Coupling of two Dirac particles

Berman, Oleg L.; Kezerashvili, Roman Ya.; Ziegler, K.

doi:10.1103/physreva.87.042513

Cited by 34 publications

(34 citation statements)

References 49 publications

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“…Following the procedure applied for the calculation of the energy spectrum of the indirect excitons formed in two parallel gapped graphene layers [70], one gets from Eq. (A9) for the spinor component at (βK − + i∂ x + ∂ y ) φ c↑(↓)v↑(↓) .…”

Section: Discussionmentioning

confidence: 99%

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High-temperature superfluidity of the two-component Bose gas in a transition metal dichalcogenide bilayer

Berman

Kezerashvili

2016

Phys. Rev. B

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The high-temperature superfluidity of two-dimensional dipolar excitons in two parallel TMDC layers is predicted. We study Bose-Einstein condensation in the two-component system of dipolar A and B excitons. The effective mass, energy spectrum of the collective excitations, the sound velocity and critical temperature are obtained for different TMDC materials. It is shown that in the Bogolubov approximation the sound velocity in the two-component dilute exciton Bose gas is always larger than in any one-component. The difference between the sound velocities for two-component and one-component dilute gases is caused by the fact that the sound velocity for a two-component system depends on the reduced mass of A and B excitons, which is always smaller than the individual mass of A or B exciton. Due to this fact, the critical temperature Tc for superfluidity for the twocomponent exciton system in a TMDC bilayer is about one order of magnitude higher than Tc in any one-component exciton system. We propose to observe the superfluidity of two-dimensional dipolar excitons in two parallel TMDC layers, which causes two opposite superconducting currents in each TMDC layer.

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Section: Discussionmentioning

confidence: 99%

“…71 and gapped graphene in Ref. 70. Since the electron-hole Coulomb interaction depends only on the relative coordinate, we introduce the new "center-of-mass" coordinates in the plane of a TMDC layer:…”

Section: Two-body Problem For Dirac Particles With a Gapmentioning

confidence: 99%

High-temperature superfluidity of the two-component Bose gas in a transition metal dichalcogenide bilayer

Berman

Kezerashvili

2016

Phys. Rev. B

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“…The multi-band spinor structure of charge carriers' quantum states should result in a formfactor renormalization of the Coulomb-potential matrix element similar to previously considered situations [76]. Interesting properties associated with two-particle states of Dirac-like carriers [77,78], e.g., the recently predicted existence of an internal angular momentum of the exciton [79], could be elucidated in greater detail. Early numerical studies [23] can serve as a benchmark for evaluating the accuracy of approximate analytical results.…”

Section: Discussionmentioning

confidence: 71%

Spherical topological insulator nanoparticles: Quantum size effects and optical transitions

et al. 2019

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We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile continuum-model description of the TI bulk band structure and the assumption of a hard-wall mass confinement. Analytical results are obtained for the wave functions of single-electron energy eigenstates and the matrix elements for optical transitions between them. As expected from spherical symmetry, quantized levels in TI nanoparticles can be labeled by quantum numbers j and m = −j, −j + 1, . . . , j for total angular momentum and its projection on an arbitrary axis. The fact that TIs are narrow-gap materials, where the charge-carrier dynamics is described by a type of two-flavor Dirac model, requires j to assume half-integer values and also causes a doubling of energy-level degeneracy where two different classes of states are distinguished by being parity eigenstates with eigenvalues (−1) j∓1/2 . The existence of energy eigenstates having the same j but opposite parity enables optical transitions where j is conserved, in addition to those adhering to the familiar selection rule where j changes by ±1. All optical transitions satisfy the usual selection rule ∆m = 0, ±1. We treat intra-and inter-band optical transitions on the same footing and establish ways for observing unusual quantum-size effects in TI nanoparticles, including oscillatory dependences of the band gap and of transition amplitudes on the nanoparticle radius. Our theory also provides a unified perspective on multi-band models for charge carriers in semiconductors and Dirac fermions from elementary-particle physics.

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“…Electronelectron interactions plays an important role Dirac materials [18] and it has been predicted that graphene may undergo a metalinsulator transition [19,20,21]. Therefore knowledge of the two body problem is an important step in the understanding of excitonic systems such as Bose-Einstein condensation [22,23,24] and Superfluidity [25,26]. However, a common consensus has not been met regarding the formation of coupled pairs in intrinsic graphene.…”

Section: Introductionmentioning

confidence: 99%

“…The inclusion of trigonal warping effects also gives rise to the possibility pair formation [30,31,32]. Pair formation has also been studied in gapped graphene [33,34,35,24] and the two body problem was considered in bilayer graphene quantum dots [36]. Excitonic effects in Dirac materials have been studied using a variety of approaches such as the Bethe-Salpeter method [37] as well as the twobody tight-binding matrix Hamiltonian [35,38,39,29], we shall employ the later method.…”

Section: Introductionmentioning

confidence: 99%