![Page 1: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/1.jpg)
Collaborators:
Oscar Najera (Orsay) Marcello Civelli (Orsay) Marcelo Rozenberg (Orsay) Tsung-Han Lee (FSU, Rutgers) Serge Florens (Grenoble)
Peierls vs. Mott: Resolving the VO2 Controversy
Vladimir Dobrosavljevic Florida State University
http://badmetals.magnet.fsu.edu
Funding: NSF grants: DMR-1410132 …
Peierls
Mott
![Page 2: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/2.jpg)
Metal-Insulator Transition
Structural transition - dimerization Resistivity jump
![Page 3: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/3.jpg)
Peierls?
2a
Peierls opening of a gap (weak coupling effect):
VO2 DFT Band-structure (DFT): insufficient for gap (3D!)
Correlations: band gap increase? (S. Biermann + A. Georges, 2005,…)
Renormalized band insulator
![Page 4: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/4.jpg)
Mott?
ρmetal
ρinsulator
U=0
t=0
ω~t
ω~U
Thermally driven transition??
![Page 5: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/5.jpg)
Thermally-Driven Mott Transitions?
Transition-Metal Oxides: V2O3 Mc Whan (1973)
Organic Mott Systems Kanoda (2005)
![Page 6: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/6.jpg)
Tc ~2%TFFermi liquid
Mott insulator
Finite temperature transport: the Mott transition at half-filling
(single-site) DMFT Theory
![Page 7: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/7.jpg)
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”
![Page 8: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/8.jpg)
Thermally-Driven Mott Transition?
Mott insulator
Fermi liquid metal
Low-T Insulator to High-T Metal:
WHY?
Mott insulator
Fermi liquid metal
![Page 9: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/9.jpg)
Entropy: Clausius-Clayperon Equation
Gas has more entropy than liquid!
(http://en.wikipedia.org/wiki/Clausius–Clapeyron_relation)
![Page 10: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/10.jpg)
Thermally-Driven Mott Transition?
Mott insulator “free spins”
Fermi liquid metal
Low-T Insulator to High-T Metal:
Mott insulator has more (spin) entropy than FL
(no inter-site spin correlations)
Mott insulator
Fermi liquid metal
![Page 11: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/11.jpg)
New experiments: MIT by heating, but without structural change?
Metallic Monoclinic Phase?
2007-2017
(Hyun-Tak Kim, 2007)
![Page 12: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/12.jpg)
Can one have a T-driven transition from a low T insulator to a high T metal
without a structural (symmetry) change???
(“Pure Mott”)
?
![Page 13: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/13.jpg)
Taming the Mott Insulator: Super-exchange?
Generates AFM correlations, order Not too important in most transition metal oxides due to Hund’s rule coupling (FM correlations)
Exception: cuprates - spin gap from J
“Pseudogap"
“Bad Metal”
![Page 14: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/14.jpg)
Spin correlations from dimerization:
Cluster DMFT on dimer (“RVB”)
(CTQMC, ITP., Exact Diag.)
“Freeze” structure (dimerization), change T
Dimer hopping
U=0U > 0
![Page 15: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/15.jpg)
The tale of two singlets: removing entropy
un-dimerized dimerizedMIT coexistence region: “spin-gap”
low T insulator high T metal
(Clausius-Clayperon)
Monoclinic (dimerized) metal: two overlapping quasiparticle bands
Monoclinic (dimerized) insulator: gap opens due to singlet formation
![Page 16: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/16.jpg)
Monoclinic Metallic Phase as seen in optics
Basov, Science (2007)
experiment (Basov)
our theory
our theory
Metallic dimerized domains form before structural transition
signal from metallic domains
![Page 17: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/17.jpg)
metal
insulator
What really happens?
Spin correlations large in insulators, weak (“screened’’) in metals
(note: effect ignored in “plain vanilla” RVB theory)
inter-site spin correlation
![Page 18: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/18.jpg)
RVBDynamical Spinon
DMFT
Σf(iω)
Jeff Tsung-Han LeeSlave-rotor representation:
Spinion excitations destroyed by charge fluctuations as soon
as the Mott gap closes
spinons
Fermi liquid
Mott insulator
Where else is this important?
![Page 19: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/19.jpg)
Physical picture of the Mott transition
The Fermi liquid and the (spinon) magnetic fluid are not “miscible”
Generic first-order transition in kappa-organics and VO2
Destruction of spin correlations when charge
gap closes
oil and wateromelette
![Page 20: Peierls vs. Mott: Resolving the VO2 Controversylptms.u-psud.fr/ecrys2017/files/2017/09/Dobrosavljevic-ECRYS-2017.pdf · Collaborators: Oscar Najera (Orsay) Marcello Civelli (Orsay)](https://reader033.vdocument.in/reader033/viewer/2022041722/5e4f4cbbb0a8bf0ee510b4c0/html5/thumbnails/20.jpg)
Super-exchange correlations: phase diagram at half-filling
High dimensions (d=3) Low dimensions d=1,2:
M2, MMP(M3) phase of VO2 ??