Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0811.3864

Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics

Masatoshi Sato·Satoshi Fujimoto
View original source ↗Read source document ↗Export metadata ↓

Abstract

The existence of edge states and zero energy modes in vortex cores is a hallmark of topologically nontrivial phases realized in various condensed matter systems such as the fractional quantum Hall states, p+ip superconductors, and Z_2 insulators (quantum spin Hall state). We examine this scenario for two dimensional noncentrosymmetric superconductors which allow the parity-mixing of Cooper pairs. It is found that even when the s-wave pairing gap is nonzero, provided that the superconducting gap of spin-triplet pairs is larger than that of spin-singlet pairs, gapless edge states and zero energy Majorana modes in vortex cores emerge, characterizing topological order. Furthermore, it is shown that for Rashba superconductors, the quantum spin Hall effect produced by gapless edge states exists even under an applied magnetic field which breaks time-reversal symmetry provided that the field direction is perpendicular to the propagating direction of the edge modes. This result making a sharp contrast to the Z_2 insulator is due to an accidental symmetry inherent in the Rashba model. It is also demonstrated that in the case with magnetic fields, the non-Abelian statistics of vortices is possible under a particular but realistic condition.

Explore related subjects

cond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Masatoshi Sato, Satoshi Fujimoto. 2009-01-14. Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics. https://doi.org/10.1103/physrevb.79.094504

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Theoretical Prediction of Optimal $T_c$ and Fermi Pockets in Nickelate Superconductors

High-pressure bilayer $La_{3-x}Sm_{x}Ni_{2}O_{7-δ}$ (LSNO) reaches a record $T_c=96 K$, triggering wide discussion on the $T_c$ ceiling of nickelate superconductors. We show monoclinic and tetragonal LSNO share the same octahedral quantum-well motif governing $T_c$ with $YBa_{2}Cu_{3}O_{7-δ}$ (YBCO). Using the Planckian quantum-well scaling $T_c = Λ/ξ^{2}$ ($ξ$: lattice-modulated quantum-well depth), we obtain $T_c=93.4 K$ and $97.1 K$ for monoclinic and tetragonal LSNO, matching experimental values $92 K$ and $96 K$. Despite distinct stoichiometry and global symmetry ($P2_1/m$ for LSNO, $Pmmm$ for orthorhombic YBCO), both systems have nearly identical $ξ$ ($3.6629$ angstrom vs. $3.6720$ angstrom) and consistent $T_c$ responses. Further calculations yield a universal $T_c$ limit $\sim100 K$ for rare-earth nickelates, irrespective of stacking sequences. We examine four nickelate multilayer stacking variants: 2222 (pure bilayer), 1212 (alternating single-bilayer), 2323 (bilayer-trilayer), and 1313 (single-trilayer). Mirror symmetry breaking of coupled twin quantum wells, unique to bilayer nickelates, dictates $γ$ Fermi pocket formation and ambient-pressure superconductivity. We further prove Fermi surfaces constitute a hologram of quantum-well electrons, establishing intrinsic links between quantum-well symmetry breaking, Fermi pocket structural evolution, and superconducting properties.

cond-mat.supr-con↗
arXiv2026

Enhanced superconductivity in palladium hydrides by non-perturbative electron-phonon effects

Palladium hydrides exhibit the largest isotope-effect anomaly in superconductivity: replacing hydrogen with heavier isotopes increases the superconducting critical temperature. Although this behavior is commonly attributed to strong anharmonic hydrogen vibrations, \textit{ab initio} treatments have so far incorporated anharmonic effects only through phonon renormalization, neglecting non-linear contributions to the electron-phonon interaction vertices. While such approaches reproduce the anomalous isotope trend, they severely underestimate the critical temperatures. Here, we show that non-linear electron-phonon coupling is essential in palladium hydrides. A straightforward inclusion of higher-order perturbative terms leads to a qualitative breakdown: the critical temperature is overestimated and the isotope anomaly is lost. We therefore adopt a non-perturbative framework based on an explicit evaluation of the ion-mediated electron-electron interaction, enabling anharmonic effects to be treated consistently in both the phonon spectra and the interaction vertices. Applied to PdH and PdD, it restores the anomalous isotope effect and brings calculated critical temperatures into significantly improved agreement with experiments.

cond-mat.supr-con↗
arXiv2026

Optical manifestations of loop currents in Haldane's model and in time-reversal-breaking superconductors

We present a theoretical study of optical manifestations of loop currents in Haldane's model and in time-reversal-breaking superconductors. For Haldane's model, we calculate the expectation value of loop currents in terms of model parameters and relate it with the integrated optical spectral weight for the frequency-dependent ac Hall conductivity. Thus, experimental measurements of the latter can provide information about the presence and magnitude of steady loop currents in the system. Then we elaborate on loop currents in a chiral superconductor on the honeycomb lattice, studied earlier by Brydon et al. (2019). We demonstrate that a sharp optical absorption peak in the ac Hall conductivity originates from excitations between the lower and upper Dirac bands, activated by the time-reversal-breaking superconductivity. The frequency of the peak is twice the energy difference between the Fermi level and the Dirac point. The optical spectral weight of the peak is directly related to the magnitude of loop currents induced in the unit cells by the chiral superconducting pairing, in similarity to Haldane's model.

cond-mat.supr-con↗