superglasses and the nature of disorder-induced si transition xiaoquan yu advisor: markus mueller...
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Superglasses and the nature of disorder-induced SI transition
Xiaoquan YuAdvisor: Markus Mueller
2,12,2012
Outline
• Introduction of spin glasses and Anderson localization.
• Superglasses- mean field phase diagram.• Hard core boson model on a Bethe lattice with
large connectivity.• Finite dimension
Anderson localization
Mobility edge
Spin glassesA spin glass is a magnet with random frustrated interactions.
Spin glasses display many metastable structures.
Ferromagnetic and antiferromagnetic bonds are randomly distributed.
Gaussion in one pure state
Many pure states.
Motivations• Glasses + quantum fluctuations- quantum
glasses. Low temperature properties?• Glasses+ superfluid ? Can two orders coexit?• Motivated by some supersoild experiments:
amorphous solids sustain more robust supersolidity.
Disorder may be a crucial element in understanding the supersolid systems
Superglasses• Model and method
Self consistent equations
Replica method
• Phasediagram
Robust to on-site disorderNot BCS type!
Gingras et al., PRL (2010).
QMC
Glassy SIT!
Exact result!
• Properties of superglasses phase
Local order parameters are anticorrelated
Non-monotonicity behavior of superfluid order parameter
Motivation and back grounds: conception
• Dirty superconductor.• Anderson’s theorem breaks down.• Localization of bosonic particles--- Bose glass.• Properties of Bosonic insulators.
Motivation and backgrounds: experiments
D. Shahar, Z. Ovadyahu, PRB 46, 10971 (1992).
J. M. Valles et al., PRL 103, 157001 (2009)
Activated behavior!
Indicating the exitence a boson mobility edge !
Activated transport near the SIT
Ioffe-Mezard’s proposal
• Model and cavity mean field method
Order parameter of conducting phase
M. V. Feigel'man, L. B. Ioffe, and M. Mezard, PRB (2010). L. B. Ioffe and M. Mezard, PRL(2010).
Cavity Hamiltonian of spin jj
• SI transition
Susceptibility
Replica method
Self-average quantity
Participation ratio
1-m
• Mobility edge Whether the pertubations relax?
Fermi golden rule
Pertubations on the boundary Matrix elements
???
Should be -1
Phase diagram
Superconductor
g
Temperature
Energy
Discrete levels
gc
Green and red line meet at zero energy
g gc
Temperature
Full localization, no mobility edge!Discrete levels
Continue spectrum
Energy
Ioffe – Mezard’s results
Superconductor
Expected scenario
L. B. Ioffe and M. Mezard, PRL(2010).
Comments
If the density of state is uniform , why one should expect there is a mobility edge? Indeed, there is no mobility edge in their model! So a mobility edge never appears? It appears in a Glassy insulator!
Phase diagram
Continue spectrum
Discrete levels
Superfluid emerges without closing mobility gap! Glassy SIT
May explain the puzzling feature (activated behavior)of transport in dirty SC films.
Thank you!
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