Quasi-bound states and resonant skew scattering in two-dimensional materials with a Mexican-hat dispersion

doi:10.1016/j.physe.2022.115492

Physica E: Low-dimensional Systems and Nanostructures

Volume 145, January 2023, 115492

https://doi.org/10.1016/j.physe.2022.115492 Get rights and content

Highlights

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Repulsive impurity creates quasi-bound states in the band spectrum with a mexican-hat dispersion.
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The quasi-bound states can transform into bound states in continuum.
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Arising quasi-bound states give rise to resonances of strongly enhanced skew scattering.
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Spin-dependent anti-resonances of the skew scattering appear in some direction.

Abstract

Mexican-hat dispersion of band electrons in two-dimensional materials attracts a lot of interest, mainly due to the Van Hove singularity of the density of states near the band edge. In this paper, we show that there is one more feature of such a dispersion, which also leads to nontrivial effects. It consists in the fact that the sign of the effective mass in the momentum space near the central extremum is opposite to the sign of the mass outside this region. For this reason, any localized potential that repels quasiparticles in the outer region attracts quasiparticles in the central region and thereby creates quasi-bound states. We study these states in the case when the Mexican-hat dispersion is formed due to the hybridization of the inverted electron and hole bands, and the potential is created by a point defect. The energy and width of the resonance of the local density of states corresponding to a quasi-bound state are found, and it is shown that, under certain conditions, a quasi-bound state can transform into a bound state in a continuum of band states. The presence of quasi-bound states leads to nontrivial effects in the spin-dependent scattering of electrons. Due to the quasi-bound state, the skew scattering is strongly enhanced for electrons with energy near the resonance, and the skewness angle varies over a wide range depending on the energy. In addition, in a certain energy range, a nontrivial effect of scattering suppression appears in the direction opposite to the skewness angle.

Introduction

Mexican-hat shaped dispersion of electronic spectrum is a relatively common property of many two-dimensional (2D) materials such as topological insulators in which the Mexican-hat dispersion naturally appears as a consequence of the band inversion [1], bilayer graphene [2], [3], monolayers of group III–IV chalcogenides [4], [5], [6]. The main interest to the Mexican-hat dispersion is usually attracted due to a Van Hove singularity of density of states close to the band edge, which opens the way for many striking effects caused by electron correlations, including the formation of a stable ferromagnetic phase [7], [8], stimulation of electron pairing [9], [10], and dramatic changes in the spectrum of the bound state in the attractive potential [11], [12]. Recent experiments reveal sharp peaks in optical conductivity due to this feature of the density of states [13].

In this paper, we show that there is another feature of the Mexican-hat dispersion which also leads to nontrivial effects. This feature consists in the fact that the sign of the effective mass in the momentum space near the central extremum is opposite to the sign of the mass outside this region. For definiteness, consider a Mexican-hat dispersion in the conduction band. The effective mass of the electrons with the wave vectors near the central maximum is negative, while outside this region the effective mass is positive. Therefore, it can be expected that a negatively charged defect that normally repels band electrons will attract electrons with momenta near the center of the Mexican hat and thereby create a quasi-bound state against the background of a continuum of band states. We show that these states do exist and study their properties in the case when the Mexican-hat dispersion is due to the hybridization of electron-like and hole-like band states described within the frame of the Bernevig–Hughes–Zhang model [14].

The energy of quasi-bound states lies above the central maximum of the Mexican hat, where they form resonances of the local density of states. The key role in the mechanism of the formation of quasi-bound states is played by the hybridization of the electron and hole bands. In particular, the hybridization parameter largely determines the width of the resonance. But besides this, the resonance width also depends on some overlap integral of the localized component of the wave function and the wave function of the continuum states near the defect. Because of this, the quasi-bound states have an interesting feature: under certain conditions, the resonance width can vanish and the quasi-bound state turns into a bound state in a continuum.

An interesting question is about the possible manifestations of quasi-bound states in the experiment. To this end, let us study how the quasi-bound state manifests itself in the process of scattering of band electrons. It turns out that the quasi-bound state strongly enhances the spin-dependent skew scattering of electrons with energies close to resonance ones, and as the energy changes, the skewness angle changes from 0 to $π$ . In addition, in a certain energy range, a nontrivial effect of spin-dependent scattering suppression occurs in the direction opposite to the skewness angle for each spin.

Section snippets

Quasi-bound states in a repulsive potential

As a model of Mexican-hat dispersion we use four-band model of Bernevig, Hughes, and Zhang (BHZ) in which such a dispersion arises due to inversion and hybridization of the electron- and hole-like bands. For simplicity the model is supposed to be symmetric with respect to the electron and hole bands. The hybridization is conveniently described by a dimensionless parameter $a = A {(B M)}^{- 1 / 2}$ , where $A$ , $B$ , and $M$ are standard parameters of the BHZ model [14]. $M$ is the mass term, $B$ the parameter describing

Electron scattering by defects with a resonant state

In this section we study the scattering of band electrons by a point-like defect with a repulsive potential that creates a quasi-bound state. Interest in this problem stems from our expectation that it is precisely in scattering that the quasi-bound states under study can manifest themselves most clearly.

The problem is solved on the basis of the Hamiltonian (1) for spin-up states. According to the standard scattering theory [19], the wave function should asymptotically, at $r \to \infty$ , be the sum of an

Discussion and concluding remarks

We have shown that in materials with a Mexican-hat dispersion, defects with a localized repulsive potential create specific quasi-bound states, which lead to the enhanced skew scattering of electrons with very nontrivial polar diagram and energy dependence. The mechanism of the formation of the quasi-bound states is due to the feature of the Mexican-hat dispersion, which has remained unexplored until now. It consists in the fact that the sign of the effective mass in the region of $k$ -space near

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was carried out in the framework of the state task for the Kotelnikov Institute of Radio Engineering and Electronics.

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Cited by (1)

Quasi-bound electron pairs in two-dimensional materials with a Mexican-hat dispersion
2023, Physics Letters, Section A: General, Atomic and Solid State Physics
We study quasi-bound states of two electrons that arise in two-dimensional materials with a Mexican-hat dispersion (MHD) at an energy above its central maximum. The width of the resonance of the local density of states created by pairs is determined by the hybridization of atomic orbitals, due to which the MHD is formed. The mechanism of the quasi-bound state formation is due to the fact that effective reduced mass of electrons near the MHD top is negative. An unusual feature of quasi-bound states is that the resonance width can vanish and then they transform into bound states in continuum. We study in detail the quasi-bound states for topological insulators, when the MHD is due to the hybridization of inverted electron and hole bands. In this case, the resonance width is extremely small at weak hybridization. The highest binding energy is achieved for singlet quasi-bound pairs with zero angular number.

View full text

Quasi-bound states and resonant skew scattering in two-dimensional materials with a Mexican-hat dispersion

Highlights

Abstract

Introduction

Section snippets

Quasi-bound states in a repulsive potential

Electron scattering by defects with a resonant state

Discussion and concluding remarks

Declaration of Competing Interest

Acknowledgments

Nat. Rev. Mater.

Quasiparticle effects in the bulk and surface-state bands of Bi2Se3 and Bi2Te3 topological insulators

Phys. Rev. B

The low energy electronic band structure of bilayer graphene

Eur. Phys. J. Spec. Top.

Extremely flat band in bilayer graphene

Sci. Adv.

Structural and electronic properties of monolayer group III monochalcogenides

Phys. Rev. B

Electronic and thermoelectric properties of van der waals materials with ring-shaped valence bands

J. Appl. Phys.

Fundamentals of lateral and vertical heterojunctions of atomically thin materials

Nanoscale

Fermi liquid theory of a Fermi ring

Phys. Rev. B

Tunable magnetism and half-metallicity in hole-doped monolayer GaSe

Phys. Rev. Lett.

Enhanced superconductivity in quasi two-dimensional systems

Phys. Rev. Lett.

Topological change of the Fermi surface in low-density Rashba gases: Application to superconductivity

Phys. Rev. Lett.

Bound states in a two-dimensional short range potential induced by the spin–orbit interaction

Phys. Rev. Lett.

Quasiparticle effects in the bulk and surface-state bands of Bi $_{2}$ Se $_{3}$ and Bi $_{2}$ Te $_{3}$ topological insulators