structure: results (J. Janik, V.D., 2005) Bands cross around r s ≈ 10

10. Applications: Mott transition, heavy fermions

11. Phase diagram: density-driven Wigner-Mott transition Density rsrs Correlated metal Large effective mass enhancement near transition: m * ~ (n – n c ) -1 Correlated metallic state wiped out by Zeeman effects (parallel field) First-order finite T transition, but only BELOW T ~ 0.03T F Wigner-Mott insulator

12. Effects of disorder: The Good, the Bad, and the Ugly

13. Friend or Foe??? Sir Neville Mott P. W. Anderson

14. (VD, Pastor, Nikolic, Europhys. Lett. 62, 76 (2003))

15. DMFT-TMT Picture of the Anderson-Mott Transition VD, Pastor, Nikolic, Europhys. Lett. 62, 76 (2003); Disorder W Byczuk, Hofstetter, Vollhardt, PRL 2004; NRG impurity solver Anomalous metallic phase sandwiched between Mott and Anderson insulators Physical trajectory: E F ~ n U ~ n 1/2 W ~ const.

16. Strong T-dependence, factor > 10 drop!!! (solve full DMFT using IPT or slave bosons) Enhanced screening at low T due to correlations, even as compressibility is small (approach to Mott transition) Strong inelastic scattering at higher T Incoherent Fermi liquid (low T* ~ T F /m*; distribution of local coherence scales) ( microscopic origin of decoherence?) Scattering rate 1/  T/T F Experiment Theory Disordered metallic phase: incoherent transport Tanaskovic, DeOliviera-Aguilar, Miranda, VD, Kotliar, Abrahams (PRL 91, 066603 (2003), cond-mat/0305511) T*

17. Sir Neville Mott P. W. Anderson “ It takes all the running you CAN do, simply to stay in one place ” From Alice in Wonderland as quoted by P.W. Anderson in his Nobel Lecture

18. Conclusions : order-parameter theory Extended DMFT: order-parameter theory for Anderson-Mott transition Non-perturbative Non-perturbative approach to correlations in disordered systems Non-Fermi liquid Non-Fermi liquid behavior as precursor to MIT; two-fluid behavior bad-metal phaseIntermediate bad-metal phase between Anderson and Mott insulators physical picture New physical picture of MIT in correlated disordered systems What’s missing? Lots! Nano-Scale Phase Separation Electron/Stripe Glass (can be incorported in DMFT framework)