Magnetic response of Majorana Kramers pairs with an order-two symmetry

Yamazaki, Yuki; Kobayashi, Shingo; Yamakage, Ai

doi:10.1103/physrevb.103.094508

Cited by 10 publications

(3 citation statements)

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“…This prediction was verified in a bilayer model with a glide plane (Pmma). In fact, our result can be applied to materials with any nonsymmorphic space group, 53) such as UCoGe, which has the crystalline symmetry of the space group Pnma. 54) Previous studies have strongly suggested that this material is a ferromagnetic superconductor at ambient pressure 55,56) and a time-reversal-invariant one at high pressure.…”

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confidence: 95%

Magnetic Response of Majorana Kramers Pairs Protected by $\mathbb{Z}_{2}$ Invariants

2020

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On the surface of time-reversal-invariant topological superconductors, Kramers pairs of Majorana fermions with chiral and crystalline symmetries exhibit completely uniaxial or octupole anisotropic magnetic response. This paper reports possible types of magnetic responses of Majorana Kramers pairs with one-dimensional Z 2 invariants defined by crystalline symmetry. In particular, the general theory predicts a new type of magnetic response where two Majorana Kramers pairs associated with the Z 2 invariant show biaxially (quadrupolar) anisotropic magnetic response, which is a novel type of response that is rarely observed in conventional and Majorana fermions.

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confidence: 95%

Magnetic Response of Majorana Kramers Pairs Protected by $\mathbb{Z}_{2}$ Invariants

2020

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“…29,[33][34][35][36][37][38][39] For example, a crystalline-symmetryprotected MKP has been shown to exhibit a magnetic dipole (Ising) or octupole response, that is, a response distinct from conventional (complex) spin-1/2 fermions. [40][41][42][43] Interestingly, the irreducible representation (irrep) of the magnetic multipole is the same as that of the bulk pair potential, which suggests that this could be a new direction for measuring the superconducting symmetry of TCSCs hosting a single MKP. However, to date only the magnetic response has been studied, and this may be difficult to use practically because of the Meissner effect.…”

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“…These phenomena have been systematically classified. 27-30, 32, 45) According to these classifications, double MKPs can only exist in magnetic chiral-and/or glide-planesymmetric systems, 30,42,44,46) as described below.…”

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Electric Multipoles of Double Majorana Kramers Pairs

Yamazaki,

Kobayashi,

Yamakage

2021

Preprint

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A single Majorana Kramers pair hosts only one component of the magnetic multipole. This can be used to determine the bulk Cooper-pair symmetry through surface-sensitive spectroscopic measurements, either by applying a magnetic field or by using a ferromagnet/superconductor junction. This paper proposes that the electric response, which is free from the Meissner effect, can be used an alternative method to measure the bulk Cooper-pair symmetry in time-reversal-invariant superconductors with double Majorana Kramers pairs. The relationships among electric multipoles, strain tensors and superconducting symmetries under a given wallpaper group on the surfaces of topological crystalline superconductors are shown. This study also reveals that only a specific irreducible representation of a uniform strain yields a gap in the double Majorana Kramers pairs for the topological-crystalline-superconductor candidate Sr 3 SnO. This highlights the viability of electric detection regarding Cooper-pair symmetry.

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Large-scale simulations of vortex Majorana zero modes in topological crystalline insulators

Wan,

Zhao,

et al. 2024

Quantum Front

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Topological crystalline insulators are known to support multiple Majorana zero modes (MZMs) at a single vortex, their hybridization is forbidden by a magnetic mirror symmetry $M_{T}$ M T . Due to the limited energy resolution of scanning tunneling microscopes and the very small energy spacing of trivial bound states, it remains challenging to directly probe and demonstrate the existence of multiple MZMs. In this work, we propose to demonstrate the existence of MZMs by studying the hybridization of multiple MZMs in a symmetry breaking field. The different responses of trivial bound states and MZMs can be inferred from their spatial distribution in a vortex. However, the theoretical simulations are very demanding since it requires an extremely large system in real space. By utilizing the kernel polynomial method, we can efficiently simulate large lattices with over 108 orbitals to compute the local density of states which bridges the gap between theoretical studies based on minimal models and experimental measurements. We show that the spatial distribution of MZMs and trivial vortex bound states differs drastically in tilted magnetic fields. The zero-bias peak elongates when the magnetic field preserves $M_{T}$ M T , while it splits when $M_{T}$ M T is broken, giving rise to an anisotropic magnetic response. Since the bulk of SnTe are metallic, we also study the robustness of MZMs against the bulk states, and clarify when can the MZMs produce a pronounced anisotropic magnetic response.

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Magnetic response of Majorana Kramers pairs with an order-two symmetry

Cited by 10 publications

References 100 publications

Magnetic Response of Majorana Kramers Pairs Protected by \(\mathbb{Z}_{2}\) Invariants

Magnetic Response of Majorana Kramers Pairs Protected by \(\mathbb{Z}_{2}\) Invariants

Electric Multipoles of Double Majorana Kramers Pairs

Large-scale simulations of vortex Majorana zero modes in topological crystalline insulators

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