Study of off-diagonal disorder using the typical medium dynamical cluster approximation

Terletska, Hanna; Ekuma, Chinedu; Moore, Conrad; Tam, Ka-Ming; Moreno, Juana; Jarrell, Mark

doi:10.1103/physrevb.90.094208

Cited by 28 publications

(29 citation statements)

References 53 publications

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“…The lack of a single method satisfying all the criteria mentioned above for phononic systems motivates us to adapt the dynamical cluster approximation (DCA) and the typical medium DCA (TMDCA) for disordered phononic systems to capture the Anderson localization of phonons since these methods have been shown to work extraordinarily well in electronic systems [58][59][60][61] . The main difficulty inhibiting the development of such a method for the study of Anderson localization of phonons lies in finding a single particle order parameter to characterize the Anderson transition in disordered phononic systems.…”

Section: Anderson Localization (Al)mentioning

confidence: 99%

Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach

et al. 2017

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The effect of disorder on lattice vibrational modes has been a topic of interest for several decades. In this work, we employ a Green's function based approach, namely the dynamical cluster approximation (DCA), to investigate phonons in mass disordered systems. Detailed benchmarks with previous exact calculations are used to validate the method in a wide parameter space. An extension of the method, namely the typical medium DCA (TMDCA), is used to study Anderson localization of phonons in three dimensions. We show that, for binary isotopic disorder, lighter impurities induce localized modes beyond the bandwidth of the host system, while heavier impurities lead to a partial localization of the low frequency acoustic modes. For a uniform (box) distribution of masses, the physical spectrum is shown to develop long tails comprising mostly localized modes. The mobility edge separating extended and localized modes, obtained through the TMDCA, agrees well with results from the transfer matrix method. A re-entrance behavior of the mobility edge with increasing disorder is found that is similar to, but somewhat more pronounced than, the behavior in disordered electronic systems. Our work establishes a new computational approach, which recovers the thermodynamic limit, is versatile and computationally inexpensive, to investigate lattice vibrations in disordered lattice systems.

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Section: Anderson Localization (Al)mentioning

confidence: 99%

Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach

et al. 2017

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“…We demonstrated that the TMDCA overcomes the shortcomings of the TMT and is able to qualitatively and quantitatively describe Anderson localization. We also extended this method to models with off-diagonal disorder 63 , multiband systems 64 , and interactions 65? .…”

Section: Introductionmentioning

confidence: 99%

Typical-medium multiple-scattering theory for disordered systems with Anderson localization

et al. 2017

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The typical medium dynamical cluster approximation (TMDCA) is reformulated in the language of multiple scattering theory to make possible first principles calculations of the electronic structure of substitutionally disordered alloys including the effect of Anderson localization. The TMDCA allows for a systematic inclusion of non-local multi-site correlations and at same time provides an order parameter, the typical density of states, for the Anderson localization transition. The relation between the dynamical cluster approximation and the multiple scattering theory is analyzed, and is illustrated for a tight-binding model.

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“…In relevant cases, our results are found to be in excellent agreement with recent large-scale exact diagonalization results 37 , as well as with recent experiments 29 . Moreover, recently developed cluster refinements of TMT demonstrated [39][40][41] that significant corrections to (single site) TMT are only found very close to the Anderson transition. All these findings provide further evidence that TMT represents a flexible and practically useful tool for successfully describing the main qualitative trends for physical observables, in the vicinity of disorder-driven metal-insulator transitions.…”

Section: Discussionmentioning

confidence: 99%

Quantum criticality at the Anderson transition: A typical medium theory perspective

Mahmoudian¹,

Tang²,

Dobrosavljević³

2015

Phys. Rev. B

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We present a complete analytical and numerical solution of the Typical Medium Theory (TMT) for the Anderson metal-insulator transition. This approach self-consistently calculates the typical amplitude of the electronic wave-functions, thus representing the conceptually simplest order-parameter theory for the Anderson transition. We identify all possible universality classes for the critical behavior, which can be found within such a meanfield approach. This provides insights into how interaction-induced renormalizations of the disorder potential may produce qualitative modifications of the critical behavior. We also formulate a simplified description of the leading critical behavior, thus obtaining an effective Landau theory for Anderson localization.

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Study of off-diagonal disorder using the typical medium dynamical cluster approximation

Cited by 28 publications

References 53 publications

Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach

Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach

Typical-medium multiple-scattering theory for disordered systems with Anderson localization

Quantum criticality at the Anderson transition: A typical medium theory perspective

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