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/FSUAlfred P. Sloan FoundationNSF grant DMR-0234215

Vladimir Dobrosavljevic

Department of Physics and National High Magnetic Field LaboratoryFlorida State University

2D MIT: distinct experimental features

Drastic change of behavior near n = nc ~ 1011 cm-2

NOTE: behavior seen up to T ~ 0.25 TF; broad density range

Mass enhancedBut not the g-factor

Large resistivity drop!

Metal destroyed by small parallelfield near transition

Low density: rs ~ 10Close to Wigner crystal?

TF ~ 10K

Experimental puzzles:

A) On the metallic side:

• Origin of small energy scale T* ~ TF/m* ~ (n-nc)

• Origin of small field scale H* ~ ~ (n-nc)

• Large T-dependence of (drop) resistivity (factor 10!!),but only close to transition.

NOTE: strong enhancements seen ONLY close to the critical density nc

nc2nc

n

STRONG CORRELATION WEAK CORRELATION

INSULATOR STRANGE METAL F. L. METAL

What does the mass enhancement ”mean“??

Lessons from THERMODYNAMIC:

• Assume large: m* ~ (n-nc)-1 !1

• Then coherence temperaure: T* ~ TF/m*! 0

(Fermi liquid destroyed above T*)

• Large specific heat C ~ m*T

• Entropy per carrier:

• Conclusion:

MASS ENHANCEMENT = “ENTROPIC” INSULATOR??!!!

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

Physical picture: Wigner crystal melting as Mott transition(Analogy with He3; 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?)

Egap

•Low density: electrons tightly bound to lattice sites (electrostatic repulsion)

•Model: disordered Hubbard-like (charge-transfer) model.

•Microscopic modelling (density-dependent parameters)?

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

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 rs ≈ 10

Applications: Mott transition, heavy fermions

Phase diagram: density-driven Wigner-Mott transition

Density

rs

Correlatedmetal

• Large effective mass enhancement near transition:

m* ~ (n – nc)-1

• Correlated metallic state wiped out by Zeeman effects (parallel field)

• First-order finite T transition, but only BELOW T ~ 0.03TF

Wigner-Mott insulator

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

Friend or Foe???Friend or Foe???

Sir Neville MottSir Neville Mott

P. W. AndersonP. W. Anderson

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

DMFT-TMT Picture of the Anderson-Mott TransitionVD, Pastor, Nikolic, Europhys. Lett. 62, 76 (2003);

Dis

ord

er W

Dis

ord

er W

Byczuk, Hofstetter, Vollhardt, PRL 2004; NRG impurity solver

Anomalous metallic phase sandwiched between Mott and Anderson insulatorsAnomalous metallic phase sandwiched between Mott and Anderson insulators

Physical trajectory:

EF ~ n

U ~ n1/2

W ~ const.

•Strong T-dependence, factor > 10 drop!!!(solve full DMFT using IPT or slave bosons)

•Enhanced screening at low T due to correlations, even ascompressibility is small(approach to Mott transition)

•Strong inelastic scattering at higher T

•Incoherent Fermi liquid (low T* ~ TF/m*; distribution of local coherence scales)(microscopic origin of decoherence?)

Sca

tter

ing

rate

1/

T/TF

Experiment Theory

Disordered metallic phase: incoherent transport Tanaskovic, DeOliviera-Aguilar, Miranda, VD, Kotliar, Abrahams

(PRL 91, 066603 (2003), cond-mat/0305511)

T*

Sir Neville MottSir Neville Mott

P. W. AndersonP. W. Anderson

““It takes all the running you CAN do, It takes all the running you CAN do, simply to stay in one placesimply to stay in one place””

From From Alice in WonderlandAlice in Wonderlandas quoted by as quoted by P.W. Anderson in his Nobel LectureP.W. Anderson in his Nobel Lecture

Conclusions:

• Extended DMFT: order-parameter theoryorder-parameter theory for Anderson-Mott transition

• Non-perturbativeNon-perturbative approach to correlations in disordered systems

• Non-Fermi liquidNon-Fermi liquid behavior as precursor to MIT; two-fluid behavior

•Intermediate bad-metal phasebad-metal phase between Anderson and Mott insulators

• New physical picturephysical picture of MIT in correlated disordered systems

• What’s missing? Lots!

Nano-Scale Phase SeparationNano-Scale Phase Separation

Electron/Stripe Electron/Stripe GlassGlass

(can be incorported in DMFT framework)