Universal dielectric breakdown and synaptic behaviour in Mott insulators

Transcription

1 Universal dielectric breakdown and synaptic behaviour in Mott insulators Marcelo Rozenberg LPS, CNRS Université Paris-Sud, Orsay IMN (Nantes, France) L. Cario E. Janod B. Corraze P. Stoliar (Nanogune) V. Guiot V. Ta Phuoc UBA (Buenos Aires, Argentina) C. Acha A. Camjayi CNEA (Buenos Aires, Argentina) R. Weht Refs: V. Guiot et al, Nat Comm (2013) P. Stoliar et al., Adv. Mat. (2013) A. Camjayi et al., Phys Rev Lett (2014) L. Cario et al Adv Func Mat (in press) Review

2 What is a Mott transition?

3 The classic example: Mott transition in V 2 O 3 T McWhan et al PRB pressure or chemical substitution

4 The Hubbard model is a minimal model for the metal insulator transition U = 0 ρ metal ~ t ω t = 0 ρ insulator ~ U ω

5 DMFT of the Mott Hubbard transition A. Georges et al. RMP 96 XY Zhang, MR, G. Kotliar PRL 92 Metal U = 1 Corr Met Mott U = 2 U = 2.5 Corr Met U = 3 Mott Insulator U = 4 Coexistance region: 2 solutions

6 The classic example: Mott transition in V 2 O 3 T McWhan et al PRB pressure or chemical substitution

7 Do Mott Hubbard systems exist in Nature? AM 4 X 8 family: tailor-made 3D Mott systems A = Ga, Ge M = V, Nb, Ta X = S, Se F 43m Å Tetrahedral Å Clusters Molecular orbitals Energy U eff Gap ~ 0.20 ev Pocha, R. et al., J. Am. Chem. Soc. 127, 8732 (2005)

8 Metal Insulator transition in GTS Pressure driven Mott transition E-field driven Mott transition Abd-Elmeguid et al., PRL 04 Non Volatile Resistive Switching, t <100 ns C. Vaju et al., Adv. Mater. 08

9 Is GaTa 4 Se 8 (GTS) really a Mott-Hubbard system? «Ideal system» 1 electron per Ta 4 cluster 3D fcc lattice Paramagnetic LDA predicts a metal But does not match some DMFT key predictions No hysteresis ρ(t) does not have non-monotonic behavior K-organics Limelette PRL (2003)

10 Conduction bands are isolated and have pure Ta character Nice system for an LDA+DMFT study

11 Wannier maximally localized molecular orbitals for Ta 4 tetrahedra Cubic FCC structure, t 2g symmetry

12 What is U? Uc = 1.2 ev hysteresis T MIT = 230K resisivity 1st order transition T Optical conductivity Resistivity (activation gap) A. Camjayi et al., Phys Rev Lett (2014)

13 Gold Silver Carbon Resistivity is nonmonotonic in the metal and has hysteresis at the IMT single x-tal! A. Camjayi et al., Phys Rev Lett (2014) Abd-Elmeguid et al., PRL 04

14 Mott physics + electronics «Mottronics» Applying strong E-fields to Mott systems

15 Do not mix up with the Mott transition in VO 2 1st order transition driven by T T T insulator metal ins met P Joule heating effect E-field effect Zimmers et al PRL 13 Driscoll PRB 12

16 Three different regimes non-volatile RS GaTa 4 Se 8 77 K Metal V t volatile RS Insulator V V t t delay t R bef R after no RS L. Cario et al. Adv. Mater. 10

17 E-field driven Mott transition in GTS E-field threshold V. Guiot et al. Nat Comm (2013)

18 Is the Mott electric-breakdown universal? Three different Mott-insulators: GaTa 4 Se 8 V 2-x Cr x O 3 NiS 2-x Se x Mott Corr Met Mott Corr Met Czjzek et al JMMM 76

19 Universal behavior: three different Mott Insulators P. Stoliar et al Adv. Mater. (2013)

20 What is the origin of the Mott electric-breakdown? Hubbard model 1D 1/ξ Δ Mott (1D) T. Oka et al F. Heidrich-Meisner et al 10 M. Eckstein et al (DMFT) A. Amaricci et al. 12 (DMFT)??? 1/ξ Δ Mott (3D)??? ξ µm (3D) Δ ~ 10-1 ev ξ ~ 1 nm = 10-7 cm F Th ~ 1 MV/cm E Th ~ 1 KV/cm!!!!

21 Model of the Mott resistive transition P. Stoliar et al Adv. Mater. (2013) Two states: MI Mott insulator CM Correlated metal R MI >> R CM P MI->CM and P CM->MI are transition probabilities

22 Model results: Threshold Mott resistive transition Experiment V S /V Th = 1.74, , 2.06 Theory

23 How the transition evolves in time? Each pixel is a cell of the resistor network model Color intensity indicates the local ΔV drops (ie local E)

24 How the transition evolves in time? (snapshots) time

25 Below threshold Threshold effect Above threshold

26 Threshold effect V S /V Th = 0.7, 1.1, 1.4, 1.8

27 Model prediction: Neuromorphic behaviour! Transition rates imply the existence of a relaxation time scale t relax Short pulses (< t delay ) are sent at intervals τ < t relax Model prediction τ Transition after 5 pulses Experiment P. Stoliar et al., Adv. Mat. (2013)

28 Summary GaTa 4 Se 8 is a new Mott-Hubbard system E-field driven Mott insulators show a universal resistive transition with threshold behavior A phenomenological model based on DMFT Mott-Hubbard physics captures the qualitative behavior of the Mott resistive transition New electronic emergent behavior: neuromorphic Refs: V. Guiot et al, Nat Comm (2013) P. Stoliar et al., Adv. Mat. (2013) A. Camjayi et al., Phys Rev Lett (2014) L. Cario et al Adv Func Mat (in press) Review