Dynamics of edge currents in a linearly quenched Haldane model

Mardanya, Sougata; Bhattacharya, Utso; Agarwal, Amit; Dutta, Amit

doi:10.1103/physrevb.97.115443

Cited by 18 publications

(11 citation statements)

References 61 publications

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“…These Dirac points play a crucial role in explaining the sudden quenching dynamics of the model. The nonequilibrium dynamics of the edge current of the semiopen Haldane model has also been reported 33 . Moreover, these symmetry protected edge states are extremely important in the study of the superconductors with Majorana Fermions 34 , spin Hall insulators [35][36][37] , three dimensional topological insulators 38 etc.…”

mentioning

confidence: 88%

“…As a consequence the NN hopping parameters are real while the NNN hopping parameters are complex. Thus, the appropriate two-level Hamiltonian of the Haldane model can be written as is characterized by the non-zero Chern number ν = ±1 21,33 . Under such condition the charge conducting edge modes occur for any finite sized system.…”

Section: The Topological Phase Diagrammentioning

confidence: 99%

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The topology and robustness of two Dirac cones in S-graphene: A tight binding approach

Bandyopadhyay

Datta

Jana

et al. 2020

Sci Rep

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Present work reports an elegant method to address the emergence of two Dirac cones in a non-hexagonal graphene allotrope S-graphene (SG). We have availed nearest neighbour tight binding (NNTB) model to validate the existence of two Dirac cones reported from density functional theory (DFT) computations. Besides, the real space renormalization group (RSRG) scheme clearly reveals the key reason behind the emergence of two Dirac cones associated with the given topology. Furthermore, the robustness of these Dirac cones has been explored in terms of hopping parameters. As an important note, the Fermi velocity of the SG system (vF $$\simeq $$≃ c/80) is almost 3.75 times that of the graphene. It has been observed that the Dirac cones can be easily shifted along the symmetry lines without breaking the degeneracy. We have attained two different conditions based on the sole relations of hopping parameters and on-site energies to break the degeneracy. Further, in order to perceive the topological aspect of the system we have obtained the phase diagram and Chern number of Haldane model. This exact analytical method along with the supported DFT computation will be very effective in studying the intrinsic behaviour of the Dirac materials other than graphene.

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mentioning

confidence: 88%

Section: The Topological Phase Diagrammentioning

confidence: 99%

The topology and robustness of two Dirac cones in S-graphene: A tight binding approach

Bandyopadhyay

Datta

Jana

et al. 2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In parallel, the unitary preparation or tuning of Chern insulating phases [17][18][19][20][21][22][23][24] of the (monolayer) Haldane model has remained a major challenge to date. While there has been a fair amount of success with respect to the experimental preparation of materials hosting Chern nontrivial phases [5][6][7][8], dynamical tuning or switching across the different Chern phases in a given Chern insulator is altogether a different challenge.…”

Section: Introductionmentioning

confidence: 99%

Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases

et al. 2021

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We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that an appropriately defined Chern number accurately maps out all the possible phases of the system and remains well defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge to date, given the impossibility of unitarily connecting inequivalent topological phases. We show that this difficulty can be circumvented by adiabatically varying the interlayer coupling in such a way that the system remains gapped at all times. In particular, complete knowledge of the phase diagram of the bilayer composite immediately allows one to identify all such adiabatic passages which may connect the different Chern inequivalent phases of the individual monolayers.

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“…The success of such dynamical preparation depends not only on the dynamical generation of a topological Hamiltonian but also on preparing the system in a topologically non-trivial dynamical state. The question whether the out-equilibrium state of a quantum many body system can be a characterised by an integer-quantised topological index and whether there exist a non-equilibrium bulk-boundary correspondence has not yet been fully understood [56][57][58][59][60][61][62][63][64][65]. The dynamical topological invariant has been recently studied in out-of-equilibrium one dimensional (1D) topological system [56,57,[62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Dissipative preparation of many-body Floquet Chern insulators

Bandyopadhyay,

Dutta

2020

Preprint

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Considering coupling to a micro-structured bath as a relaxation mechanism in a periodically driven dissipative Haldane model, we establish that the system may be tuned to a stroboscopic topological steady state at all finite temperatures. The amplitude and frequency of the periodic drive is so chosen that the Floquet Hamiltonian describing the Haldane model at stroboscopic instants of time in the unitary situation is topologically non-trivial. We establish that in the stroboscopic steady state, the system reaches a thermal state of the Floquet Hamiltonian at a controlled temperature. Further, it is observed that even with a coupling to a quasi-local bath, remarkably a Chern insulator can indeed be prepared in a Chern non-trivial pure steady state which is expected to exhibit a stroboscopic bulkboundary correspondence. Using the non-uniqueness of the macroscopic bulk electric polarisation of a Chern insulator in its topological phase, we propose a generalised Chern invariant that reflects the topology of out-of-equilibrium many-body stroboscopic states of the Haldane model even in a dissipative ambience. The generalised topology of dynamical Chern insulators being dependent on single-particle correlations, is expected to manifest in experiments probing many-body quantum observables.

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Dynamics of edge currents in a linearly quenched Haldane model

Cited by 18 publications

References 61 publications

The topology and robustness of two Dirac cones in S-graphene: A tight binding approach

The topology and robustness of two Dirac cones in S-graphene: A tight binding approach

Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases

Dissipative preparation of many-body Floquet Chern insulators

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