Quantum criticality at the Chern-to-normal insulator transition

Xue, Y. Y.; Prodan, Emil

doi:10.1103/physrevb.87.115141

Cited by 28 publications

(29 citation statements)

References 116 publications

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“…While this is consistent with the scaling theory [5,23], here it is based on numerical model simulations using the conventional Kubo formula. Our results are consistent with the experimental finding that the electron-electron interaction only comes into play as a temperature-dependent relaxation time [1/τ in ∝ (kT ) 2 ], which does not change the localization length exponent ν.…”

supporting

confidence: 78%

“…On the other hand, there are no well-established results for understanding the temperature-scaling law [12,20] in a microscopic model incorporating disorder and inelastic-scattering effects. For noninteracting systems, recent numerical studies based on the noncommutative Kubo formula support that with the input of 1/τ in ∝ kT (where k denotes the Boltzmann constant), one obtains a κ = 1/2ν ∼ 0.2 [23]. However, the physical origin for the finite-temperature scaling behavior remains poorly understood.…”

mentioning

confidence: 99%

“…Theoretically, based on the scaling argument [20,35], it is known that the inelastic-scattering exponent has values p = 1 for noninteracting and p = 2 for electron-electron interacting systems [20]. For the disordered systems we study, it is not well established how the finite relaxation time will affect the Hall conductance, which has been studied recently based on the noncommutative Kubo formula [23]. Here, we take a different approach by following the Kubo formula [Eq.…”

mentioning

confidence: 99%

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Scaling behavior of the insulator-to-plateau transition in a topological band model

Priest

Lim

2014

Phys. Rev. B

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Scaling behavior of the quantum phase transition from an insulator to a quantum Hall plateau state has often been examined within systems realizing Landau levels. We study the topological transition in an energy-band model with nonzero Chern number, which has the same topological property as a Landau level. We find that a topological band generally realizes the same universality class as the integer quantum Hall system under uniform magnetic flux for strong enough disorder scattering. Furthermore, the symmetry of the transition characterized by relations σ xy ( E) = 1 − σ xy (− E) for Hall conductance and σ T ( E) = σ T (− E) for longitudinal Thouless conductance is observed near the transition region. We also establish that the finite-temperature dependence of Hall conductance is determined by inelastic-scattering relaxation time, while the localization exponent ν remains unchanged by such scattering.

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supporting

confidence: 78%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Scaling behavior of the insulator-to-plateau transition in a topological band model

Priest

Lim

2014

Phys. Rev. B

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“…A critical behavior is found at the gate voltage V c g , where the ρ xx approaches a constant value and σ xx saturates to a finite conductivity (around 0.5e 2 =h) as T →0. Since the QAH insulator and the Anderson insulator carry different Chern numbers, this is a topological QPT [19,20], similar to the insulator to plateau transition in the QH effect. The significance of disorder in our sample also implies an equivalence between the QPT studied in this work and that seen in the topological Anderson insulator [21].…”

mentioning

confidence: 95%

Observation of the Quantum Anomalous Hall Insulator to Anderson Insulator Quantum Phase Transition and its Scaling Behavior

Chang

Zhao

et al. 2016

Phys. Rev. Lett.

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Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in the quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. We expect that our work will motivate much further investigation of many properties of quantum phase transition in this new context. DOI: 10.1103/PhysRevLett.117.126802 The quantum anomalous Hall (QAH) state is a topological quantum state displaying quantized Hall resistance and zero longitudinal resistance, similar to the quantum Hall (QH) state. However, while the QH effect requires a large external magnetic field, the origin of the QAH effect is the exchange interaction between electron spin and magnetic moments in ferromagnetic materials, and thus can occur even in the absence of an external magnetic field [1][2][3]. Ever since the discovery of the QAH effect in magnetically doped ðBi; SbÞ 2 Te 3 films [2][3][4][5][6][7], intensive research effort has focused on the global phase diagram and the novel transport properties of this effect, including nonlocal transport [6,8], zero Hall conductance plateau [9][10][11], delocalization behavior [7], and giant anisotropic magnetoresistance [12]. These experimental observations reveal an equivalence between the QAH effect and QH effect in terms of their topological nature.In the QH effect, the appearance of stable quantized Hall plateaus is intimately tied to the Anderson localization of bulk carriers of a two dimensional electron gas (2DEG) under a strong external magnetic field. The quantum phase transition (QPT) point between two Hall plateaus (known as plateau to plateau transition) is marked by the emergence of an extended state, which can be viewed, for a smoothly varying disorder, as the transition where the QH droplets of a state with one Chern number in the background of a QH state of another Chern number begin to percolate. Since this percolation process involves quantum tunneling between nearby chiral edge modes encircling individual droplets, it leads to a different critical exponent from that describing a classical percolation transition [13][14][15]. The QPT between an insulator and ν ¼ 1 plateau belongs to the same universality class as the plateau to plateau transition, and serves as the prototype for the QPT studied in the present work. In the QAH effect, one may expect a similar percolation picture for chiral edge states around magnetic domains at the quantum critical point. In the experiment by Checkelsky et al. [7], evidence for quantum criticality and delocalization was shown while approaching the QAH state, but the scaling behavior was...

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“…When considering the real experimental implementation, the physical system will have an inevitable interaction with the surrounding environment. Many studies of DTQW report that due to the decoherence induced by the environment, the position distribution pattern of QW change to a binomial distribution that is similar to the distribution of the classical walk [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. For the coherent QW, the variance of position distribution in the QW grows quadratically with time.…”

Section: Introductionmentioning

confidence: 99%

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

Chen

Zhang

2016

Phys. Rev. A

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The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position distribution of AQW have been obtained. Taking the broken line noise and coin-decoherence as examples of decoherence, we find that when the decoherence only emerges in one direction, the anisotropic position distribution pattern appears, and not all the motions of quantum walkers exhibit the transition from quantum to classical behaviors. The correlations between the walkers and the coin in 2D AQW have been discussed. The anisotropic correlations between walkers and coin have been revealed in the presence of decoherence.

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Quantum criticality at the Chern-to-normal insulator transition

Cited by 28 publications

References 116 publications

Scaling behavior of the insulator-to-plateau transition in a topological band model

Scaling behavior of the insulator-to-plateau transition in a topological band model

Observation of the Quantum Anomalous Hall Insulator to Anderson Insulator Quantum Phase Transition and its Scaling Behavior

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

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