Unit cell consistency of maximally localized Wannier functions

Yang, Xiaolong; He, Zhouyi; Zheng, Xiao

doi:10.1088/2516-1075/ab5e5a

Cited by 4 publications

(5 citation statements)

References 39 publications

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“…(Q2) to which extent is such a formula affected by a different choice of the spin current operator, namely J Sz conv versus J Sz prop ? Moreover, any formula for spin transport coefficients should satisfy the socalled unit cell consistency (UCC), namely the requirement that any prediction on macroscopic transport must be independent of the choice of the fundamental cell [69].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A New Approach to Transport Coefficients in the Quantum Spin Hall Effect

Marcelli

Panati

Teufel

2020

Ann. Henri Poincaré

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We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator $$H_0$$ H 0 does not commute with the spin operator in view of Rashba interactions, as in the typical models for the quantum spin Hall effect. A gapped periodic one-particle Hamiltonian $$H_0$$ H 0 is perturbed by adding a constant electric field of intensity $$\varepsilon \ll 1$$ ε ≪ 1 in the j-th direction, and the linear response in terms of a S-current in the i-th direction is computed, where S is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (unit cell consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper S-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic S-current as the trace per unit volume of the S-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

A New Approach to Transport Coefficients in the Quantum Spin Hall Effect

Marcelli

Panati

Teufel

2020

Ann. Henri Poincaré

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“…Moreover, as the size of the molecule increases to a certain extent, the energies at integer electron numbers may become less accurate. For such systems, the correction offered by the GSC approach may be inadequate, and the LOSC method with sizeconsistent corrections (Su et al, 2020;Yang et al, 2020) to DFA should be used.…”

Section: Resultsmentioning

confidence: 99%

Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach

2020

Self Cite

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Molecular quasiparticle and excitation energies determine essentially the spectral characteristics measured in various spectroscopic experiments. Accurate prediction of these energies has been rather challenging for ground-state density functional methods, because the commonly adopted density function approximations suffer from delocalization error. In this work, by presuming a quantitative correspondence between the quasiparticle energies and the generalized Kohn–Sham orbital energies, and employing a previously developed global scaling correction approach, we achieve substantially improved prediction of molecular quasiparticle and excitation energies. In addition, we also extend our previous study on temporary anions in resonant states, which are associated with negative molecular electron affinities. The proposed approach does not require any explicit self-consistent field calculation on the excited-state species, and is thus highly efficient and convenient for practical purposes.

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“…(Q2) to which extent is such a formula affected by a different choice of the spin current operator, namely J Sz conv versus J Sz prop ? Moreover, any formula for spin transport coefficients should satisfy the so-called Unit Cell Consistency (UCC), namely the requirement that any prediction on macroscopic transport must be independent of the choice of the fundamental cell [69].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A new approach to transport coefficients in the quantum spin Hall effect

Marcelli,

Panati,

Teufel

2020

Preprint

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We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator H 0 does not commute with the spin operator in view of Rashba interactions, as in the typical models for the Quantum Spin Hall effect.A gapped periodic one-particle Hamiltonian H 0 is perturbed by adding a constant electric field of intensity ε ≪ 1 in the j-th direction, and the linear response in terms of a S-current in the i-th direction is computed, where S is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (Unit Cell Consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper S-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number.The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic S-current as the trace per unit volume of the S-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models. Results on theS-conductivity 5.1. The linear response coefficient 5.2. When S is (approximately) conserved 6. Proofs 6.1. Diagonal and off-diagonal operators 6.2. Inverse Liouvillian 6.3. NEASS 6.4. Well-posedness of the proper S-conductivity 6.5. Chern-like and extra contributions to the S-conductivity Appendix A. Unit Cell Consistency and vanishing of persistent S-currents A.1. Results on the Unit Cell Consistency A.2. Models with discrete rotational symmetries A.3. Vanishing of persistent S-current when S is conserved References

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Unit cell consistency of maximally localized Wannier functions

Cited by 4 publications

References 39 publications

A New Approach to Transport Coefficients in the Quantum Spin Hall Effect

A New Approach to Transport Coefficients in the Quantum Spin Hall Effect

Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach

A new approach to transport coefficients in the quantum spin Hall effect

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