Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

Electronic Griffiths Phases and Quantum Criticality at Disordered Mott Transitions

V. Dobrosavljević

Published Feb 29, 2012• 0 citations
OpenAlex

Abstract

The effects of disorder are investigated in strongly correlated electronic systems near the Mott metal-insulator transition. Correlation effects are found1 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 increases2 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.

Related papers

Electronic Griffiths Phase of the d=2 Mott Transition

Eric C. Andrade, E. Miranda, V. Dobrosavljević

We investigate the effects of disorder within the T = 0 Brinkman-Rice scenario for the Mott metal-insulator transition in two dimensions. For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticle weights Z_{i} and strong screening of the renormalized site energies at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of quasiparticle parameters are strongly enhanced in the critical regime, with a distribution function P(Z) approximately Z;{alpha-1} and alpha --> 0 at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the metal-insulator transition, in a fashion surprisingly reminiscent of the "infinite randomness fixed point" scenario for disordered quantum magnets.

arXiv:0808.0913•Physical Review Letters•May 20, 2009•50 citations

Screening of disorder due to interaction near the Mott transition

1. Quantum Ripples in Strongly Correlated Metals Authors: E. C. Andrade, E. Miranda, and V. Dobrosavljevic Phys. Rev. Lett. 104, 236401 (2010) 2. Energy-Resolved Spatial Inhomogeneity of Disordered Mott Systems Authors: E. C. Andrade, E. Miranda, and V. Dobrosavljevic Physica B 404, 3167 (2009) 3. Electronic Griffiths Phase of the d = 2 Mott Transition […]

Journal Club for Condensed Matter Physics•Jan 29, 2012•0 citations

Universal Quantum Criticality at the Mott-Anderson Transition

Maria C. O. Aguiar, V. Dobrosavljević

We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify the quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wave functions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid ("electronic Griffiths phase") behavior, which is found only in the strongly correlated regime.

arXiv:1208.5053•Physical Review Letters•Feb 5, 2013•24 citations

Mean Field Theory of the Mott-Anderson Transition

V. Dobrosavljević, Gabriel Kotliar

We present a theory for disordered interacting electrons that can describe both the Mott and Anderson transitions in the respective limits of zero disorder and zero interaction. We use it to investigate the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ Mott-Anderson transition at a fixed electron density, as the disorder strength is increased. Surprisingly, we find two critical values of disorder ${W}_{\mathrm{nfl}}$ and ${W}_{c}$. For $W>{W}_{\mathrm{nfl}}$, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, ${W\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W}_{c}>{W}_{\mathrm{nfl}}$ the system undergoes a metal-insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.

arXiv:cond-mat/9611100•Physical Review Letters•May 19, 1997•195 citations

Effects of strong disorder in strongly correlated superconductors

Debmalya Chakraborty, Rajdeep Sensarma, Amit Ghosal

We investigate the effect of strong disorder on a system with strong electronic repulsion. In the absence of disorder, the system has a d-wave superconducting ground state with strong non-BCS features due to its proximity to a Mott insulator. We find that while strong correlations make superconductivity in this system immune to weak disorder, superconductivity is destroyed efficiently when disorder strength is comparable to the effective bandwidth. The suppression of charge motion in regions of strong potential fluctuation leads to the formation of Mott insulating patches, which anchor a larger nonsuperconducting region around them. The system thus breaks into islands of Mott insulating and superconducting regions, with Anderson insulating regions occurring along the boundary of these regions. Thus, electronic correlation and disorder, when both are strong, aid each other in destroying superconductivity, in contrast to their competition at weak disorder. Our results shed light on why zinc impurities are efficient in destroying superconductivity in cuprates, even though it is robust to weaker impurities.

arXiv:1608.05087•Physical review. B./Physical review. B•Jan 23, 2017•16 citations

Quantum Phase Transitions in Electronic Systems

T. R. Kirkpatrick, D. Belitz

Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.

arXiv:cond-mat/9707001•IMPERIAL COLLEGE PRESS eBooks•Dec 1, 1999•30 citations
The effects of disorder are investigated in strongly correlated electronic systems near the Mott metal-insulator transition. Correlation effects are found1 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 increases2 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.
We investigate the effects of disorder within the T = 0 Brinkman-Rice scenario for the Mott metal-insulator transition in two dimensions. For sufficiently weak disorder the transition retains the Mott character, as signaled by the vanishing of the local quasiparticle weights Z_{i} and strong screening of the renormalized site energies at criticality. In contrast to the behavior in high dimensions, here the local spatial fluctuations of quasiparticle parameters are strongly enhanced in the critical regime, with a distribution function P(Z) approximately Z;{alpha-1} and alpha --> 0 at the transition. This behavior indicates a robust emergence of an electronic Griffiths phase preceding the metal-insulator transition, in a fashion surprisingly reminiscent of the "infinite randomness fixed point" scenario for disordered quantum magnets.
We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify the quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wave functions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid ("electronic Griffiths phase") behavior, which is found only in the strongly correlated regime.
We present a theory for disordered interacting electrons that can describe both the Mott and Anderson transitions in the respective limits of zero disorder and zero interaction. We use it to investigate the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 Mott-Anderson transition at a fixed electron density, as the disorder strength is increased. Surprisingly, we find two critical values of disorder Wnfl{W}_{\mathrm{nfl}}Wnfl​ and Wc{W}_{c}Wc​. For W>WnflW>{W}_{\mathrm{nfl}}W>Wnfl​, the system enters a ``Griffiths'' phase, displaying metallic non-Fermi liquid behavior. At even stronger disorder, W=Wc>Wnfl{W\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W}_{c}>{W}_{\mathrm{nfl}}W=Wc​>Wnfl​ the system undergoes a metal-insulator transition, characterized by the linear vanishing of both the typical density of states and the typical quasiparticle weight.
We investigate the effect of strong disorder on a system with strong electronic repulsion. In the absence of disorder, the system has a d-wave superconducting ground state with strong non-BCS features due to its proximity to a Mott insulator. We find that while strong correlations make superconductivity in this system immune to weak disorder, superconductivity is destroyed efficiently when disorder strength is comparable to the effective bandwidth. The suppression of charge motion in regions of strong potential fluctuation leads to the formation of Mott insulating patches, which anchor a larger nonsuperconducting region around them. The system thus breaks into islands of Mott insulating and superconducting regions, with Anderson insulating regions occurring along the boundary of these regions. Thus, electronic correlation and disorder, when both are strong, aid each other in destroying superconductivity, in contrast to their competition at weak disorder. Our results shed light on why zinc impurities are efficient in destroying superconductivity in cuprates, even though it is robust to weaker impurities.
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.