Velocity-determined anisotropic behaviors of RKKY interaction in 8-Pmmn borophene

Zhang, Shuhui; Shao, Ding-Fu; Yang, Wen

doi:10.1016/j.jmmm.2019.165631

Cited by 18 publications

(8 citation statements)

References 90 publications

(124 reference statements)

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“…the free GF G 0 )and extra GF constructed through the right-going intrinsic states and its left-going reflection states by the PNJ interface. The free GF º ( ) E G G r r , , 0 0 F 2 1 is constructed completely by the intrinsic states and has the form: which is consistent with the result derived through the straightforward Fourier transformation of the GF in momentum space [40]. When x 2 >0, equation (15) is the mathematical description of figure 2(e), which is constructed through the right-going intrinsic states of the n region and its right-going transmission states of the p region.…”

Section: Green's Functionsupporting

confidence: 71%

“…The well-established continuum model of 8-Pmmn borophene make it be very suitable to the model study. This anisotropy and tilt of type-I Dirac fermions brings about unique features to various physical properties of 8-Pmmn borophene, including plasmon [33,34], the optical conductivity [35], Weiss oscillations [36], oblique Klein tunneling [37], metal-insulator transition induced by strong electromagnetic radiation [38], and RKKY interaction [39,40]. Thus, it is expected that the anisotropy and tilt will strongly affect the negative refraction of MDFs cross 8-Pmmn borophene PNJ.…”

Section: Introductionmentioning

confidence: 99%

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Anomalous caustics and Veselago focusing in 8-Pmmn borophene p–n junctions with arbitrary junction directions

Zhang

Yang

2019

New J. Phys.

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Negative refraction usually demands complex structure engineering while it is very natural for massless Dirac fermions (MDFs) across the p-n junction (PNJ), this leads to Dirac electron optics. The emergent Dirac materials may exhibit hitherto unidentified phenomenon due to their nontrivial band structures in contrast to the isotropic MDFs in graphene. Here, as a specific example, we explore the negative refraction induced caustics and Veselago focusing of tilted MDFs across 8-Pmmn borophene PNJs. To this aim, we develop a technique to effectively construct the electronic Green's function (GF) in PNJs with arbitrary junction directions. Based on analytical discussions and numerical calculations, we demonstrate the strong dependence of interference pattern on the junction direction. As the junction direction perpendicular to the tilt direction, Veselago focusing or normal caustics (similar to that in graphene) appears resting on the doping configuration of the PNJs, otherwise anomalous caustics (different from that in graphene) occurs which is manipulated by the junction direction and the doping configuration. Finally, the developed GF technique is generally promising to uncover the unique transport of emergent MDFs, and the discovered anomalous caustics makes tilted MDFs potential applications in Dirac electron optics.

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Section: Green's Functionsupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Anomalous caustics and Veselago focusing in 8-Pmmn borophene p–n junctions with arbitrary junction directions

Zhang

Yang

2019

New J. Phys.

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“…δρ(r,ε) is measured easily by STM. FOs of δρ(r,ε) are dominated by the backscattering events along the constant energy contour 42,43 . Focusing on the intervalley scattering, the corresponding physical process of Eq.…”

Section: δρ(Rε)mentioning

confidence: 99%

Robust wavefront dislocations of Friedel oscillations in gapped graphene

Zhang,

Yang,

Shao

et al. 2021

Preprint

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Friedel oscillation is a well-known wave phenomenon, which represents the oscillatory response of electron waves to imperfection. By utilizing the pseudospin-momentum locking in gapless graphene, two recent experiments demonstrate the measurement of the topological Berry phase by corresponding to the unique number of wavefront dislocations in Friedel oscillations. Here, we study the Friedel oscillations in gapped graphene, in which the pseudospin-momentum locking is broken. Unusually, the wavefront dislocations do occur as that in gapless graphene, which expects the immediate verification in the current experimental condition. The number of wavefront dislocations is ascribed to the invariant pseudospin winding number in gaped and gapless graphene. This study deepens the understanding of correspondence between topological quantity and wavefront dislocations in Friedel oscillations, and implies the possibility to observe the wavefront dislocations of Friedel oscillations in intrinsic gapped two-dimensional materials, e.g., transition metal dichalcogenides.

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“…Among them, 2D tilted Dirac materials host tilted dispersions along a certain direction of wave vector and have been attracting increasing interests theoretically and experientially [3,[9][10][11][12][13][16][17][18][19][20]. They exhibit many significant qualitative differences in physical behaviors compared to their untilted counterparts, including plasmons [21][22][23][24][25], optical conductivities [21,[26][27][28][29][30][31][32], Weiss oscillation [33], Klein tunneling [34,35], Kondo effects [36], RKKY interactions [37,38], planar Hall effect [39], and thermoelectric effects [40].…”

Section: Introductionmentioning

confidence: 99%

Signatures of Lifshitz transition in the optical conductivity of tilted Dirac materials

Tan¹,

Hou²,

Chang-Xu³

et al. 2021

Preprint

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Lifshitz transition is a kind of topological phase transition in which the Fermi surface is reconstructed. It can occur in the two-dimensional (2D) tilted Dirac materials when the energy bands change between the type-I phase (0 < t < 1) and the type-II phase (t > 1) through the type-III phase (t = 1), where different tilts are parameterized by the values of t. In order to characterize the Lifshitz transition therein, we theoretically investigate the longitudinal optical conductivities (LOCs) in type-I, type-II, and type-III Dirac materials within linear response theory. In the undoped case, the LOCs are independent of the tilt parameter in both type-I and type-III phases, but is determined by the tilt parameter in the type-II phase. In the doped case, the LOCs are anisotropic and share two resonance peaks determined by ω = ω1(t) and ω = ω2(t). The tilt parameter and chemical potential can be extracted from optical experiments by measuring the positions of these two peaks and their separation ∆ω(t) = ω2(t) − ω1(t). With increasing the tilt, the separation goes larger in the type-I phase whereas smaller in the type-II phase. The LOCs in the asymptotical region are exactly the same as that in the undoped case. The type of 2D tilted Dirac bands can be determined by the asymptotic background values, resonance peaks and their separation in the LOCs. These can therefore be taken as signatures of Lifshitz transition therein. The results of this work are expected to be qualitatively valid for a large number of monolayer tilted Dirac materials such as 8-Pmmn borophene tuned by gate voltage and different compounds of T -phase transition metal dichalcogenides.

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Velocity-determined anisotropic behaviors of RKKY interaction in 8-Pmmn borophene

Cited by 18 publications

References 90 publications

Anomalous caustics and Veselago focusing in 8-Pmmn borophene p–n junctions with arbitrary junction directions

Anomalous caustics and Veselago focusing in 8-Pmmn borophene p–n junctions with arbitrary junction directions

Robust wavefront dislocations of Friedel oscillations in gapped graphene

Signatures of Lifshitz transition in the optical conductivity of tilted Dirac materials

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