Session Q10: Invited Session: Rare Fluctuation Effects in Strongly Disordered Systems

Rare Fluctuation Effects in the Anderson Model of Localization

Two significant advances in the theory of disordered systems in the past three decades have been (i) the development of large disorder Renormalization Group methods, and (ii) a more concerted effort to study of the effects of rare fluctuations or configurations, such as Griffiths' phenomena. A major problem facing the latter in many-body systems has been the enormous numerical resources needed to see these rare phenomena. In this talk, we examine the issue of rare configuration effects in Anderson's original model of localization (1958). In this talk, we examine the issue of rare configuration effects in Anderson's original model of localization. We show that effects due to resonant tunneling among neighboring sites leads not only to anomalous behavior of electronic eigenstates far in the Lifshitz tail, where the density of states is exponentially suppressed, but also leads to singularities in average properties (i.e. the inverse participation ratio) as a function of energy, where the density of states is large. The singular behavior, which separates resonant, Lifshitz-like states from typical, Anderson-localized states, occurs \emph{in the insulating phase}, and thus is present in \emph{all} dimensions [1]. Using the analytic solution of a toy model, as well as numerical results of the Anderson model for several different disorder distributions in dimensions d = 1, 2 and 3, we show that this separation of eigenstates due to rare fluctuations is a ubiquitous property of the Anderson model with \emph {bounded} disorder. This suggests that the half-century-old model, being solvable in polynomial time, is a prime candidate for detailed numerical studies of rare fluctuation effects in disordered systems. \\[4pt] [1] Sonika Johri and R. N. Bhatt, arXiv1106.1131; and in preparation.   

Electronic Griffiths Phases and Quantum Criticality at Disordered Mott Transitions

The effects of disorder are investigated in strongly correlated electronic systems near the Mott metal-insulator transition. Correlation effects are found\footnote{E. C. Andrade, E. Miranda, and V. Dobrosavljevic, Phys. Rev. Lett., \textbf{102}, 206403 (2009).} to lead to strong disorder screening, a mechanism restricted to low-lying electronic states, very similar to what is observed in underdoped cuprates. These results suggest, however, that this effect is not specific to disordered d-wave superconductors, but is a generic feature of all disordered Mott systems. In addition, the resulting spatial inhomogeneity rapidly increases\footnote{E. C. Andrade, E. Miranda, and V. Dobrosavljevic, Phys. Rev. Lett., \textbf{104} (23), 236401 (2010).} as the Mott insulator is approached at fixed disorder strength. This behavior, which can be described as an Electronic Griffiths Phase, displays all the features expected for disorder-dominated Infinite-Randomness Fixed Point scenario of quantum criticality.   

Gaps and Pseudogaps across the inhomogeneous superconductor to paired insulator transition

The mechanism for the disorder-tuned superconductor to insulator transition (SIT) in thin films and the nature of the resulting insulator are still debated, despite decades of research. We use quantum Monte Carlo simulations [1] that treat, on an equal footing, inhomogeneous amplitude variations and phase fluctuations, and go beyond our earlier Bogoliubov-deGennes analysis [2]. We gain new microscopic insights into the SIT, compare our theory with experiments [3] and make testable predictions for local spectroscopic probes. The energy gap in the single-particle density of states survives across the transition, but coherence peaks exist only in the superconducting state. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has signatures of pairing with a two-particle gap scale that vanishes at the superconductor--insulator transition, despite a robust single-particle gap. The impact of rare regions on the gaps will also be discussed. In collaboration with K. Bouadim, Y.L.Loh and N. Trivedi. \\[4pt] [1] K. Bouadim, Y.L.Loh, M. Randeria and N. Trivedi, Nature Phys. 7, 884 (2011). \\[0pt] [2] A. Ghosal, M. Randeria, and N. Trivedi, Phys. Rev. B 65, 014501 (2001). \\[0pt] [3] B. Sacepe et al., Nature Comm. 1, 140 (2010); Nature Phys. 7, 239 (2011); M. Mondal et al., Phys. Rev. Lett. 106, 047001 (2011).   

Infinite-randomness criticality in disordered metals and superconductors

Quantum phase transitions in disordered systems often display unconventional behavior which is dominated by rare strongly coupled spatial regions. In this talk, we investigate magnetic and superconducting quantum phase transitions in disordered metallic systems. We develop a strong-disorder renormalization group method that accounts for both quenched disorder and the dissipation of the critical modes due to the Fermi sea. We find that the quantum phase transition in Heisenberg anti-ferromagnets and the pair-breaking superconductor-metal transition are both governed by non-perturbative infinite-randomness critical points. Even stronger disorder effects arise for metallic magnets with Ising spin symmetry in which the quantum phase transition is completely destroyed by smearing. We determine thermodynamic and transport properties at these transitions and in the associated quantum Griffiths phases. We also discuss the current status of experimental observations of these exotic disorder phenomena in a variety of systems including transition metal compounds, heavy-fermion systems, and superconducting nanowires.