Spin Hall conductivity in insulators with nonconserved spin

Monaco, Domenico; Ulčakar, Lara

doi:10.1103/physrevb.102.125138

Cited by 14 publications

(8 citation statements)

References 25 publications

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“…A much richer and mathematically more challenging situation would be to consider systems in which spin is not conserved, for example due to the presence of Rashba spin-orbit coupling in the model. While formulae for the (appropriate generalization of) spin conductivity have been already investigated analytically [22,23] and numerically [28] within linear response, the existence of possible power-law correction to these formulae remains to be studied. We postpone this investigation to future work.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Purely linear response of the quantum Hall current to space-adiabatic perturbations

Marcelli,

Monaco

2021

Preprint

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Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond the linear response regime. In particular, we prove that, in quantum Hall systems and Chern insulators, the transverse response current is quantized up to any order in the strength of the inducing electric field. The latter is introduced as a perturbation to a periodic, spectrally gapped equilibrium Hamiltonian by means of a linear potential; existing proofs of the exactness of Kubo formula rely instead on a time-dependent magnetic potential. The result applies to both continuum and discrete crystalline systems modelling the quantum (anomalous) Hall effect.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Purely linear response of the quantum Hall current to space-adiabatic perturbations

Marcelli,

Monaco

2021

Preprint

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“…describes spin transport, and σ s II quantifies the rate of change of the spin density due to spin nonconservation in the Hamiltonian [144][145][146][147]. Our definition of σ s II differs slightly from that in Ref.…”

Section: Spectral Flow Of the P±-wilson Loopmentioning

confidence: 99%

“…Our definition of σ s II differs slightly from that in Ref. [144] in that we have chosen to include in σ s II all contributions to the spin Hall conductivity that vanish when spin is conserved. The spin Chern number gives a topological contribution to σ s I even when spin is not conserved.…”

Section: Spectral Flow Of the P±-wilson Loopmentioning

confidence: 99%

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Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

Lin¹,

Palumbo²,

Guo³

et al. 2022

Preprint

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Topological insulating (TI) phases were originally highlighted for their disorder-robust bulk responses, such as the quantized Hall conductivity of 2D Chern insulators. With the discovery of time-reversal-(T -) invariant 2D TIs, and the recognition that their spin Hall conductivity is generically non-quantized, focus has since shifted to boundary states as signatures of 2D and 3D TIs and symmetry-enforced topological crystalline insulators (TCIs). However, in T -invariant (helical) 3D TCIs such as bismuth, BiBr, and MoTe2 -termed higher-order TCIs (HOTIs) -the boundary signatures manifest as 1D hinge states, whose configurations are dependent on sample details. It is hence desirable to elucidate bulk signatures of helical TCIs, and their relationship to sample-independent experimental observables. In this work, we introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the bulk topological properties of Iand T -protected helical HOTIs. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetal states with gapless spin spectra, and T -doubled axion insulator (T-DAXI) states with nontrivial partial axion angles θ ± = π indicative of a 3D spin-magnetoelectric bulk response. We provide experimental signatures of each spin-stable regime of helical HOTIs, including surface Fermi arcs in spin-Weyl semimetals under strong Zeeman fields, and half-quantized 2D TI states on the gapped surfaces of T-DAXIs originating from a partial parity anomaly. Lastly, we use ab-initio calculations to demonstrate that the candidate HOTI β-MoTe2 realizes a spin-Weyl state with 8 total spin-Weyl points.

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“…Thus, in this class of discrete models fulfilling a discrete rotational symmetry, despite at the operator level J s prop,1 = J s conv,1 , at the expectation value level (that is, in the sense of the corresponding conductivities) there is no difference. One can construct models in which this further symmetry is broken and which then produce different values for σ s prop,1 and σ s conv,1 [21].…”

Section: Spin Conductivitymentioning

confidence: 99%

From charge to spin: analogies and differences in quantum transport coefficients

Marcelli,

Monaco

2022

Preprint

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We review some recent results from the mathematical theory of transport of charge and spin in gapped crystalline quantum systems. The emphasis will be in transport coefficients like conductivities and conductances. As for the former, those are computed as appropriate expectations of current operators in a non-equilibrium almost-stationary state (NEASS), which arises from the perturbation of an equilibrium state by an external electric field. While for charge transport the usual double-commutator Kubo formula is recovered (also beyond linear response), we obtain formulas for appropriately-defined spin conductivities which are still explicit but more involved. Certain "Kubo-like" terms in these formulas are also shown to agree with corresponding contributions to the spin conductance.In addition to that, we employ similar techniques to show a new result, namely that even in systems with non-conserved spin there is no generation of spin torque, namely the spin torque operator has an expectation in the NEASS which vanishes faster than any power of the intensity of the perturbing field. Contents

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Spin Hall conductivity in insulators with nonconserved spin

Cited by 14 publications

References 25 publications

Purely linear response of the quantum Hall current to space-adiabatic perturbations

Purely linear response of the quantum Hall current to space-adiabatic perturbations

Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

From charge to spin: analogies and differences in quantum transport coefficients

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