Reconstruction of the polarization distribution of the Rice-Mele model

Yahyavi, Mohammad; Hetényi, Balázs

doi:10.1103/physreva.95.062104

Cited by 17 publications

(28 citation statements)

References 36 publications

(85 reference statements)

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“…To compute the cumulants numerically, it is advantageous to use an alternative formulation (written here for a single occupied band in 1D) [29] ∆k M −1 i=0 ln u ki |u ki+1 = n=1 (i∆k) n n! C n (C15)…”

Section: Definition Of Gauge-invariant Cumulantsmentioning

confidence: 99%

“…c n ≡ u 0 (k)|(i∂ k ) n |u 0 (k) , and the periodic gauge is assumed for the valence-band Bloch wavefunction ψ 0k (r) = u 0k (r)e ikr . The quantity C 3 is a member of a set of gauge invariant quantities, C n , that are cumulants of the electronic polarization [29,30]. The quantity C 1 is exactly the average macroscopic polarization, which coincides with the first moment of the polarization distribution [25].…”

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confidence: 99%

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Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs

et al. 2018

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The dash-dotted curve in Figure 3b is a fit to |σ shg zzz | based on the two-photon term in equation (3). Given the simplicity of the model relative to the complexity of the full 3D bandstructure of TaAs, the 3D version of the RM model describes the data remarkably well. The peak position, low, and high energy tails of the spectrum are best described using parameterst = 1.5,δ = 1.4,t AB = 0.02, and ∆ = 0.428. The lattice parameters for TaAs are c = 1.165 nm, and b = a = 0.344 nm.The theory discussed above helps to identify the factors that contribute to a large SHG response. The first is a polar crystal structure such as 4mm (TaAs, NbAs, etc.) or mm2 (single layer monochalcogenides) consistent with a phenomenological description in terms of coupled ferroelectric chains. However, even when this description is possible there is a global bound on the frequency integrated second-order response, Σ shift z , of a system described by H RM that is given by,where G is also a dimensionless function of the dimensionless parameters, with a global maximum 0.604 [17]. Given this bound on Σ shift z , it is clear that the single most important factor in optimizing the second-order response of a 3D crystal is the effective aspect ratio parameter c 2 /ab.We conclude by addressing the question of ultimate bounds on Σ shift z , which is relevant not only to SHG, but to sensitivity of photodetectors and efficiency of solar cells based on Berry curvature generated intrinsic photogalvanic effects [21,28] as well. We have discovered a new connection between Σ shift z and the modern theory of polarization that generalizes the formulae for spectral weight beyond the RM Hamiltonian. Specifically we show that Σ shift z is unbounded and potentially divergent when the possibility of next-neighbor hopping is included.As demonstrated in the Supplementary Information, Σ shift z in two band systems, regardless of dimensionality d and range of electron hopping amplitude is given by,

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Section: Definition Of Gauge-invariant Cumulantsmentioning

confidence: 99%

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confidence: 99%

Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs

et al. 2018

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“…Here we give the basic expressions for the gauge invariant cumulants, for the reconstruction of the polarization we refer the reader to Ref. [27].…”

Section: Polarization and Gauge Invariant Cumulantsmentioning

confidence: 99%

“…These quantities can be shown to be gauge invariant. If the Wannier functions associated with the Bloch functions are sufficiently localized, they correspond to the cumumlants of the probability distribution of the total position, and can be used in its reconstruction [27]. From the inversion of this cumulant series it is also possible to obtain gauge invariant moments.…”

Section: Polarization and Gauge Invariant Cumulantsmentioning

confidence: 99%

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Variational study of the interacting, spinless Su–Schrieffer–Heeger model

Yahyavi

Saleem

Hetényi

2018

J. Phys.: Condens. Matter

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We study the phase diagram and the total polarization distribution of the Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane-Mele-Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution 'walks across' smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as it happens when a Rice-Mele onsite potential is turned on.

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Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials

Requist

Gross

2018

J. Phys. Chem. Lett.

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The many-body Berry phase formula for macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This formula accurately reproduces the exact polarization in the Rice−Mele−Hubbard model across the band insulator−Mott insulator transition. A similar formula based on a reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.

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Reconstruction of the polarization distribution of the Rice-Mele model

Cited by 17 publications

References 36 publications

Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs

Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs

Variational study of the interacting, spinless Su–Schrieffer–Heeger model

Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials

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