Transcript Superglasses and the nature of SI transition
Superglasses and the nature of disorder-induced SI transition
Xiaoquan Yu Advisor: 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 glasses
A spin glass is a magnet with random frustrated interactions. Ferromagnetic and antiferromagnetic bonds are randomly distributed. Spin glasses display many metastable structures.
Many pure states.
Gaussion in one pure state
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
QMC Gingras et al., PRL (2010).
Robust to on-site disorder Glassy SIT!
Not BCS type!
Exact result!
• Properties of superglasses phase
Non-monotonicity behavior of superfluid order parameter Local order parameters are anticorrelated
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
Activated transport near the SIT
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 !
Ioffe-Mezard’s proposal
M. V. Feigel'man, L. B. Ioffe, and M. Mezard, PRB (2010).
L. B. Ioffe and M. Mezard, PRL(2010).
• Model and cavity mean field method Cavity Hamiltonian of spin j j Order parameter of conducting phase
• SI transition Self-average quantity Susceptibility Replica method Participation ratio
1-m
• Mobility edge Whether the pertubations relax?
???
Matrix elements Fermi golden rule Pertubations on the boundary Should be -1
Ioffe – Mezard’s results
Phase diagram
Expected scenario L. B. Ioffe and M. Mezard, PRL(2010).
Temperature
Energy Green and red line meet at zero energy
Temperature
Energy Full localization, no mobility edge!
Discrete levels Discrete levels Continue spectrum
Superconductor Superconductor
g c
g
g c
g
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
Glassy SIT Superfluid emerges without closing mobility gap !
May explain the puzzling feature (activated behavior)of transport in dirty SC films.