Josephson junctions in two-dimensional topological insulators with embedded magnetic domains can host a number of topological phases, in particular, Jackiw-Rebbi solitons and Majorana zero modes. These different non-trivial phases appear in such junctions for multiple-domain magnetic islands, showing a rich multi-gap structure. Features related to the interplay between superconductivity and magnetism in these systems cannot be easily discerned looking at behavior of the Andreev spectrum and the concomitant dc Josephson effect. Instead, the thermal conductance is very sensitive to the nature of the junction and the domain structure of the magnetic island. We present a detailed analysis of these properties in the case of a topological Josephson junction with a single and two-domain magnetic island. Configurations hosting soliton magnetic modes lead to a peculiar behavior of the thermal conductance relative to the thermal quantum, characterized by a negative slope as a function of the temperature, just above the superconducting critical temperature. At low temperatures, these junctions also show characteristic coherence patters in the behavior of the thermal conductance as function of the Josephson phase bias and the angle between the magnetizations of the domains.
Ever since its first proposal in 1976, Jackiw-Rebbi zero-mode has been drawing extensive attention for its charming properties including charge fractionalization, topologically protected zero-energy and possible non-Abelian statistics. We investigate these properties through the Jackiw-Rebbi zero-modes in quantum spin Hall insulator. Though charge fractionalization is not manifested, Jackiw-Rebbi zero-mode's zero-energy nature leads to a double-frequency Aharonov-Bohm effect, implying that it can be viewed as a special case of Majorana zero-mode breaking particle-hole symmetry. Such relation i…
Shot noise signatures identifying non-Abelian properties of Jackiw-Rebbi zero modes
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）；State Key Laboratory of Surface Physics, Fudan University（复旦大学表面物理国家重点实验室）；Hefei National Laboratory（合肥国家实验室）
We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nano-wires. We modelled the non-uniform nano-wires as junction between two cylindrical nano-wires with different radius. In the limit of wire length being much larger than its radius, the surface state of the nanowire splits into one dimensional Dirac modes propagating along the axis of the cylinder owing to radial confinement. The sign of the mass gap in each of these Dirac mode is decided by angular momentum quantum number corresponding to the rotational …
We present a new perspective to the classification of topological phases in free fermion insulators by generalizing the Jackiw-Rebbi model to arbitrary dimensions. We show that a generalized Jackiw-Rebbi model where the Dirac mass ($m$) satisfies $m(x)=-m(-x)$ is invariant under a parity transformation ($P$) that relates the $x>0$ half to the $x<0$ half. Determining the form of $P$ gives rise to a Clifford algebra that has been shown to give a complete topological classification of free fermion insulators. Gapless edge states are a natural consequence of our construction and their topological …
Electric and magnetic resonances of dielectric particles have recently uncovered a range of exciting applications in steering of light at the nanoscale. Breaking of particle inversion symmetry further modifies its electromagnetic response giving rise to bianisotropy known also as magneto-electric coupling. Recent studies suggest the crucial role of magneto-electric coupling in realization of photonic topological metamaterials. To further unmask this fundamental link, we design and test experimentally one-dimensional array composed of dielectric particles with overlapping electric and magnetic …
Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture
Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics, South China Normal University（华南师范大学物理学院）；Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University（华南师范大学前沿物理研究院）
We investigate laser emission at the interface of a topological and trivial phases with loss and gain. The system is described by a Su-Schrieffer-Heeger model with site-dependent hopping parameters. We study numerically and analytically the interface states. The ground state is described by the Jackiw-Rebbi mode with a pure imaginary energy, reflecting the non-Hermiticity of the system. It is strictly localized only at the A sites. We also find a series of analytic solutions of excited states based on SUSY quantum mechanics, where the A and B sites of the bipartite lattice form SUSY partners. …
We study hybrid superconducting-semiconducting nanowires in the presence of Rashba spin-orbit interaction as well as helical magnetic fields. We show that the interplay between them leads to a competition of phases with two topological gaps closing and reopening, resulting in unexpected reentrance behavior. Besides the topological phase with localized Majorana fermions (MFs) we find new phases characterized by fractionally charged fermion (FF) bound states of Jackiw-Rebbi type. The system can be fully gapped by the magnetic fields alone, giving rise to FFs that transmute into MFs upon turning …
We study theoretically transport through a semiconducting nanowire (NW) in the presence of Rashba spin orbit interaction, uniform magnetic field, and spatially modulated magnetic field. The system is fully gapped, and the interplay between the spin orbit interaction and the magnetic fields leads to fractionally charged fermion (FF) bound states of Jackiw-Rebbi type at each end of the nanowire. We investigate the transport and noise behavior of a N/NW/N system, where the wire is contacted by two normal leads (N), and we look for possible signatures that could help in the experimental detection …
We show that carbon nanotubes (CNT) can be driven through a topological phase transition using either strain or a magnetic field. This can naturally lead to Jackiw-Rebbi soliton states carrying fractionalized charges, similar to those found in a domain wall in the Su-Schrieffer-Heeger model, in a setup with a spatially inhomogeneous strain and an axial field. Two types of fractionalized states can be formed at the interface between regions with different strain: a spin-charge separated state with integer charge and spin zero (or zero charge and spin $\pm \hbar/2$), and a state with charge $\pm…
We study topological phase transitions in one dimensional (1-D) Rashba nanowire under a spatially varying Zeeman field when coupled to an $s$-wave superconductor substrate. We show that this system supports both Majorana bound states (MBS) and fractionally charged bound states (FBS) of Jackiw-Rebbi type. By disassembling Zeeman Hamiltonian into multiple helical components, we find that each helical component is relating to a corresponding topological region, characterized by the emergence of MBS. FBS arises in the overlapping gapped area created by any two helical components with topologically…
In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple `minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and pro…
Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
