We study a hybrid structure, comprising the single-level quantum dot attached to the topological superconducting nanowire, inspecting dynamical transfer of the Majorana quasiparticle onto normal region. Motivated by the recent experimental realization of such heterostructure and its investigation under the stationary conditions [L. Schneider et al., https://doi.org/10.1038/s41467-020-18540-3, Nature Communications 11, 4707 (2020)] where the quantum dot energy level can be tuned by gate potential we examine how much time is needed for the Majorana mode to leak into the normal region. We estimate, that for typical hybrid structures this dynamical process would take about 20 nanoseconds. We propose a feasible empirical protocol for its detection by means of the time-resolved Andreev tunneling spectroscopy.
We show anomalous features of Majorana Bound State leakage in the situation where topological Rashba nanowire is dimerized according to the Su-Schrieffer-Heeger (SSH) scenario and an impurity is present at one of the ends of the system. We find that two topological branches: usual, indigenous to Rashba nanowire and dimerized one, existing as a result of SSH dimerization of nanowire, have different asymmetry of spin polarization that can be explained by opposite order of bands taking part in topological transitions. Additionally, introduction of an impurity to the dimerized nanowire influences …
This paper presents a coupled channel model for transport in 2D semiconductor Majorana nanowires coupled to normal leads. When the nanowire hosts a zero mode, conspicuous signatures on the linear conductance are predicted. An effective model in second quantization allowing a fully analytical solution is used to clarify the physics. We also discuss the nonlinear current response ($dI/dV$)
We study quasiparticle spectrum of the correlated quantum dot deposited on superconducting substrate which is side-coupled to the Rashba nanochain, hosting Majorana end modes. Ground state of an isolated quantum dot proximitized to superconducting reservoirs is represented either by the singly occupied site or BCS-type superposition of the empty and doubly occupied configurations. Quantum phase transition between these distinct ground states is spectroscopically manifested by the in-gap Andreev states which cross each other at the Fermi level. This qualitatively affects leakage of the Majorana…
Recent experiments show the possibility of realization of the Majorana quasiparticles at the end of the low dimensional structures. In this type of systems, interplay between spin orbit coupling, superconductivity and magnetic field leads to the emergence of the Majorana bound states in the topologically non-trivial phase. Here, we study the nanowire located partially at the normal and superconducting base, using microscopic model of this structure and the Bogoliubov--de~Gennes technique. We discuss the possibility of the leakage of the Majorana bound state, located at the part above supercond…
Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances $L$, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of $L$. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called `tetron' design. By assessing d…
Unambiguous identification of Majorana physics presents an outstanding problem whose solution could render topological quantum computing feasible. We develop a numerical approach to treat finite-size superconducting chains supporting Majorana fermions, which is based on iterative application of a two-site Bogoliubov transformation. We demonstrate the applicability of the method by studying a resonant level attached to the superconductor subject to external perturbations. In the topological phase, we show that the spectrum of a single resonant level allows to distinguish peak coming from Majora…
We investigate quantum transport through a quantum dot connected to source and drain leads and side-coupled to a topological superconducting nanowire (Kitaev chain) sustaining Majorana end modes. Using a recursive Green's function approach, we determine the local density of states (LDOS) of the system and find that the end Majorana mode of the wire leaks into the dot thus emerging as a unique dot level {\it pinned} to the Fermi energy $\varepsilon_F$ of the leads. Surprisingly, this resonance pinning, resembling in this sense a "Kondo resonance", occurs even when the gate-controlled dot level …
The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound states in a one-dimensional topological superconductor has inspired many proposals aiming at demonstrating this property in transport. In particular, transport through the mode from a lead attached to the left bound state to a lead attached to the right will result in current cross-correlations. For ideal zero modes on a grounded superconductor, the cross-correlations are however completely suppressed in favor of purely local Andreev reflection. In order to obtain a non-vanishing cross-correlation, previous studies h…
The signatures of Majorana zero-energy mode leaking into a spin-charge entangled double quantum dot are investigated theoretically in the strong electron correlation regime. The considered setup consists of two capacitively coupled quantum dots attached to external contacts and side-attached to topological superconducting wire hosting Majorana quasiparticles. We show that the presence of Majorana mode gives rise to unique features in the local density of states in the $SU(4)$ Kondo regime. Moreover, it greatly modifies the gate voltage dependence of the linear conductance, leading to fractiona…
A pair of counter-propagating Majorana edge modes appears in chiral p-wave superconductors and in other superconducting systems belonging to the same universality class. These modes can be described by an Ising conformal field theory. We show how a superconducting flux qubit attached to such a system couples to the two chiral edge modes via the disorder field of the Ising model. Due to this coupling, measuring the back-action of the edge states on the qubit allows to probe the properties of Majorana edge modes.
The transport behavior of a double quantum dot side-attached to a topological superconducting wire hosting Majorana zero-energy modes is studied theoretically in the strong correlation regime. It is shown that Majorana modes can leak to the whole nanostructure, giving rise to a subtle interplay between the two-stage Kondo screening and the half-fermionic nature of Majorana quasiparticles. In particular, the coupling to the topological wire is found to reduce the effective exchange interaction between the two quantum dots in the absence of normal leads. Interestingly, it also results in an enha…
We investigate the spectral and transport properties of a double quantum dot laterally attached to a topological superconducting nanowire, hosting the Majorana zero-energy modes. Specifically, we consider a geometry, in which the outer quantum dot is embedded between the external normal and superconducting leads, forming a circuit. First, we derive analytical expressions for the bound states in the case of an uncorrelated system and discuss their signatures in the tunneling spectroscopy. Then, we explore the case of strongly correlated quantum dots by performing the numerical renormalization g…
In this work, we consider a single-level quantum dot (QD) and a Majorana bound state (MBS) placed at the end of a topological superconducting nanowire (TSW). Both are coupled to the continuum and do not have a direct connection between them. We addressed the behavior of MBS leaking phenomena and its consequences into the QD physics in non-interacting and Coulomb blockade regime. By employing Green's function formalism via the equation of motion procedure, we calculate the physical quantities of interest. Our results show that the leakage of the MBS into the continuum state is achieved and can …
We examine the transport properties of a double quantum dot system coupled to a topological superconducting nanowire hosting Majorana quasiparticles at its ends, with the central quantum dot attached to the left and right leads. We focus on the behavior of the local density of states and the linear conductance, calculated with the aid of the numerical renormalization group method, to describe the influence of the Majorana coupling on the low-temperature transport properties induced by the Kondo correlations. In particular, we show that the presence of Majorana quasiparticles in the system affe…
We study the optical properties of a hybrid device composed by a quantum dot (QD) resonantly coupled to a photonic mode of an optical microcavity and a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. In the regime of strong light-matter coupling, it is demonstrated that the leakage of the Majorana mode into the QD opens new optical transitions between polaritonic states formed due to hybridisation of material excitation with cavity photons, which leads to the reshaping of the Jaynes-Cummings ladder and can lead to the formatio…
We investigate theoretically the thermoelectric transport properties of a T-shaped double quantum dot side-coupled to a topological superconducting nanowire hosting Majorana zero-energy modes. The calculations are performed using the numerical renormalization group method focusing on the transport regime, where the system exhibits the two-stage Kondo effect. It is shown that the leakage of Majorana quasiparticles into the double dot system results in a half-suppression of the second stage of the Kondo effect, which is revealed through fractional values of the charge and heat conductances and g…
We apply the Niemi-Semenoff index theorem to an s-wave superconductor junction system attached with a magnetic insulator on the surface of a three-dimensional topological insulator. We find that the total number of the Majorana zero energy bound states is governed not only by the gapless helical mode but also by the massive modes localized at the junction interface. The result implies that the topological protection for Majorana zero modes in class D heterostructure junctions may be broken down under a particular but realistic condition.
We study by means of the recursive Green's function technique the local density-of-states of (finite and semi-infinite) multi-band spin-orbit coupled semiconducting nanowires in proximity to an s-wave superconductor and attached to normal-metal electrodes. When the nanowire is coupled to a normal electrode, the zero-energy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, ev…
We design and investigate an experimental system capable of entering an electron transport blockade regime in which a spin-triplet localized in the path of current is forbidden from entering a spin-singlet superconductor. To stabilize the triplet a double quantum dot is created electrostatically near a superconducting lead in an InAs nanowire. The dots are filled stochastically with electrons of either spin. The superconducting lead is a molecular beam epitaxy grown Al shell. The shell is etched away over a wire segment to make room for the double dot and the normal metal gold lead. The quantu…
Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inver…
