Anomalous Hall effect in superconductors with spin-orbit interaction

Sacramento, P. D.; Araújo, M. A. N.; Vieira, V. R.; Dugaev, V. K.; Barnaś, J.

doi:10.1103/physrevb.85.014518

Cited by 11 publications

(20 citation statements)

References 79 publications

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“…(other cases were considered in 27,36 ). The energy eigenvalues and eigenfunction may be obtained solving the Bogoliubov-de Gennes equations…”

Section: Two-dimensional Triplet Superconductormentioning

confidence: 99%

Fate of Majorana fermions and Chern numbers after a quantum quench

Sacramento

2014

Phys. Rev. E

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The stability of Majorana fermions at the edges of a two-dimensional topological supercondutor is studied, after quenches to either non-topological phases or other topological phases. Both instantaneous and slow quenches are considered. In general, the Majorana modes decay and, in the case of instantaneous quenches, their revival times scale to infinity as the system size grows. Considering fast quantum quenches within the same topological phase, leads, in some cases, to robust edge modes. Quenches to a topological Z2 phase reveal some robustness of the Majorana fermions. Comparing strong spin-orbit coupling with weak spin-orbit coupling, it is found that the Majorana fermions are fairly robust, if the pairing is not aligned with the spin-orbit Rashba coupling. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number oscillates between increasing values. In some cases, the time average Chern number seems to converge to the appropriate value, but often the decay is very slow. The effect of varying the rate of change in slow quenches is also analysed. It is found that the defect production is non-universal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.

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“…(other cases were considered in 27,36 ). The energy eigenvalues and eigenfunction may be obtained solving the Bogoliubov-de Gennes equations…”

Section: Two-dimensional Triplet Superconductormentioning

confidence: 99%

Fate of Majorana fermions and Chern numbers after a quantum quench

Sacramento

2014

Phys. Rev. E

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“…(10) of Ref. 26 . We consider both the unitary and the non-unitary cases, relaxing the restriction that ity.…”

Section: Chern Numbers and Hall Conductivitymentioning

confidence: 99%

“…A dense magnetic impurity distribution leads to the destruction of superconductivity if the pairing is a spin singlet but magnetization and superconductivity may coexist if the pairing is of triplet origin such as in a p-wave superconductor. In this case the Hall conductivity was shown to be non-vanishing if the spin-orbit coupling is present 26 .…”

Section: Introductionmentioning

confidence: 99%

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Hall conductivity as bulk signature of topological transitions in superconductors

Sacramento¹,

Araújo²,

Castro³

2014

EPL

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Topological superconductors may undergo transitions between phases with different topological numbers which, like the case of topological insulators, are related to the presence of gapless (Majorana) edge states. In Z topological insulators the charge Hall conductivity is quantized, being proportional to the number of gapless states running at the edge. In a superconductor, however, charge is not conserved and, therefore, σxy is not quantized, even in the case of a Z topological superconductor. Here it is shown that while the σxy evolves continuously between different topological phases of a Z topological superconductor, its derivatives display sharp features signaling the topological transitions. We consider in detail the case of a triplet superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO) coupling and externally applied Zeeman spin splitting. Generalization to the cases where the pairing vector is not aligned with that of the SO coupling is given. We generalize also to the cases where the normal system is already topologically non-trivial.

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“…In the p-wave case the quantum critical point occurs at higher coupling values and for µ = 0 it is rather flat up to high coupling values. Note that the effect of a single impurity is significant in the properties of the system as shown before [31,32,33,34], including its effect on transport properties inducing, for instance, currents [35] and an anomalous Hall effect [36], if spin-orbit is present.…”

Section: One Impuritymentioning

confidence: 99%

Magnetic chains on a triplet superconductor

Sacramento

2015

J. Phys.: Condens. Matter

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Abstract. The topological state of a two-dimensional triplet superconductor may be changed by an appropriate addition of magnetic impurities. A ferromagnetic magnetic chain at the surface of a superconductor with spin-orbit coupling may eliminate the edge states of a finite system giving rise to localized zero modes at the edges of the chain. The coexistence/competition between the two types of zero modes is considered. The reduction of the system to an effective 1d system gives partial information on the topological properties but the study of the two sets of zero modes requires a twodimensional treatment. Increasing the impurity density from a magnetic chain to magnetic islands leads to a finite Chern number. At half-filling small concentrations are enough to induce chiral modes.

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Anomalous Hall effect in superconductors with spin-orbit interaction

Cited by 11 publications

References 79 publications

Fate of Majorana fermions and Chern numbers after a quantum quench

Fate of Majorana fermions and Chern numbers after a quantum quench

Hall conductivity as bulk signature of topological transitions in superconductors

Magnetic chains on a triplet superconductor

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