Majorana Bound States Research Articles

Perspective on Majorana bound-states in hybrid superconductor-semiconductor nanowires

A personal perspective is given on a decade of research on Majorana bound states (MBS) in hybrid devices of semiconducting nanowires covered with a superconductor. Predicted experimental signatures like zero-bias anomalies turned out to be false positive evidence for topological MBS. Zero-bias conductance peaks have found alternative explanations in terms of material disorder and smooth boundary potentials. A recount is given on various predictions, observations and re-interpretations, as well as the lessons learned in retrospect and an outlook on the future.

Quantum dot based Kitaev chains: Majorana quality measures and scaling with increasing chain length

Realizing Majorana bound states (MBSs) in short, well-controllable chains of coupled quantum dots sidesteps the problem of disorder but requires finetuning and does not give the true topological protection inherent to long chains. Here, we introduce a quality measure that is also applicable in the presence of strong electron-electron interactions and that quantifies the closeness to topological protection of finetuned MBSs in short quantum dot chains. We call this measure local distinguishability (LD) because it puts a bound to the degree an arbitrary local measurement can distinguish between two states. We study the LD for quantum dot chains of different length. The three-dot chain is studied in detail, and we find that it may not always be an improvement over the two-dot case, a fact that can be understood within an effective model derived from perturbation theory. For longer chains, the LD vanishes exponentially, signaling a transition to a topological phase with two ground states that cannot be distinguished by any local measurement. Published by the American Physical Society 2024

Topological superconductivity in Fibonacci quasicrystals

We investigate the properties of a Fibonacci quasicrystal (QC) arrangement of a one-dimensional topological superconductor, such as a magnetic atom chain deposited on a superconducting surface. We uncover a general mutually exclusive competition between the QC properties and the topological superconducting phase with Majorana bound states (MBS): there are no MBS inside the QC gaps and the MBS never behave as QC subgap states and, likewise, no critical or winding QC subgap states exist inside the topological superconducting gaps. Surprisingly, despite this competition, we find that the QC is still highly beneficial for realizing topological superconductivity with MBS. It both leads to additional large nontrivial regions with MBS in parameter space, that are topologically trivial in crystalline systems, and increases the topological gap protecting the MBS. We also find that shorter approximants of the Fibonacci QC display the largest benefits. As a consequence, our results promote QCs, and especially their short approximants, as an appealing platform for improved experimental possibilities to realize MBS as well as generally highlight the fundamental interplay between different topologies. Published by the American Physical Society 2024

Progress in Superconductor-Semiconductor Topological Josephson Junctions

Majorana bound states (MBSs) are quasiparticles that are their own antiparticles. They are predicted to emerge as zero-energy modes localized at the boundary of a topological superconductor. No intrinsic topological superconductor is known to date. However, by interfacing conventional superconductors and semiconductors with strong spin-orbit coupling, it is possible to create a system hosting topological states. Hence, epitaxial superconductors and semiconductors have emerged as an attractive material system with atomically sharp interfaces and broad flexibility in device fabrications incorporating Josephson junctions. We discuss the basics of topological superconductivity and provide insight into how to go beyond current state-of-the-art experiments. We argue that the ultimate success in realizing MBS physics requires the observation of non-Abelian braiding and fusion experiments. Published by the American Physical Society 2024

Josephson Diode Effect in Parallel-Coupled Double-Quantum Dots Connected to Unalike Majorana Nanowires.

We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin-orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.

Majorana-Free Bound State in the Continuum in the Double-Channel Fano–Anderson Structure

Abstract We investigate the electron transport through a double-channel Fano–Anderson structure, by considering the side-coupling of Majorana bound states (MBSs). It is found that the bound state in the continuum (BIC) phenomenon can be induced when interchannel dot–lead couplings are identical to the intrachannel dot–lead couplings, whose signature is manifested as a halved quantum transmission ability. If the balance between the dot–lead couplings is broken, the BIC phenomenon will also be destroyed, leading to further suppression of the transmission ability. Next, when MBSs are introduced to this system, the BIC phenomenon can be modified efficiently. For the case of two MBSs side-coupled to the quantum dots in a symmetric way, level degeneracy causes a new BIC phenomenon. As only one MBS is incorporated, it suppresses the electron transmission by inducing new transmission dips. When the interdot Coulomb interaction is considered, the BIC phenomena are still robust despite the complicated changes of the transmission ability spectra. One can then understand the realization of BICs in coupled quantum dots and their variation due to the presence of side-coupled MBSs.

Quantum Transport through a Quantum Dot Coupled to Majorana Nanowire and Two Ferromagnets with Noncollinear Magnetizations.

We study the electron tunneling (ET) and local Andreev reflection (AR) processes in a quantum dot (QD) coupled to the left and right ferromagnetic leads with noncollinear ferromagnetisms. In particular, we consider that the QD is also side-coupled to a nanowire hosting Majorana bound states (MBSs) at its ends. Our results show that when one mode of the MBSs is coupled simultaneously to both spin-up and spin-down electrons on the QD, the height of the central peak is different from that if the MBS is coupled to only one spin component electrons. The ET and AR conductances, which are mediated by the dot-MBS hybridization, strongly depend on the angle between the left and right magnetic moments in the leads. Interaction between the QD and the MBSs will result in sign change of the angle-dependent tunnel magnetoresistance. This is very different from the case when the QD is coupled to regular fermonic mode, and can be used for detecting the existence of MBSs, a current challenge in condensed matter physics under extensive investigations.

Fraunhofer pattern in the presence of Majorana zero modes

We propose a new platform to detect signatures of the presence of Majorana bound states (MBSs) in the Fraunhofer pattern of Josephson junctions featuring quantum spin Hall edge states on the normal part and Majorana bound states at the NS interfaces. We use a tight-binding model to demonstrate a drastic change in the periodicity of the Fraunhofer pattern when comparing trivial and nontrivial regimes. We explain these results in terms of the presence of additional parallel-spin electron-hole reflections, which due to the spin-momentum locking, occur as cross Andreev reflections, accumulating a different magnetic flux and yielding a change in the Fraunhofer periodicity. We show that this detection scheme exhibits some advantages compared to previous ones as it is robust against disorder and finite temperature and works in equilibrium. Furthermore, we introduce a scattering model that captures the main results of the microscopic calculations with MBSs and extend our discussion to the main differences found using accidental zero-energy Andreev bound states. Published by the American Physical Society 2024

A two-site Kitaev chain in a two-dimensional electron gas.

Artificial Kitaev chains can be used to engineer Majorana bound states (MBSs) in superconductor-semiconductor hybrids1-4. In this work, we realize a two-site Kitaev chain in a two-dimensional electron gas by coupling two quantum dots through a region proximitized by a superconductor. We demonstrate systematic control over inter-dot couplings through in-plane rotations of the magnetic field and via electrostatic gating of the proximitized region. This allows us to tune the system to sweet spots in parameter space, where robust correlated zero-bias conductance peaks are observed in tunnelling spectroscopy. To study the extent of hybridization between localized MBSs, we probe the evolution of the energy spectrum with magnetic field and estimate the Majorana polarization, an important metric for Majorana-based qubits5,6. The implementation of a Kitaev chain on a scalable and flexible two-dimensional platform provides a realistic path towards more advanced experiments that require manipulation and readout of multiple MBSs.

Nonlinear Seebeck and Peltier effects in a Majorana nanowire coupled to leads

Abstract We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states (MBSs) at its two ends, a system named as Majorana nanowire (MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient (thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.

Probing Majorana bound states via thermoelectric transport

We propose a set of thermoelectric experiments based on Aharonov-Bohm interferometry to probe Majorana bound states (MBS), which are generated in 2D topological insulators (TI) in the presence of superconducting and ferromagnetic correlations via the proximity effect. The existence and nature (coupled or uncoupled) of these MBS can be determined by studying the charge and heat transport, specifically, the behavior of various thermoelectric coefficients like the Seebeck coefficient, Peltier coefficient, thermal conductance, and violations of Wiedemann-Franz law as a function of the Fermi energy and Aharonov-Bohm flux piercing the TI ring with the embedded MBS.

Transport properties of a Majorana trijunction

By considering three topological-superconductor nanowires that host Majorana bound states (MBSs) to be coupled with one another in the T-shaped manner, we construct the Majorana trijunction and investigate the transport characteristics driven by the MBSs. It is shown that the MBS-lead coupling manners and the Majorana-mode natures in the topological-superconductor nanowires play different roles in governing the transport properties in this trijunction. The former determines the relationships between the zero-bias Fano factors and differential conductances, and its change induces two different expressions of such relationships. Instead, the latter makes its dominant contribution to the differential conductance lineshapes and the zero-bias conductance values. We believe that these results can be helpful in further understanding the transport properties of MBS-based junctions.

Resonance and Anti-resonance in transport through quantum dots-Majorana bound states hybrid structure

We calculate the linear conductance through a double quantum-dot system with a normal metal lead, which is enclosed in a closed shape where quantum dot-1 is connected to Majorana bound states (MBSs). The Quantum dots configuration from parallel to series allows for a transition in the shape of resonant to non-resonant in the spectrum. This is caused by quantum interference between the energy levels. This process results in the formation of bonding and antibonding states that are involved in electron transport. An asymmetric quantum dots configuration can produce a Fano resonance, and its position can be adjusted by altering the energy levels.

Decoupling of Majorana bound states in T-shaped double-quantum-dot structure with ferromagnetic leads

The significant potential applications of Majorana bound state (MBS) in topological quantum computing manifest the importance and necessity of relevant in-depth research. To understand the physical properties of MBS, the most practical approach is to integrate it to a mesoscopic circuit and then investigate its quantum transport behaviors. In this work, we investigate the transport properties in the systems with MBS, and provide theoretical support for its further understanding and detection, by utilizing the nonequilibrium Green’s function method and scattering matrix theory. Specifically, we investigate theoretically the transport properties in a T-shaped double-quantum dot structure, by considering MBS to be coupled to the dot in the main channel, which shows that in the linear transmission region, when the level of side-coupled dot is tuned to the Fermi energy level, the contribution of MBS to the conductance is eliminated under weak and strong Coulomb interaction. The side-coupled dot is far away from the Fermi energy level, leading to different results. When Majorana zero mode is added, the linear conductance is independent of the level of the side-coupled quantum dot, and the conductance plateau appears. However, with coupling between the MBSs, the linear conductance is the same as that without coupling between the MBSs. The decoupling phenomenon of the MBS remains strong. Therefore, the signature of the MBS can be eliminated by adjusting the level of the side-coupled quantum dot or the inter-MBS coupling. When ferromagnetic leads are introduced, the appearance or disappearance of the conductance plateau is clearly dependent on the difference between the magnetic field direction and the lead polarization direction in the system, whereas the decoupling behavior of the MBS is still existent. This work contributes to further explaining the decoupling phenomenon of MBSs in a T-shaped double-quantum-dot system, and presents a theoretical approach to more in-depth understanding and detection of the MBS.

Tunable Josephson Current through a Semiconductor Quantum Dot Hybridized to Majorana Trijunction

We investigate theoretically the Josephson current through one semiconductor quantum dot (QD) coupled to triple nanowires (junctions) with Majorana bound states (MBSs) prepared at their ends. We find that not only the strength but also the period of the Josephson current flowing between the left and right Josephson junctions via the dot can be fully controlled in terms of the third junction side-coupled to the QD. When the phase factor is zero in the third junction, which acts as a current regulator, the Josephson current is a 2π-period function of the difference in phases of the left and right junctions. Now, the magnitude of the current is suppressed by hybridization between the QD and the regulator junction. The period of the current becomes 4π under the condition of nonzero phase factor in the regular junction, and thus either the magnitude or the sign (flow direction) of the current can be controlled in this trijunction device. This is difficult to realize in the usual tow-terminal structure. It is also found that the direct overlap between the MBSs in the regulator junction generally enhances the current’s amplitude, but those in the left and right Majorana junctions suppress the current. The above results are explained with the help of the device’s energy diagram and the current carrying density of states (CCDOS) and might be applied for adjusting the current density in the superconducting coated conductors technologies.

Thermophase Seebeck Coefficient in Hybridized Superconductor-Quantum-Dot-Superconductor Josephson Junction Side-Coupled to Majorana Nanowire.

The dc Josephson current is generated from phase difference between two superconductors separated by a mesoscopic thin film (Josephson junction) without external bias voltage. In the presence of a temperature gradient across the superconductors, a thermal phase is induced under the condition of open circuit. This is very similar to the Seebeck effect in the usual thermoelectric effect, and the thermal phase is thus named as thermophase Seebeck coefficient (TPSC). Here we find obvious enhancement and sign change of the TPSC unique to the Josephson junction composing of two superconductors connected to a semiconductor quantum dot (QD), which is additionally side-coupled to a nanowire hosting Majorana bound states (MBSs), the system denoted by S-MQD-S. These result arise from the newly developed states near the Fermi level of the superconductors due to the QD-MBS hybridization when the dot level is within the superconducting gap. The sign change of the TPSC provides a strong evidence of the existence of MBSs, and is absent if the QD is coupled to regular fermion, such as another QD (system denoted by S-DQD-S). We show that the magnitude and sign of the TPSC are sensitive to the physical quantities including interaction strength between the QD and MBSs, direct overlap between the MBSs, system equilibrium temperature, as well as hopping amplitude between the QD and the superconductors. The obtained results are explained with the help of the current-carrying density of the states (CCDOS), and may be useful in interdisciplinary research areas of Josephson and Majorana physics.

Hallmarks of orbital-flavored Majorana states in Josephson junctions based on oxide nanochannels

We investigate the topological properties of a Josephson junction obtained by constraining a two-dimensional electron gas at oxide interface to form a quasi-1D conductor. We reveal an anomalous critical current behaviour with a magnetic field applied perpendicular to the Rashba spin-orbit one. We relate the observed critical current enhancement at small magnetic fields with a non-trivial topology, accompanied by Majorana bound states (MBSs) pinned at the edges of the superconducting leads. Signatures of MBSs also include a sawtooth profile in the current-phase relation. Our findings allow to recognize fingerprints of topological superconductivity in non-centrosymmetric materials and confined systems with Rashba spin-orbit interaction, and to explain recent experimental observations for which a microscopic description is still lacking.

Enhancement of the Josephson Current in a Quantum Dot Connected to Majorana Nanowires.

We investigate the behavior of the Josephson current in a system composed of a quantum dot (QD) sandwiched between two nanowires by using the nonequilibrium Green's function technique. We consider that the nanowires are in proximity to s-wave superconducror substrates, and Majorana bound states (MBSs) are induced at their ends. It is also assumed that the two nanowires are not aligned in the same orientation, but form a bent angle with respect to each other. It is found that when only one spin state on the QD is coupled to the left nanowire, the Josephson current is the typical sinusoidal function of the phase difference between the two nanowires. If both spin states hybridize to the MBSs with equal coupling strengths, the Josephson current then is not a sinusoidal function of the phase difference. In particular, when the bent angle between the two nanowires is π/2 and the two modes of the MBSs in each nanowire are decoupled from each other, the Josephson current is enhanced by about twenty times in magnitude as compared to the former case. Moreover, the simultaneously enhanced currents of the two spin directions are of the same magnitude but flow in opposite directions and they induce a large pure spin current. Our results also show that this abnormally enhanced Josephson current will be suppressed by a vertical magnetic field applied to the QD.

Monolayer Superconductivity and Tunable Topological Electronic Structure at the Fe(Te,Se)/Bi2 Te3 Interface.

The interface between 2D topological Dirac states and an s-wave superconductor is expected to support Majorana-bound states (MBS) that can be used for quantum computing applications. Realizing these novel states of matter and their applications requires control over superconductivity and spin-orbit coupling to achieve spin-momentum-locked topological interface states (TIS) which are simultaneously superconducting. While signatures of MBS have been observed in the magnetic vortex cores of bulk FeTe0.55 Se0.45 , inhomogeneity and disorder from doping make these signatures unclear and inconsistent between vortices. Here superconductivity is reported in monolayer (ML) FeTe1-y Sey (Fe(Te,Se)) grown on Bi2 Te3 by molecular beam epitaxy (MBE). Spin and angle-resolved photoemission spectroscopy (SARPES) directly resolve the interfacial spin and electronic structure of Fe(Te,Se)/Bi2 Te3 heterostructures. For y= 0.25, the Fe(Te,Se) electronic structure is found to overlap with the Bi2 Te3 TIS and the desired spin-momentum locking is not observed. In contrast, for y= 0.1, reduced inhomogeneity measured by scanning tunneling microscopy (STM) and a smaller Fe(Te,Se) Fermi surface with clear spin-momentum locking in the topological states are found. Hence, it is demonstrated that the Fe(Te,Se)/Bi2 Te3 system is a highly tunable platform for realizing MBS where reduced doping can improve characteristics important for Majorana interrogation and potential applications.

Parity flipping mediated by a quantum dot in Majorana Josephson junctions

The detection of the Majorana bound states (MBSs) is a central issue in the current investigation of the topological superconductors, and the topological Josephson junction is an important system for resolving this issue. In this work, we introduce an external quantum dot (QD) to Majorana Josephson junctions (MJJs), and study the parity flipping of the junction induced by the coupling between the QD and the MBSs. We demonstrate Landau-Zener (LZ) transitions between opposite Majorana parity states when the energy level of the QD is modulated. The resulted parity flipping processes exhibit voltage signals across the junction. In the presence of a periodic modulation on the QD level, we show Landau-Zener-Stückelberg (LZS) interference on the parity states. We demonstrate distinctive interference patterns at distinct driving frequencies. These results can be used as signals for detecting the existence of the MBSs.