Mott metal insulator transitions

1. Mott Metal Insulator
Transitions
Satej Soman, Robert Tang-Kong
March 21, Physics 141A
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2. Definitions:
What is a Mott Insulator?
● Metal that stops conducting at low
temperature or high pressure, despite
classical theory predicting conduction
● "Inverse superconductor"
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3. Mott Insulator: Outline
● Band Gap Theory
○ Conduction and valence bands
○ Tuning the bandgap
● Mott Insulators
○ Origins
○ Theory
○ Superfluids
● Examples & Applications
○ VO2
○ Memristors
○ Actuators
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4. Band Gap Theory
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5. ● Band Gap (or lack thereof)
responsible for conductors,
semiconductors, and insulators.
Band Gap Theory and Conduction
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● Fermi Level: naturally half-way
between conduction and valence
bands

6. Example of Bandgap Tuning
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7. Mott Insulator Theory
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8. Mott Insulators: Origins
● Sir Nevill Francis
Mott (1977 Nobel
Laureate)
● Pointed out fatal
flaw in central
approximation in
band theory: Inter-
electron forces are
not negligible
http://en.wikipedia.org/wiki/Nevill_Francis_Mott
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9. Mott Insulators: Theory
● Partially filled band should allow conduction
○ Application of E-field would allow conduction.
● Transition metals cause problems
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Chzran,
MSE102,
Lec 7

10. Mott Insulators: Theory
● Partially filled band should allow conduction
○ Application of E-field would allow conduction.
● Transition metals cause problems
9
Chzran,
MSE102,
Lec 7

11. Mott Insulators: Theory
● Balancing act:
○ Confining potential (potential
well)
○ Coulombic repulsion of
electrons
● Classically allowed under
Pauli exclusion principle
● Can be caused by:
○ Temperature
○ Pressure
Erwin, Steven C. Nature 441, (2006)
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12. Superfluid to Mott Insulator
● Similar theory, applied to condensed atomic
gas.
Greiner and Bloch. “Quantum Phase Transition from a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms.” Nature 415
● Kronig-Penny potential generated by
Optical standing waves
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13. Examples & Applications
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14. Mott Insulators: VO2
Martens, K, Journal of Applied Physics 112, no. 12 (2012): 124501. doi:10.1063/1.4767473.
● MIT splits conduction band
● Comes with free phase transition!
● Characteristic of Mott Insulators
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15. Mott Insulators: Memristors
● Leon Chua's "Memory Resistors" -->
● Low Power Memory
● Machine learning
Driscoll, T., “Phase-transition Driven Memristive System.” Applied Physics Letters 95, no. 4 (2009) 14

16. Mott Insulators: Actuators
● Bimorph
Actuators
● Thermal
Sensing
Liu, Kai, “Giant-Amplitude, High-Work Density Microactuators... Nanolayer Bimorphs.” Nano Letters 12, no. 12 (December 12, 2012)
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17. Mott Insulators: Recap
● How things conduct
○ Band Gap
○ Fermi Level
● Why some things don't conduct
○ Large Band Gap
○ Mott Insulators
● Why not conducting can be awesome.
○ Actuators
○ Memristors
○ and more!
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18. Conclusions
● Low-temperature quantum effects cause
divergent behavior from classical theory,
resulting in anomalous behavior in certain
materials.
● Kronig-Penney model, despite being a "toy"
model, is used in active research
● Crystal structures matter!
● Mott insulators have important applications
in MEMS and computing
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19. References
● Mott, N. F. Metal-Insulator Transitions. 2nd ed. Tayor & Francis: London. 1990
http://badmetals.magnet.fsu.edu/pdfs/Mott90book-chap8.pd
● Kohsaka, Y.; Taylor, C.; Wahl, P.; et al. (August 28, 2008). "How Cooper pairs vanish approaching the Mott
insulator in Bi2Sr2CaCu2O8+δ". Nature 454 (7208): 1072–1078. Bibcode 2008Natur.454.1072K. doi:10.1038
/nature07243. PMID 18756248.
● Imada, Masatoshi, Atsushi Fujimori, and Yoshinori Tokura. “Metal-insulator Transitions.” Reviews of Modern
Physics 70, no. 4 (1998): 1039.
● Sze, Simon M., and Kwok Kwok. Ng. Physics of Semiconductor Devices. Hoboken, NJ: Wiley-Interscience, 2006.
Print.
● Erwin, Steven C. “Solid-state Physics: When Is a Metal Not a Metal?” Nature 441, no. 7091 (2006): 295–296.
● Martens, K., I. P. Radu, S. Mertens, X. Shi, L. Nyns, S. Cosemans, P. Favia, et al. “The VO2 Interface, the Metal-insulator
Transition Tunnel Junction, and the Metal-insulator Transition Switch On-Off Resistance.” Journal of Applied Physics 112,
no. 12 (2012): 124501. doi:10.1063/1.4767473.
● http://www.physics.fsu.edu/users/Dobrosavljevic/Phase%20Transitions/mott-paper.pdf
● Driscoll, T., H.-T. Kim, B.-G. Chae, M. Di Ventra, and D. N. Basov. “Phase-transition Driven Memristive System.” Applied
Physics Letters 95, no. 4 (2009): 043503. doi:10.1063/1.3187531.
● Liu, Kai, Chun Cheng, Zhenting Cheng, Kevin Wang, Ramamoorthy Ramesh, and Junqiao Wu. “Giant-Amplitude, High-Work
Density Microactuators with Phase Transition Activated Nanolayer Bimorphs.” Nano Letters 12, no. 12 (December 12,
2012): 6302–6308. doi:10.1021/nl303405g.
● Greiner, Markus, Olaf Mandel, Tilman Esslinger, Theodor W. Hänsch, and Immanuel Bloch. “Quantum Phase Transition
from a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms.” Nature 415, no. 6867 (2002): 39–44.
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20. Appendix
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