Coulomb bound states and atomic collapse in tilted Dirac materials

Fu, Wei; Ke, Sha-Sha; Lu, Ming‐Xing; Lü, Haifeng

doi:10.1016/j.physe.2021.114841

Cited by 6 publications

(3 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The presence of a space-dependent tilt parameter in these systems allows for the exploration of nontrivial spacetime geometry and gravitomagnetic effects. The rising interest in tilted Dirac materials has led to the revisiting of several well-known problems in graphene, such as Klein tunneling [70], atomic collapse [71],…”

Section: Introductionmentioning

confidence: 99%

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

Hartmann,

Portnoi

2024

Phys. Scr.

View full text Add to dashboard Cite

We show that the (2+1)-dimensional massless Dirac equation, which includes a tilt term, can be reduced to the biconfluent Heun equation for a broad range of scalar confining potentials, including the well-known Morse potential. Applying these solutions, we investigate a bipolar electron waveguide in 8--$Pmmn$ borophene, formed by a well and barrier, both described by the Morse potential. We demonstrate that the ability of two-dimensional materials with tilted Dirac cones to localize electrons in both a barrier and a well can be harnessed to create pseudogaps in their electronic spectrum. These pseudogaps can be tuned through varying the applied top-gate voltage. Potential opto-valleytronic and terahertz applications are discussed.

show abstract

Section: Introductionmentioning

confidence: 99%

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

Hartmann,

Portnoi

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…In addition, it was predicted that atomic collapse effect may happen in another material, a donor cluster in SrTiO3 [17] and might be controlled by a size of a cluster. Another way to control the critical charge is a tilt of Dirac cones in 2D materials [18]. Theoretical studies has also shown that the supercritical instability can be induced dynamically by charged ions passing through graphene samples [19].…”

Section: Introductionmentioning

confidence: 99%

Size effects on atomic collapse in the dice lattice

Oriekhov,

Voronov

2023

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value. This effect, together with enhancement of gap due to spatial quantization, makes it more difficult to observe the dive-into-continuum phenomenon in small quantum dots. At the same time, we show that if in-gap states are filled, the resonant tunneling to bound state in the impurity potential might occur at much smaller charge, which demonstrates non-monotonous dependence with the size of sample lattice. In addition, we study the possibility of creating supercritical localized potential well on different sublattices, and show that it is possible only on rim sites, but not on hub site. The predicted effects are expected to naturally occur in artificial flat band lattices.

show abstract

“…In this paper, we study the bound state formation in two-dimensional Dirac materials. Exact solutions of the Dirac equation are not only useful in analyzing the electronic properties in the Dirac materials, but also important for testing numerical and perturbative methods [37][38][39][40][41][42][43][44][45][46]. Until now, the solutions of the Dirac equation with the position-dependent Fermi velocity are far from well-studied, and several unphysical velocity distributions are considered to obtain exact solution.…”

mentioning

confidence: 99%

Bound states of Dirac fermions in the presence of a Fermi velocity modulation

Kalim,

Ren,

et al. 2023

EPL

View full text Add to dashboard Cite

We investigate the effect of a position-dependent Fermi velocity on the electronic properties of two-dimensional Dirac materials. A physical Fermi velocity distribution, which approaches a finite value at infinity and experiences a modulation near x = 0, is considered. Such a position-dependent Fermi velocity could be realized in the curved graphene or by applying strain. It is shown that the bound states are absent in the presence of a pure Fermi velocity modulation without an electrostatic potential well. However, an extra electrostatic potential modulation could produce the bound states. A set of discrete energy level spectrum and the corresponding wave functions are obtained by solving the Dirac equation exactly. Local probes such as scanning tunnel microscopy should be able to observe the predicted bound states in two-dimensional materials.

show abstract

Coulomb bound states and atomic collapse in tilted Dirac materials

Cited by 6 publications

References 56 publications

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

Size effects on atomic collapse in the dice lattice

Bound states of Dirac fermions in the presence of a Fermi velocity modulation

Contact Info

Product

Resources

About