Anomalous chiral edge states in spin-1 Dirac quantum dots

Xu, Hongya; Lai, Ying Cheng

doi:10.1103/physrevresearch.2.013062

“…For example, the orbital susceptibility 17,18 and the topological berry phase 19 can be tuned with the parameter α, and in contrast with graphene the plasmon branch is pinched in to a single point 20 . More recently, it has been found that this kind of Hamiltonian leads to an unexpected family of in-gap chiral edge states for noninverted spin-1 Dirac quantum dots 21 . There are some other previous works concerning the structure of the electromagnetic-dressed electron spectrum [22][23][24] .…”

Section: Introductionmentioning

confidence: 99%

Electron transitions for Dirac Hamiltonians with flat bands under electromagnetic radiation: Application to the α−T3 graphene model

Mojarro

¹

,

Ibarra-Sierra

²

,

Sandoval-Santana

³

et al. 2020

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In a system with a Dirac-like linear dispersion there are always states that fulfill the resonance condition for electromagnetic radiation of arbitrary frequency Ω. When a flat band is present two kinds of resonant transitions are found. Considering the α − T3 graphene model as a minimal model with a flat band and Dirac cones, and describing the dynamics using the interaction picture, we study the band transitions induced by an external electromagnetic field. We found that transitions depend upon the relative angle between the electron momentum and the electromagnetic field wavevector. For parallel incidence, the transitions are found using Floquet theory while for other angles perturbation theory is used. In all cases, the transition probabilities and the frequencies are found. For some special values of the parameter α or by charge doping, the system behaves as a three-level or a two-level Rabi system. All these previous results were compared with numerical simulations. A good agreement was found between both. The obtained results are useful to provide a quantum control of the system.

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“…In comparing with the graphene, there is an extra lattice site (per unit cell) in the center of hexagon of honeycomb lattice 24 – 26 . The low-energy physics of the dice lattice are also described by the Dirac equation, but its pseudospin instead of 27 , 28 . There are two schemes to obtain this kind of lattices: one is to fabricate the trilayer structure of cubic lattice (e.g.…”

Section: Introductionmentioning

confidence: 99%

Superfluid density and collective modes of fermion superfluid in dice lattice

Wu

¹

,

Zhang

²

,

Liu

³

et al. 2021

Sci Rep

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The superfluid properties of attractive Hubbard model in dice lattice are investigated. It is found that three superfluid order parameters increase as the interaction increases. When the filling factor falls into the flat band, due to the infinite large density of states, the resultant superfluid order parameters are proportional to interaction strength, which is in striking contrast with the exponentially small counterparts in usual superfluid (or superconductor). When the interaction is weak, and the filling factor is near the bottom of the lowest band (or the top of highest band), the superfluid density is determined by the effective mass of the lowest (or highest) single-particle band. When the interaction is strong and filling factor is small, the superfluid density is inversely proportional to interaction strength, which is related to effective mass of tightly bound pairs. In the strong interaction limit and finite filling, the asymptotic behaviors of superfluid density can be captured by a parabolic function of filling factor. Furthermore, when the filling is in flat band, the superfluid density shows a logarithmic singularity as the interaction approaches zero. In addition, there exist three undamped collective modes for strong interactions. The lowest excitation is gapless phonon, which is characterized by the total density oscillations. The two others are gapped Leggett modes, which correspond relative density fluctuations between sublattices. The collective modes are also reflected in the two-particle spectral functions by sharp peaks. Furthermore, it is found that the two-particle spectral functions satisfy an exact sum-rule, which is directly related to the filling factor (or density of particle). The sum-rule of the spectral functions may be useful to distinguish between the hole-doped and particle-doped superfluid (superconductor) in experiments.

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“…The above Eq. (28) shows that the integral of spectral functions is proportional to filling factor n − 3 (relative to the half filling). If the filling factor is half filling (n − 3 = 0), the integral of spectral functions is exactly zero.…”

Section: Two-particle Spectral Functionsmentioning

confidence: 99%

Superfluid density and collective modes of fermion superfluid in dice lattice

Wu,

Zhang,

Liu

et al. 2022

Preprint

0

View full text Add to dashboard Cite

The superfluid properties of attractive Hubbard model in dice lattice are investigated. It is found that three superfluid order parameters increase as the interaction increases. When the filling factor falls into the flat band, due to the infinite large density of states, the resultant superfluid order parameters are proportional to interaction strength, which is in striking contrast with the exponentially small counterparts in usual superfluid (or superconductor). When the interaction is weak, and the filling factor is near the bottom of the lowest band (or the top of highest band), the superfluid density is determined by the effective mass of the lowest (or highest) single-particle band. When the interaction is strong and filling factor is small, the superfluid density is inversely proportional to interaction strength, which is related to effective mass of tightly bound pairs. In the strong interaction limit and finite filling, the asymptotic behaviors of superfluid density can be captured by a parabolic function of filling factor. Furthermore, when the filling is in flat band, the superfluid density shows a logarithmic singularity as the interaction approaches zero. In addition, there exist three undamped collective modes for strong interactions. The lowest excitation is gapless phonon, which is characterized by the total density oscillations. The two others are gapped Leggett modes, which correspond relative density fluctuations between sublattices. The collective modes are also reflected in the two-particle spectral functions by sharp peaks. Furthermore, it is found that the two-particle spectral functions satisfy an exact sum-rule, which is directly related to the filling factor (or density of particle). The sum-rule of the spectral functions may be useful to distinguish between the hole-doped and particle-doped superfluid (superconductor) in experiments.

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Anomalous chiral edge states in spin-1 Dirac quantum dots

Cited by 17 publications

References 70 publications

Electron transitions for Dirac Hamiltonians with flat bands under electromagnetic radiation: Application to the α−T3 graphene model

Electron transitions for Dirac Hamiltonians with flat bands under electromagnetic radiation: Application to the α−T3 graphene model

Superfluid density and collective modes of fermion superfluid in dice lattice

Superfluid density and collective modes of fermion superfluid in dice lattice

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