Atomic collapse in pseudospin-1 systems

Han, Chen Di; Xu, Hongya; Huang, Danhong; Lai, Ying Cheng

doi:10.1103/physrevb.99.245413

Cited by 15 publications

(13 citation statements)

References 79 publications

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“…The fact that we observe a discretized spectrum originating from E = 0 instead of a continuum of peaks as in the continuum model [30] can be explained from the fact that in the lattice model the localization is limited by the distance between the lattice size preventing a continuum of localized states that are theoretically possible in the continuum model [28,29]. The linear E ∼ β dependence of these flat band states on β can thus be understood from the sharp spatial localization of these states and the fact that the energy is given by E = V (r 0 ) ∼ β.…”

Section: Flat Band Bound Statesmentioning

confidence: 75%

“…Notice that, in Ref. [28] the S-like resonances was not studied. Because we use the tight-binding Hamilton and do not have any index related with the angular momentum (L) as in the continuum approach of Ref.…”

Section: Atomic Collapse Statesmentioning

confidence: 99%

“…The effect of a charged impurity on charge carriers in graphene has attracted a great deal of interest due to the prediction [22,23] and detection [24][25][26][27] of the atomic collapse phenomenon seen as the emergence of distinct resonances visible in the hole continuum. The effect of a charged impurity on the electronic states in a Dice lattice was recently investigated within the low energy continuum approximation as described by the Dirac-Weyl equation with pseudospin one [28,29]. In such an approach, effects due to the discrete lattice are neglected which are preserved in a tightbinding approach.…”

Section: Introductionmentioning

confidence: 99%

“…In such an approach, effects due to the discrete lattice are neglected which are preserved in a tightbinding approach. For a pseudospin-1 fermion system, Han et al [28] obtained analytical solutions for the spinor wavefunctions and found a criterion for the occurrence of atomic collapse, β > (L 2 + 1/4) 1/2 that depend on the angular momentum L (β is the dimensionless strength of the Coulomb potential). In the case of graphene this condition is β > L + 1/2.…”

Section: Introductionmentioning

confidence: 99%

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Coulomb impurity on a Dice lattice: atomic collapse and bound states

Wang,

Van Pottelberge,

Zhao

et al. 2021

Preprint

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The modification of the quantum states in a Dice lattice due to a Coulomb impurity are investigated. The energy band structure of a pristine Dice lattice consists of a Dirac cone and a flat band at the Dirac point. We use the tight binding formalism and find that the flat band states transform into a set of discrete bound states whose electron density is localized on a ring around the impurity mainly on two of the three sublattices. The energy is proportional to the strength of the Coulomb impurity. Beyond a critical strength of the Coulomb potential atomic collapse states appear that have some similarity with those found in graphene with the difference that the flat band states contribute with an additional ring-like electron density that is spatially decoupled from the atomic collapse part. At large value of the strength of the Coulomb impurity the flat band bound states anti-cross with the atomic collapse states.

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Section: Flat Band Bound Statesmentioning

confidence: 75%

Section: Atomic Collapse Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coulomb impurity on a Dice lattice: atomic collapse and bound states

Wang,

Van Pottelberge,

Zhao

et al. 2021

Preprint

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“…For example, a longranged Coulomb potential of type I (with three same diagonal elements in usual basis), an arbitrary weak Coulomb potential can destroy completely the flat band 41,42 . In two-dimensional spin-1 systems, a strong Coulomb potential can result in a wave function collapse near the the origin 41,43 . For one-dimensional case, an arbitrarily weak Coulomb potential also causes the wave function collapse 44 .…”

Section: Introductionmentioning

confidence: 99%

Bound States in the Continuum (BIC) Protected By Self-Sustained Potential Barriers in a Flat Band System

Zhang

2021

Preprint

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In this work, we investigate the bound states in the continuum (BIC) of a one-dimensional spin-1 flat band system with a potential of type III, which has a unique non-vanishing matrix element in basis |1⟩. It is found that, for such a kind of potential, there exists an effective attractive potential well surrounded by infinitely high self-sustained barriers. Some bound states in the continuum (BIC) can appear for sufficiently strong potential. These bound states (BIC) are protected by the infinitely high potential barriers, which could not decay into the continuum. Taking a long-ranged Coulomb potential and a short-ranged exponential potential as two examples, the bound state energies are obtained. For a Coulomb potential, there exists a series of critical potential strength, near which the bound state energy can goes to infinite. For a sufficiently strong exponential potential, there exists two different bound states with a same number of wave function nodes. The existences of BIC protected by the self-sustained potential barriers is quite a universal phenomenon in the flat band system under a strong potential. A necessary condition for existence of BIC is that the maximum value of potential is larger than two times band gap.

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Coulomb bound states and atomic collapse in tilted Dirac materials

et al. 2021

Physica E: Low-dimensional Systems and Nanostructures

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Atomic collapse in pseudospin-1 systems

Cited by 15 publications

References 79 publications

Coulomb impurity on a Dice lattice: atomic collapse and bound states

Coulomb impurity on a Dice lattice: atomic collapse and bound states

Bound States in the Continuum (BIC) Protected By Self-Sustained Potential Barriers in a Flat Band System

Coulomb bound states and atomic collapse in tilted Dirac materials

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