Majorana Doublet Research Articles

Andreev reflection properties of Majorana doublets modulated by ferromagnetic leads

We investigate Andreev reflection properties contributed by the Majorana doublets, by introducing two ferromagnetic leads coupled to the ends of the time-reversal-invariant topological superconducting nanowire. It is found that the local and crossed Andreev reflections are influenced by the polarization strengths and directions in the ferromagnetic leads. This directly leads to the dependence of the shot noise Fano factors on the ferromagnetic leads, as well as their correspondence to the Andreev conductances. In addition, the coupling manners between the Majorana doublets and leads take effects to the conductance and Fano factors. This work provides useful information for the understanding of the Andreev reflection properties of Majorana doublets.

Toverline{T} -deformed fermionic theories revisited

We revisit Toverline{T} deformations of d = 2 theories with fermions with a view toward the quantization. As a simple illustration, we compute the deformed Dirac bracket for a Majorana doublet and confirm the known eigenvalue flows perturbatively. We mostly consider those Toverline{T} theories that can be reconstructed from string-like theories upon integrating out the worldsheet metric. After a quick overview of how this works when we add NSR-like or GS-like fermions, we obtain a known non-supersymmetric Toverline{T} deformation of a mathcal{N} = (1, 1) theory from the latter, based on the Noether energy-momentum. This world- sheet reconstruction implies that the latter is actually a supersymmetric subsector of a d = 3 GS-like model, implying hidden supercharges, which we do construct explicitly. This brings us to ask about different Toverline{T} deformations, such as manifestly supersymmetric Toverline{T} and also more generally via the symmetric energy-momentum. We show that, for theories with fermions, such choices often lead us to doubling of degrees of freedom, with potential unitarity issues. We show that the extra sector develops a divergent gap in the “small deformation” limit and decouples in the infrared, although it remains uncertain in what sense these can be considered a deformation.

Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

Generalized Euler index, holonomy saddles, and wall-crossing

We formulate Witten index problems for theories with two supercharges in a Majorana doublet, as in d = 3 mathcal{N} = 1 theories and dimensional reduction thereof. Regardless of spacetime dimensions, the wall-crossing occurs generically, in the parameter space of the real superpotential W. With scalar multiplets only, the path integral reduces to a Gaussian one in terms of dW, with a winding number interpretation, and allows an in-depth study of the wall-crossing. After discussing the connection to well-known mathematical approaches such as the Morse theory, we move on to Abelian gauge theories. Even though the index theorem for the latter is a little more involved, we again reduce it to winding number countings of the neutral part of dW. The holonomy saddle plays key roles for both dimensions and also in relating indices across dimensions.

Signatures of Majorana doublet in the Fano–Rashba interferometer

We theoretically study the quantum transport through a Fano–Rashba interferometer with an embedded Majorana doublet which generates at one end of the DIII-class topological superconductor. It shows that the Rasbha spin–orbit interaction in the reference arm drives the apparent and terminal-dependence spin polarization of the electron tunneling and crossed Andreev reflection, accompanied by their opposite directions. However, spin degeneracy holds in the local Andreev reflection. Next once the Majorana doublet is replaced by the Andreev bound state, the spin-polarization properties of the Andreev reflections are interchanged. Therefore, the Fano–Rashba interferometer can be a promising candidate for differentiating the Majorana doublet from other bound states.

Majorana Doublets, Flat Bands, and Dirac Nodes in s-Wave Superfluids.

Topological superfluids protected by mirror and time-reversal symmetries are exotic states of matter possessing Majorana Kramers pairs (MKPs), yet their realizations have long been hindered by the requirement of unconventional pairing. We propose to realize such a topological superfluid by utilizing s-wave pairing and emergent mirror and time-reversal symmetries in two coupled 1D ultracold atomic Fermi gases with spin-orbit coupling. By stacking such systems into 2D, we discover topological and Dirac-nodal superfluids hosting distinct MKP flat bands. We show that the emergent symmetries make the MKPs and their flat bands stable against pairing fluctuations that otherwise annihilate Majorana pairs. Exploiting new experimental developments, our scheme provides a unique platform for exploring MKPs and their applications in quantum computation.

Fano-Josephson effect in the junction with DIII-class topological and s-wave superconductors

We investigate the Josephson effects in the junction formed by the direct and indirect couplings between DIII-class topological and s-wave superconductors. As a result, the Josephson current is found to oscillate in period 2π. The presence of Majorana doublet in the DIII-class superconductor renders the current finite at the case of zero phase difference, with its sign determined by the fermion parity of such a junction. In addition to the dot level and intradot Coulomb interaction, the Fano interference is an important factor to adjust the Josephson current. It is believed that these results will be helpful in understanding the transport properties of the DIII-class superconductor.

High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity

We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical considerations on the Green's function. The order parameter induced on the wire, the pair correlation function, and the renormalization of the Fermi points are analyzed in detail, as well as the topological phase diagram in the case of weak coupling. We highlight optimal Hamiltonian parameters to access the nontrivial topological phase which could display time-reversal invariant Majorana doublets at the boundaries of the wire.

Kondo effect modified by Majorana doublet at end of a DIII-class topological superconductor

By coupling one quantum dot to a normal metal, the Kondo structure is constructed, and then its change is investigated in the case of the dot connected with a DIII-class topological superconductor supporting Majorana doublets at its ends. It is observed that Kondo correlations occur between the localized state in the dot and two continuum states simultaneously, i.e., the continuum state in the metal and the continuum Andreev reflection state between the metal and topological superconductor. This causes the Kondo-model Hamiltonian to be topologically protected by the $\text{SU}{(2)}_{s}\ensuremath{\rtimes}{Z}_{2}^{T}$ symmetry. Besides, the system Kondo temperature can be altered via adjusting the structural parameters. This work clarifies the special influence of Majorana doublet on the Kondo effect.

Josephson effects in the junction formed by DIII-class topological and s-wave superconductors with an embedded quantum dot.

We investigate the Josephson effects in the junction formed by the indirect coupling between DIII-class topological and s-wave superconductors via an embedded quantum dot. Due to the presence of two kinds of superconductors, three dot-superconductor coupling manners are considered, respectively. As a result, the Josephson current is found to oscillate in period 2π. More importantly, the presence of Majorana doublet in the DIII-class superconductor renders the current finite at the case of zero phase difference, with its sign determined by the fermion parity of such a junction. In addition, the dot-superconductor coupling plays a nontrivial role in adjusting the Josephson current. When the s-wave superconductor couples to the dot in the weak limit, the current direction will have an opportunity to reverse. It is believed that these results will be helpful for understanding the transport properties of the DIII-class superconductor.

Influence of an embedded quantum dot on the Josephson effect in the topological superconducting junction with Majorana doublets

One Majorana doublet can be realized at each end of the time-reversal-invariant Majorana nanowires. We investigate the Josephson effect in the Majorana-doublet-presented junction modified by different inter-doublet coupling manners. It is found that when the Majorana doublets couple indirectly via a non-magnetic quantum dot, only the normal Josephson effect occurs, and the fermion parity in the system just affects the current direction and amplitude. However, one magnetic field applied on the dot can induce the fractional Josephson effect in the odd-parity case. Next if the direct and indirect couplings between the Majorana doublets coexist, no fractional Josephson effect takes place, regardless of the presence of magnetic field. Instead, there almost appears the π-period-like current in some special cases. All the results are clarified by analyzing the influence of the fermion occupation in the quantum dot on the parity conservation in the whole system. We ascertain that this work will be helpful for describing the dot-assisted Josephson effect between the Majorana doublets.

Kondo physics in the Josephon junction with DIII-class topological and s-wave superconductors

We discuss the Kondo effect in the Josephson junction formed by the indirect coupling between a one-dimensional DIII-class topological and s-wave superconductors via a quantum dot. By performing the Schrieffer-Wolff transformation, we find that the single-electron occupation in the quantum dot induces various correlation modes, such as the Kondo and singlet-triplet correlations between the quantum dot and the s-wave superconductor and the spin-exchange correlation between the dot and Majorana doublet. Also, it modifies the Josephson effect by introducing the high-order anisotropic Kondo-like correlation and extra spin-exchange correlations. However, the Kondo temperature is still governed by the antiferromagnetic correlation between the dot and s-wave superconductor. We believe that this work shows the fundamental property of the DIII-class topological superconductor.

Microwave signatures of Majorana states in a topological Josephson junction

We find the admittance of a topological Josephson junction $Y(\omega,\varphi_0, T)$ as a function of frequency $\omega$, the static phase bias $\varphi_0$ applied to the superconducting leads, and temperature $T$. The dissipative part of $Y$ allows for spectroscopy of the sub-gap states in the junction. The resonant frequencies $\omega_{\mathcal{M}, n} (\varphi_0)$ for transitions involving the Majorana ($\mathcal{M}$) doublet exhibit characteristic kinks in the $\varphi_0$-dependence at $\varphi_0=\pi$. The kinks -- associated with decoupled Majorana states -- remain sharp and the corresponding spectroscopic lines are bright at any temperature, as long as the leads are superconducting. The developed theory may help extracting quantitative information about Majorana states from microwave spectroscopy.

Influence of Majorana doublet on transport through a quantum dot system with ferromagnetic leads

We investigate the electron transport through a quantum dot connected with two ferromagnetic leads, by coupling one Majorana doublet laterally to the quantum dot. It is found that Majorana doublet keeps the value of zero-bias conductance to be independent of the shift of structural parameters, including dot level, relative lead-magnetization direction, and magnetic field on the dot. Even in the cases of asymmetric dot-lead couplings, the zero-bias conductance is weakly dependent on the relative lead-magnetization direction. On the other hand, when Majorana doublet is replaced by Majorana singlet, the zero-bias conductance value becomes sensitive to the structural parameters. Via analyzing the respective particle motion processes, the different influences of Majorana doublet and singlet are explained. We believe that this work can be helpful for understanding the peculiar properties of Majorana doublet.

Topological superfluid in one-dimensional ultracold atomic system with spin-orbit coupling

We propose a one-dimensional Hamiltonian H 1D which supports Majorana fermions when d x² − y²-wave superfluid appears in the ultracold atomic system and obtain the phase diagrams both for the time-reversal-invariant (TRI) case and time-reversal-symmetry-breaking (TRSB) case. From the phase diagrams, we find that the Majorana doublets and the single Majorana fermions exist in the topological superfluid (TSF) regions for the TRI case and the TRSB case, respectively, and we can reach these regions by tuning the chemical potential μ and spin-orbit coupling α R . Importantly, the spin-orbit coupling has been realized in ultracold atoms by the recent experimental achievement of synthetic gauge field, therefore, our one-dimensional ultra-cold atomic system described by H 1D is a promising platform to find the mysterious Majorana fermions.