Mott Metal Insulator Transitions Satej Soman, Robert Tang-Kong March 21, Physics 141A 1
Mott Metal Insulator Transitions
Satej Soman, Robert Tang-KongMarch 21, Physics 141A
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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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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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Band Gap Theory
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● 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
Example of Bandgap Tuning
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Mott Insulator Theory
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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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Mott Insulators: Theory
● Partially filled band should allow conduction○ Application of E-field would allow conduction.
● Transition metals cause problems9
Chzran, MSE102, Lec 7
Mott Insulators: Theory
● Partially filled band should allow conduction○ Application of E-field would allow conduction.
● Transition metals cause problems9
Chzran, MSE102, Lec 7
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)10
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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Examples & Applications
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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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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
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)15
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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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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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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Appendix
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