Eightfold quantum Hall phases in a time reversal symmetry broken tight binding model

Saha, Sudarshan; Nag, Tanay; Mandal, Saroj

doi:10.1103/physrevb.103.235154

Cited by 8 publications

(7 citation statements)

References 68 publications

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“…Having motivated by the HOT phases in C 3 symmetry broken graphene-like system [26,29,54], here we analyze the evolution of eight-fold phases [65] for extended Haldane model in the anistropic limit. We extensively explore the interplay between the IS breaking sub-lattice mass, TRS breaking Zeeman field and SOC interaction in engendering the corner modes for the dipolar phase.…”

Section: Discussionmentioning

confidence: 99%

“…To this end, we consider η = 1 to investigate various FOT phases before exploring their second-order counterparts. The Zeeman field g destroys the φ → −φ symmetry by shrinking or expanding different phases as compared to g = 0 case where the eight-fold FOT phases can symmetrically appear under φ → −φ [65]. The size of QSHI (QAHI) phases increases (reduces) referring to fact that magnetic field stabilizes QSHI phases (see Fig.…”

Section: Model Hamiltonianmentioning

confidence: 99%

“…ij along the two bonds the electron traverses going from site j to i [5,65]. The momentum space Hamiltonian, obtained from Eq.…”

Section: Model Hamiltonianmentioning

confidence: 99%

“…Given the fact that inversion symmetry (IS) protected HO-QAHI can be generated only in absence of sub-lattice mass [54], we here seek the answers for the following question: Can we engineer mid-gap zero-energy HOT states using the interplay of sub-lattice mass, Zeeman exchange field and SOC interaction? To be precise, the HO analogue of QAHI, QSHI and quantum anomalous spin Hall insulator (QASHI) phases, as already observed in the extended Haldane model [65], is the main focus of the present work.…”

Section: Introductionmentioning

confidence: 98%

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Dipolar quantum spin Hall insulator phase in extended Haldane model

Saha¹,

Nag²,

Mandal³

2022

Preprint

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The higher-order corner modes for quantum anomalous Hall insulator in C3 symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice mass, time reversal symmetry breaking Zeeman field and spin-orbit coupling interaction where we find that only the quantum spin Hall insulator can host the second-order dipolar phase while the remaining two first-order topological phases do not morph into the latter. Remarkably, four-fold degeneracy of zero-energy dipolar states can be reduced to two-fold under the application (withdrawn) of sub-lattice mass (Zeeman field) term when the spin-orbit coupling is already present. On the other hand, the sub-lattice mass and Zeeman field terms compete with each other to pin down the two mid-gap states at zero-energy in absence or presence of spin-orbit coupling. Interestingly, the bulk-polarization can topologically characterize the dipolar phase irrespective of the energy of the mid-gap states as long as inversion symmetry is preserved. The effective gap criterion can qualitatively mimic the extent of SOT phase originated by the interplay between finite Zeeman exchange field, sub-lattice mass, and SOC interaction.

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Section: Discussionmentioning

confidence: 99%

Section: Model Hamiltonianmentioning

confidence: 99%

“…ij along the two bonds the electron traverses going from site j to i [5,65]. The momentum space Hamiltonian, obtained from Eq.…”

Section: Model Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Dipolar quantum spin Hall insulator phase in extended Haldane model

Saha¹,

Nag²,

Mandal³

2022

Preprint

Self Cite

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show abstract

“…To confirm the topological properties, we also calculate and discuss the edge states, with the corresponding density distribution and the spin polarization. In the reference, [ 39 ] Saha et al investigated the TR‐symmetry‐broken Kane–Mele model and discussed the fate of the QSH phase and QAH phase. Unlike the results they obtained, our results show that the QAH and TR‐broken QSH on the square–hexagon lattice are induced by the spin‐dependent and spin‐independent staggered potentials.…”

Section: Discussionmentioning

confidence: 99%

Quantum Anomalous Hall Phase and Time‐Reversal‐Symmetry‐Broken Quantum Spin Hall Phase on the Square–Hexagon Lattice

Wang

2022

Physica Status Solidi (b)

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The topological properties of the square–hexagon lattice are studied when the time‐reversal (TR) symmetry is broken. Based on the Chern number and spin Chern number, the topological trivial and nontrivial phases can be determined. When the spin‐dependent and ‐independent staggered potentials are taken into consideration, rich phase diagrams are obtained. A number of topological nontrivial phases, including the TR‐symmetry‐broken quantum spin Hall phase and quantum anomalous Hall (QAH) phase, can be achieved by tuning the spin‐dependent staggered potential. When the spin‐independent staggered potential is varied, it is possible to observe the topological phase transition from the metal phase to the QAH phase. The evolutions of the bulk bandgap and spin spectrum gap are also presented together. To support the identification of the topological phases, helical and chiral edge states are given numerically. Moreover, the corresponding density distribution and spin polarization are analyzed and discussed.

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Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

Gregefalk,

Black‐Schaffer,

Nag

2023

Annalen der Physik

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Considering models with tilted linear and quadratic band touching dispersions, the effect of the transverse linear tilt on the transmission spectra is analyzed through a harmonically driven potential well oriented longitudinally. Employing the Floquet scattering matrix formalism, Fano resonances are found as an outcome of matching between the Floquet sidebands and quasi‐bound states, where the tilt renormalizes their energies and wave vectors. It is found that the Fano resonance energy decreases (increases) for linear (quadratic) band touchings as the magnitude of the transverse momentum increases, indicating a distinct signature of the underlying band dispersion in the transmission profile. The sign of the product of the transverse momentum and the tilt also determines the relative shift in the Fano resonance energy with respect to the untilted case for both band dispersions, suggesting a possible tunability of the Fano resonance for tilted systems. Importantly, the tilt strength can also be directly determined by measuring the Fano resonance energy as function of the transverse momenta direction. The shot noise spectra and their differential property are further studied where an inflection region and undulation, respectively, is found around the Fano resonance energy. Interestingly, differential shot noise and transmission spectra both qualitatively behave in a similar fashion and might thus serve as important observables for future experiments on driven solid‐state systems.

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Eightfold quantum Hall phases in a time reversal symmetry broken tight binding model

Cited by 8 publications

References 68 publications

Dipolar quantum spin Hall insulator phase in extended Haldane model

Dipolar quantum spin Hall insulator phase in extended Haldane model

Quantum Anomalous Hall Phase and Time‐Reversal‐Symmetry‐Broken Quantum Spin Hall Phase on the Square–Hexagon Lattice

Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

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