Applications In Topological Quantum Computation Research Articles

Transport measurement of fractional charges in topological models

The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in electronic systems is quite challenging. We propose an electronic transport measurement scheme in which both the charge amount and the spatial distribution of the TFC can be extracted from the differential conductance through a quantum dot coupled to the topological system being measured. For one-dimensional Su–Schrieffer–Heeger (SSH) model, both the e/2 charge of the TFC and its distribution can be verified. As for the disorder effect, it is shown that the Anderson disorder, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while having little effect on the one-dimensional SSH chain. Nonetheless, our measurement scheme can still work well for specific higher-order topological insulator materials, for instance, the 2e/3 TFC in the breathing kagome model could be confirmed even in the presence of disorder effect. These conclusions about spatial dimension and disorder effect are quite universal, which also applies to other topological systems such as topological classic wave system.

Recent progress on Majorana in semiconductor-superconductor heterostructures—engineering and detection

Majorana zero modes (MZMs) are exotic excitations (in condensed matter systems) that have potential applications in topological quantum computation. Though MZMs have been predicted on many platforms, their existence of them is still under debate. In this paper, we review the recent progress of engineering and detecting MZMs in semiconductor-superconductor heterostructures. We also briefly review the protocols of implementing topological quantum computation by hybrid semiconductor-superconductor nanowires.

Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors

It is well known that Majorana zero modes can be harnessed for applications in topological quantum computation. Transitions away from the ground-state subspace, where computations are performed, are detrimental. The authors study the diabatic error which quantifies these transitions as Majorana zero modes are transported across a superconducting wire. Using the `piano key' approach for transport, the authors find that there exists an optimal number of keys which reduces the diabatic error.

First-Principles Assessment of CdTe as a Tunnel Barrier at the α-Sn/InSb Interface.

Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as β-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between α-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [ npj Computational Materials 2020, 6, 180]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for α-Sn and CdTe. For CdTe, the z-unfolding method [ Advanced Quantum Technologies 2022, 5, 2100033] is used to resolve the contributions of different kz values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/α-Sn, InSb/CdTe, and CdTe/α-Sn, as well as in trilayer interfaces of InSb/CdTe/α-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the α-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor-superconductor devices in future Majorana zero modes experiments.

Evolution of local edge state braiding and spin topological transport characterization of Te-doped monolayer 1T'-MoS2.

We conducted first-principles calculations to investigate the dynamic braiding of local edge states and the spin topological transport mechanism in a strong topological MoS1.75Te0.25 matrix. The presence of type-II Van Hove singularity in the middle of the X-S path indicates a strong cohesive interaction and a paring condensation mechanism within the matrix. The surface state data of MoS1.75Te0.25 clearly demonstrate the characteristic features of strong regular loop braiding in spin transport. The spin Hall conductivity of the matrix was determined from the anisotropic characteristics of the spin Berry curvature. The phase transition of the spin Hall conductivity was evidenced by the positive sign of local spin polarization strength, primarily contributed by the dz2 orbital of Mo atoms, and the negative sign of spin polarization strength, mainly contributed by the p-px orbitals of S atoms. Moreover, the inclusion of Te selectively tuned the spin transport efficiency of the dz2 and px orbitals. Comprehensive braiding and readout of edge states can be achieved using an artificially designed MoS1.75Te0.25 spintronic device. This 2D fractional braiding holds significant potential for applications in topological quantum computation.

Evidence of decoupling of surface and bulk states in Dirac semimetal Cd3As2

Dirac semimetals have attracted a great deal of current interests due to their potential applications in topological quantum computing, low-energy electronic devices, and single photon detection in the microwave frequency range. Herein are results from analyzing the low magnetic (B) field weak-antilocalization behaviors in a Dirac semimetal Cd3As2 thin flake device. At high temperatures, the phase coherence length l ϕ first increases with decreasing temperature (T) and follows a power law dependence of l ϕ ∝ T −0.4. Below ∼3 K, l ϕ tends to saturate to a value of ∼180 nm. Another fitting parameter α, which is associated with independent transport channels, displays a logarithmic temperature dependence for T > 3 K, but also tends to saturate below ∼3 K. The saturation value, ∼1.45, is very close to 1.5, indicating three independent electron transport channels, which we interpret as due to decoupling of both the top and bottom surfaces as well as the bulk. This result, to our knowledge, provides first evidence that the surfaces and bulk states can become decoupled in electronic transport in Dirac semimetal Cd3As2.

Majorana zero modes induced by superconducting phase bias

Majorana zero modes in condensed matter systems have been the subject of much interest in recent years. Their non-Abelian exchange statistics, making them a unique state of matter, and their potential applications in topological quantum computation, earned them attention from both theorists and experimentalists. It is generally understood that in order to form Majorana zero modes in quasi-one-dimensional topological insulators, time-reversal symmetry must be broken. The straightforward mechanisms for doing so—applying magnetic fields or coupling to ferromagnets—turned out to have many unwanted side effects, such as degradation of superconductivity and the formation of sub-gap states, which is part of the reason Majorana zero modes have been eluding direct experimental detection for a long time. Here we review several proposal that rely on controlling the phase of the superconducting order parameter, either as the sole mechanism for time-reversal-symmetry breaking, or as an additional handy knob used to reduce the applied magnetic field. These proposals hold practical promise to improve Majorana formation, and they shed light on the physics underlying the formation of the topological superconducting state.

Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. Here, we study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.

Majorana zero mode in the vortex of artificial topological superconductor

Majorana zero mode, the bound state of Majorana fermion in a condensed matter system, plays a critical role in fault-tolerant topological quantum computation. It can be realized in the vortex of a two-dimensional topological superconductor as a zero-energy excitation. A topological superconductor can be constructed by coupling superconductivity to the topological surface states by the proximity effect. In this review article, we discuss the fabrication of such artificially engineered topological superconductors by molecular beam epitaxy. The topological phase and superconductivity are exhibited in Bi2Se3/NbSe2 and Bi2Te3/NbSe2 heterostructures simultaneously. Several characteristic features of Majorana zero mode have been revealed in the vortex by a low-temperature scanning tunneling microscope and corroborated by theoretical results. The discovery of Majorana zero mode may pave the way for further applications in topological quantum computing.

Topological and holonomic quantum computation based on second-order topological superconductors

Majorana fermions feature non-Abelian exchange statistics and promise fascinating applications in topological quantum computation. Recently, second-order topological superconductors (SOTSs) have been proposed to host Majorana fermions as localized quasiparticles with zero excitation energy, pointing out a new avenue to facilitate topological quantum computation. We provide a minimal model for SOTSs and systematically analyze the features of Majorana zero modes with analytical and numerical methods. We further construct the fundamental fusion principles of zero modes stemming from a single or multiple SOTS islands. Finally, we propose concrete schemes in different setups formed by SOTSs, enabling us to exchange and fuse the zero modes for non-Abelian braiding and holonomic quantum gate operations.

From fractional solitons to Majorana fermions in a paradigmatic model of topological superconductivity

Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two relevant gapped phases, separated by a gapless point, exist. In one of the phases, topological boundary states are absent, while the other one supports Majorana bound states. We show that a customary model violates this paradigm. The phase that should not host Majorana fermions supports a fractional soliton exponentially localized at only one end. By varying the parameters of the model, we describe analytically the transition between the fractional soliton and two Majorana fermions. Moreover, we provide a possible physical implementation of the model. We further characterize the symmetry of the superconducting pairing, showing that the odd-frequency component is intimately related to the spatial profile of the Majorana wavefunctions.

Highly skewed current\u2013phase relation in superconductor\u2013topological insulator\u2013superconductor Josephson junctions

Three-dimensional topological insulators (TIs) in proximity with superconductors are expected to exhibit exotic phenomena, such as topological superconductivity (TSC) and Majorana-bound states (MBS), which may have applications in topological quantum computation. In superconductor–TI–superconductor Josephson junctions, the supercurrent versus the phase difference between the superconductors, referred to as the current–phase relation (CPR), reveals important information including the nature of the superconducting transport. Here, we study the induced superconductivity in gate-tunable Josephson junctions (JJs) made from topological insulator BiSbTeSe2 with superconducting Nb electrodes. We observe highly skewed (non-sinusoidal) CPR in these junctions. The critical current, or the magnitude of the CPR, increases with decreasing temperature down to the lowest accessible temperature (T ~ 20 mK), revealing the existence of low-energy modes in our junctions. The gate dependence shows that close to the Dirac point the CPR becomes less skewed, indicating the transport is more diffusive, most likely due to the presence of electron/hole puddles and charge inhomogeneity. Our experiments provide strong evidence that superconductivity is induced in the highly ballistic topological surface states (TSS) in our gate-tunable TI-based JJs. Furthermore, the measured CPR is in good agreement with the prediction of a model which calculates the phase-dependent eigenstate energies in our system, considering the finite width of the electrodes, as well as the TSS wave functions extending over the entire circumference of the TI.

Evidence of anisotropic Majorana bound states in 2M-WS2

Searching for Majorana bound states has become an important topic because of its potential applications in topological quantum computing. 2M-phase WS2, a newly synthesized superconductor, not only presents the highest superconducting transition temperature (Tc = 8.8 K) among the intrinsic transition metal dichalcogenides but also is predicted to be a promising candidate as a topological superconductor. Using scanning tunnelling microscopy, we observe a U-shaped superconducting gap in 2M-WS2. Probable Majorana bound states are observed in magnetic vortices, which manifest as a non-split zero-energy state coexisting with the ordinary Caroli–de Gennes–Matricon bound states. Such non-split bound states in 2M-WS2 show highly spatial anisotropy, originating from the anisotropy of the superconducting order parameter and Fermi velocity. Due to its simple layered structure and substitution-free lattice, 2M-WS2 can be a building block to construct novel heterostructures and provides an ideal platform for the study of Majorana bound states. Potential Majorana bound states are seen in the vortex cores of a transition metal dichalcogenide. The properties of the superconductor mean that the bound states are highly anisotropic, and can appear at higher temperatures than other materials.

Rabi splitting and optical Kerr nonlinearity of quantum dot mediated by Majorana fermions

Majorana fermions (MFs), due to their significance in fundamental physics and potential applications in topological quantum computation based on solid-state devices, have drawn widespread attention. Here, we design a hybrid semiconductor/superconductor ring (S/SR) device and put forward an optical method for detecting a pair of MFs in the S/SR device with a quantum dot (QD) with the popular optical pump-probe scheme, which is very different from the present electrical method only considering one nearby MF coupled to the QD. The symmetric and unsymmetric Rabi splitting and optical Kerr nonlinear effect of QD mediated by MFs are investigated under uncoupled and coupled majorana modes, respectively. The coherent optical spectra indicate that a pair of MFs coupled to the QD induced remarkable splitting under different parameters regime and the physical origin of these phenomena are elaborated detailedly. Due to QD-MFs coupling, the probe absorption spectra present the phenomenon of Majorana modes induced transparency (MMIT) which will induce remarkable phenomena of slow light. The coherent optical spectra afford a potential supplement for probing MFs and support Majorana fermions-based topological quantum computation.

Second Quantization and Majorana Modes

This article reviews the basic concepts of second quantization as used in condensed matter physics. The Kitaev chain was the first system shown to exhibitMajorana zeromodes, which exhibit novel statistics and thus find enormous applications in topological quantum computation. Simple calculations of the band structure and density of states showing the presence of Majorana zero modes are presented.

Proximity-Induced Superconductivity with Subgap Anomaly in Type II Weyl Semi-Metal WTe2.

Due to the nontrivial topological band structure in type II Weyl semi-metal tungsten ditelluride (WTe2), unconventional properties may emerge in its superconducting phase. While realizing intrinsic superconductivity has been challenging in the type II Weyl semi-metal WTe2, the proximity effect may open an avenue for the realization of superconductivity. Here, we report the observation of proximity-induced superconductivity with a long coherence length along the c axis in WTe2 thin flakes based on a WTe2/NbSe2 van der Waals heterostructure. Interestingly, we also observe anomalous oscillations of the differential resistance during the transition from the superconducting to the normal state. Theoretical calculations show excellent agreement with experimental results, revealing that such a subgap anomaly is the intrinsic property of WTe2 in superconducting state induced by the proximity effect. Our findings enrich the understanding of the superconducting phase of type II Weyl semi-metals and pave the way for their future applications in topological quantum computing.

Dirac state in a centrosymmetric superconductor α−PdBi2

Topological superconductor (TSC) hosting Majorana fermions has been established as a milestone that may shift our scientific trajectory from research to applications in topological quantum computing. Recently, superconducting Pd-Bi binaries have attracted great attention as a possible medium for the TSC phase as a result of their large spin-orbit coupling strength. Here, we report a systematic high-resolution angle-resolved photoemission spectroscopy (ARPES) study on the normal state electronic structure of superconducting $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{PdBi}}_{2}\phantom{\rule{4pt}{0ex}}({T}_{c}=1.7$ K). Our results show the presence of Dirac states at higher-binding energy with the location of the Dirac point at 1.26 eV below the chemical potential at the zone center. Furthermore, the ARPES data indicate multiple band crossings at the chemical potential, consistent with the metallic behavior of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{PdBi}}_{2}$. Our detailed experimental studies are complemented by first-principles calculations, which reveal the presence of surface Rashba states residing in the vicinity of the chemical potential. The obtained results provide an opportunity to investigate the relationship between superconductivity, topology, and the Majorana fermion, as well as explore pathways to possible future platforms for topological quantum computing.

Polygon sign rules of Majorana fermions in two-dimensional topological superconductors

Recently, Majorana fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation. They are proposed to exist in various two-dimensional (2D) topological systems, such as [Formula: see text] topological superconductor (SC) and nanowire–superconducting hybridization system. In this paper, we point out that Majorana fermions in different topological systems obey different types of polygon sign rules. A numerical approach is described to identify the type of polygon sign rule of the Majorana fermions. Applying the approach to study two 2D topological systems, we find that vortex-induced Majorana fermions obey topological polygon sign rule and line-defect-induced Majorana fermions obey normal polygon sign rule.

Fractionalized flux, Majorana fermions and non-Abelian anyons in topological superfluid on optical lattices

Recently, topological excitations obeying non-Abelian statistics attracted intensive attention because of their exotic statistics and possible applications in topological quantum computation. In this paper, based on a topological s-wave superfluid on a Peierls lattice, we find fractionalized flux and non-Abelian anyons, and then give a realistic proposal to realize the universal topological quantum computation, and especially show how to perform the single-qubit gate–phase-shift gate. Finally, we discuss the experimental realization on optical lattices.

Andreev reflection in a T-shaped double quantum-dot with coupled Majorana bound states

Owing to their potential applications in topological quantum computation and because of their fundamental interest, Majorana fermions are currently attracting increasing attention. Numerous theoretical and experimental studies exactly show that the quantum dot (QD) structure is a good candidate for the detection of Majorana bound state (MBSs). QD system has many unique transport properties and interesting quantum phenomena, such as quantum interference effect, Fano effect, etc. In addition, compared with a single QD, a coupled QD structure has many adjustable parameters, and thus has more important theoretical and practical value, which provides an excellent platform to detect MBSs. In addition, QD coupled with normal metallic conductor and with superconducting electrode structure exhibits interesting transport properties. One of these properties is the so-called Andreev reflection (AR). Especially, in the subgap regime, the current almost entirely originates from the anomalous Andreev channel; such spectroscopy can thus directly probe any in-gap state. In the present paper, we consider a T-shaped double QD structure with side-coupled to MBSs and investigate the transport properties through the system by adding a normal and a superconducting lead. We calculate the AR conductance through the system in the subgap transport. Here we focus on the effects of MBSs on AR through the system. We find that the AR conductance presents a resonant peak around zero Fermi energy when only one QD (QD1) connects to metal and superconducting leads. As a consequence of quantum interference, when using another QD2 side-attached to QD1, a pair of new Fano-type resonant peaks appear and is distributed aside the zero point and the Fano antiresonant point is at the energy level of the QD2. If an MBS is introduced to couple to QD2, the AR conductance shows several new features. First, a pair of new Fano-type resonance curves appears and the original ones also persist except for the position shifting. In addition, the AR conductance value at the zero Fermi energy point is exactly equal to 1/2G0(G0=2e2/h) in the presence of QD-MBS coupling and zero inter-MBS coupling, which is not dependent on the inert-dot coupling nor the energy levels of QD nor the strength of the QD-MBS coupling. This feature is different from which the T-shaped DQD structure side-coupled to a traditional fermions, showing the robust properties of the Majorana fermions. We also show that in the Andreev reflection conductance curves appear resonance zone changes into antiresonance near zero Fermi energy by adjusting the coupling strength between the double quantum dots in the system without MBSs, while the antiresonance disappears and new resonance peaks appear if an MBS is introduced to couple to QD2. We hope that these results will be helpful for understanding the quantum interference in MBS-assisted AR and may find significant applications, especially in quantum computation.