We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.

We report an implementation of the momentum space quantum Monte Carlo (QMC) method on the interaction model for the twisted bilayer graphene (TBG). The long-range Coulomb repulsion is treated exactly with the flat bands, spin and valley degrees of freedom of electrons taking into account. We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered. By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation, we benchmark the QMC data with the exact band gap obtained at the chiral limit, to reveal the insulating ground states at the charge neutrality point (CNP). Then, with the exact Green's functions from QMC, we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP. Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.

The reversal of perpendicular magnetization (PM) by electric control is crucial for high-density integration of low-power magnetic random-access memory. Although the spin-transfer torque and spin-orbit torque technologies have been used to switch the magnetization of a free layer with perpendicular magnetic anisotropy, the former has limited endurance because of the high current density directly through the junction, while the latter requires an external magnetic field or unconventional configuration to break the symmetry. Here we propose and realize the orbit-transfer torque (OTT), that is, exerting torque on the magnetization using the orbital magnetic moments, and thus demonstrate a new strategy for current-driven PM reversal without external magnetic field. The perpendicular polarization of orbital magnetic moments is generated by a direct current in a few-layer WTe$_{2}$ due to the existence of nonzero Berry curvature dipole, and the polarization direction can be switched by changing the current polarity. Guided by this principle, we construct the WTe$_{2}$/Fe$_{3}$GeTe$_{2}$ heterostructures to achieve the OTT driven field-free deterministic switching of PM.

Hermitian systems possess unitary scattering. However, the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary. Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity. The energy conservation is violated in the scattering process and recovers after scattering. The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian. These findings provide fundamental insights on the unitary scattering, pseudo-Hermiticity, and energy conservation, and are promising for light propagation, mesoscopic electron transport, and quantum interference in non-Hermitian systems.

We demonstrate the in situ growth of ultra-thin InAs nanowires with an epitaxial Al film by molecular-beam epitaxy. Our InAs nanowire diameter ($\sim $30 nm) is much thinner than before ($\sim $100 nm). The ultra-thin InAs nanowires are pure phase crystals for various different growth directions. Transmission electron microscopy confirms an atomically abrupt and uniform interface between the Al shell and the InAs wire. Quantum transport study on these devices resolves a hard induced superconducting gap and 2$e$-periodic Coulomb blockade at zero magnetic field, a necessary step for future Majorana experiments. By reducing wire diameter, our work presents a promising route for reaching fewer sub-band regime in Majorana nanowire devices.

Sulfur and lanthanum hydrides under compression display superconducting states with high observed critical temperatures. It has been recently demonstrated that carbonaceous sulfur hydride displays room temperature superconductivity. However, this phenomenon has been observed only at very high pressure. Here, we theoretically search for superconductors with very high critical temperatures, but at much lower pressures. We describe two of such sodalite-type clathrate hydrides, YbH$_{6}$ and LuH$_{6}$. These hydrides are metastable and are predicted to superconduct with $T_{\rm c} \sim 145$ K at 70 GPa and $T_{\rm c} \sim 273$ K at 100 GPa, respectively. This striking result is a consequence of the strong interrelationship between the $f$ states present at the Fermi level, structural stability, and the final $T_{\rm c}$ value. For example, TmH$_{6}$, with unfilled 4$f$ orbitals, is stable at 50 GPa, but has a relatively low value of $T_{\rm c}$ of 25 K. The YbH$_{6}$ and LuH$_{6}$ compounds, with their filled $f$-shells, exhibit prominent phonon “softening”, which leads to a strong electron-phonon coupling, and as a result, an increase in $T_{\rm c}$.

Enhancing the dopability of semiconductors via strain engineering is critical to improving their functionalities, which is, however, largely hindered by the lack of basic rules. In this study, for the first time, we develop a universal theory to understand the total energy changes of point defects (or dopants) with different charge states under strains, which can exhibit either parabolic or superlinear behaviors, determined by the size of defect-induced local volume change ($\Delta V$). In general, $\Delta V$ increases (decreases) when an electron is added (removed) to (from) the defect site. Consequently, in terms of this universal theory, three basic rules can be obtained to further understand or predict the diverse strain-dependent doping behaviors, i.e., defect formation energies, charge-state transition levels, and Fermi pinning levels, in semiconductors. These three basic rules could be generally applied to improve the doping performance or overcome the doping bottlenecks in various semiconductors.

The coupling between electric ordering and magnetic ordering in two-dimensional (2D) materials is important for both fundamental research of 2D multiferroics and future development of magnetism-based information storage and operation. Here, we introduce a scheme for realizing a magnetic phase transition through the transition of electric ordering. We take CuMoP$_{2}$S$_{6}$ monolayer as an example, which is a member of the large 2D transition-metal chalcogen-phosphates family. Based on first-principles calculations, we find that it is a multiferroic with unprecedented characters, namely, it exhibits two different phases: an antiferroelectric-antiferromagnetic phase and a ferroelectric-ferromagnetic phase, in which the electric and magnetic orderings are strongly coupled. Importantly, the electric polarization is out-of-plane, so the magnetism can be readily switched by using the gate electric field. Our finding reveals a series of 2D multiferroics with special magnetoelectric coupling, which hold great promise for experimental realization and practical applications.

Human experts cannot efficiently access physical information of a quantum many-body states by simply “reading” its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements. We demonstrate that convolutional neural network (CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states (or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.

We predict that the square lattice layer formed by [Co$_2$N$_2$]$^{2-}$ diamond-like units can host high-temperature superconductivity. The layer appears in the stable ternary cobalt nitride, BaCo$_2$N$_2$. The electronic physics of the material stems from Co$_2$N$_2$ layers where the dimerized Co pairs form a square lattice. The low energy physics near Fermi energy can be described by an effective two-orbital model. Without considering interlayer couplings, the two orbitals are effectively decoupled. This electronic structure satisfies the “gene” character proposed for unconventional high-temperature superconductors. We predict that the leading superconducting pairing instability is driven from an extended $s$-wave ($s^\pm$) to a $d$-wave by hole doping, e.g., in Ba$_{1-x}$K$_x$Co$_2$N$_2$. This study provides a new platform to establish the superconducting mechanism of unconventional high-temperature superconductivity.

Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen (EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering (EPR steering) [C. Y. Chiu et al., npj Quantum Inf. 2, 16020 (2016)] based on a mutual information criterion for EPR steering.

A magnetic tunnel junction (MTJ) is the core component in memory technologies, such as the magnetic random-access memory, magnetic sensors and programmable logic devices. In particular, MTJs based on two-dimensional van der Waals (vdW) heterostructures offer unprecedented opportunities for low power consumption and miniaturization of spintronic devices. However, their operation at room temperature remains a challenge. Here, we report a large tunnel magnetoresistance (TMR) of up to 85% at room temperature ($T = 300$ K) in vdW MTJs based on a thin ($ < 10$ nm) semiconductor spacer WSe$_{2}$ layer embedded between two Fe$_{3}$GaTe$_{2}$ electrodes with intrinsic above-room-temperature ferromagnetism. The TMR in the MTJ increases with decreasing temperature up to 164% at $T = 10$ K. The demonstration of TMR in ultra-thin MTJs at room temperature opens a realistic and promising route for next-generation spintronic applications beyond the current state of the art.

Van der Waals magnet VI$_{3}$ demonstrates intriguing magnetic properties that render it great for use in various applications. However, its microscopic magnetic structure has not been determined yet. Here, we report neutron diffraction and susceptibility measurements in VI$_{3}$ that revealed a ferromagnetic order with the moment direction tilted from the $c$-axis by $\sim $$36^{\circ}$ at 4 K. A spin reorientation accompanied by a structure distortion within the honeycomb plane is observed, before the magnetic order completely disappears at $T_{\rm C} = 50$ K. The refined magnetic moment of $\sim $$1.3 \mu_{\scriptscriptstyle {\rm B}}$ at 4 K is much lower than the fully ordered spin moment of $2\mu_{\scriptscriptstyle {\rm B}}$/V$^{3+}$, suggesting the presence of a considerable orbital moment antiparallel to the spin moment and strong spin–orbit coupling in VI$_{3}$. This results in strong magnetoelastic interactions that make the magnetic properties of VI$_{3}$ easily tunable via strain and pressure.

High-energy-density rechargeable lithium batteries are being pursued by researchers because of their revolutionary potential nature. Current advanced practical lithium-ion batteries have an energy density of around 300 W$\cdot$h$\cdot$kg$^{-1}$. Continuing to increase the energy density of batteries to a higher level could lead to a major explosion development in some fields, such as electric aviation. Here, we have manufactured practical pouch-type rechargeable lithium batteries with both a gravimetric energy density of 711.3 W$\cdot$h$\cdot$kg$^{-1}$ and a volumetric energy density of 1653.65 W$\cdot$h$\cdot$L$^{-1}$. This is achieved through the use of high-performance battery materials including high-capacity lithium-rich manganese-based cathode and thin lithium metal anode with high specific energy, combined with extremely advanced process technologies such as high-loading electrode preparation and lean electrolyte injection. In this battery material system, the structural stability of cathode material in a widened charge/discharge voltage range and the deposition/dissolution behavior of interfacial modified thin lithium electrode are studied.

We periodically modulate the lattice trapping potential of a $^{87}$Sr optical clock to Floquet engineer the clock transition. In the context of atomic gases in lattices, Floquet engineering has been used to shape the dispersion and topology of Bloch quasi-energy bands. Differently from these previous works manipulating the external (spatial) quasi-energies, we target the internal atomic degrees of freedom. We shape Floquet spin quasi-energies and measure their resonance profiles with Rabi spectroscopy. We provide the spectroscopic sensitivity of each band by measuring the Fisher information and show that this is not depleted by the Floquet dynamical modulation. The demonstration that the internal degrees of freedom can be selectively engineered by manipulating the external degrees of freedom inaugurates a novel device with potential applications in metrology, sensing and quantum simulations.

Recently, intrinsic antiferromagnetic topological insulator MnBi$_{2}$Te$_{4}$ has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi$_{2}$Te$_{4}$. However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 meV, which vanishes as the sample becomes paramagnetic with increasing temperature. The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy. Combining these results, the magnetism-induced gap in topological surface states of MnBi$_{2}$Te$_{4}$ is revealed.

We report $^{121/123}$Sb nuclear quadrupole resonance (NQR) and $^{51}$V nuclear magnetic resonance (NMR) measurements on kagome metal CsV$_3$Sb$_5$ with $T_{\rm c}=2.5$ K. Both $^{51}$V NMR spectra and $^{121/123}$Sb NQR spectra split after a charge density wave (CDW) transition, which demonstrates a commensurate CDW state. The coexistence of the high temperature phase and the CDW phase between $91$ K and $94$ K manifests that it is a first-order phase transition. At low temperature, electric-field-gradient fluctuations diminish and magnetic fluctuations become dominant. Superconductivity emerges in the charge order state. Knight shift decreases and $1/T_{1}T$ shows a Hebel–Slichter coherence peak just below $T_{\rm c}$, indicating that CsV$_3$Sb$_5$ is an s-wave superconductor.

In the last decade, perovskite solar cells (PSCs) have greatly drawn researchers' attention, with the power conversion efficiency surging from 3.8% to 25.5%. PSCs possess the merits of low cost, simple fabrication process and high performance, which could be one of the most promising photovoltaic technologies in the future. In this review, we focus on the summary of the updated progresses in single junction PSCs including efficiency, stability and large area module. Then, the important progresses in tandem solar cells are briefly discussed. A prospect into the future of the field is also included.

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter. They break the fermion-boson dichotomy and obey non-Abelian braiding statistics: their interchanges yield unitary operations, rather than merely a phase factor, in a space spanned by topologically degenerate wavefunctions. They are the building blocks of topological quantum computing. However, experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto, in spite of various theoretical proposals. Here, we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice. By implementing the ground states of the toric-code model with twists through quantum circuits, we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons, i.e., the Ising anyons. In particular, we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type, and can be explored to encode topological logical qubits. Furthermore, we demonstrate how to implement both single- and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits. Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons, offering a new lens into the study of such peculiar quasiparticles.

Semiconductivity and superconductivity are remarkable quantum phenomena that have immense impact on science and technology, and materials that can be tuned, usually by pressure or doping, to host both types of quantum states are of great fundamental and practical significance. Here we show by first-principles calculations a distinct route for tuning semiconductors into superconductors by diverse large-range elastic shear strains, as demonstrated in exemplary cases of silicon and silicon carbide. Analysis of strain driven evolution of bonding structure, electronic states, lattice vibration, and electron-phonon coupling unveils robust pervading deformation induced mechanisms auspicious for modulating semiconducting and superconducting states under versatile material conditions. This finding opens vast untapped structural configurations for rational exploration of tunable emergence and transition of these intricate quantum phenomena in a broad range of materials.

We report the discovery of superconductivity on the border of antiferromagnetic order in a quasi-one-dimensional material RbMn$_{6}$Bi$_{5}$ via measurements of resistivity and magnetic susceptibility under high pressures. Its phase diagram of temperature versus pressure resembles those of many magnetism-mediated superconducting systems. With increasing pressure, its antiferromagnetic ordering transition with $T_{\rm N} = 83$ K at ambient pressure is first enhanced moderately and then suppressed completely at a critical pressure of $P_{\rm c} \approx 13$ GPa, around which bulk superconductivity emerges and exhibits a dome-like $T_{\rm c}(P)$ with a maximal $T_{\rm c}^{\rm onset} \approx 9.5$ K at about 15 GPa. In addition, the superconducting state around $P_{\rm c}$ is characterized by a large upper critical field $\mu_{0}H_{\rm c2}(0)$ exceeding the Pauli paramagnetic limit, implying a possible unconventional paring mechanism. The present study, together with our recent work on KMn$_{6}$Bi$_{5}$ (the maximum $T_{\rm c}^{\rm onset} \approx 9.3$ K), makes $A$Mn$_{6}$Bi$_{5}$ ($A$ = alkali metal) a new family of Mn-based superconductors with relatively high $T_{\rm c}$.

Owing to the nonequilibrium nature, the energy state of metallic glasses (MGs) can vary a lot and has a critical influence on the physical properties. Exploring new methods to modulate the energy state of glasses and studying its relationship with properties have attracted great interests. Herein, we systematically investigate the energy state, mixing entropy and physical properties of Zr–Ti–Cu–Ni–Be multicomponent high entropy MGs by experiments and simulations. We find that the energy state increases along with the increase of mixing entropy. The yield strength and thermal stability of MGs are also enhanced by high mixing entropy. These results may open a new door on regulation of energy states and thus physical properties of MGs.

To understand the intriguing many-body states and effects in the correlated quantum materials, inference of the microscopic effective Hamiltonian from experiments constitutes an important yet very challenging inverse problem. Here we propose an unbiased and efficient approach learning the effective Hamiltonian through the many-body analysis of the measured thermal data. Our approach combines the strategies including the automatic gradient and Bayesian optimization with the thermodynamics many-body solvers including the exact diagonalization and the tensor renormalization group methods. We showcase the accuracy and powerfulness of the Hamiltonian learning by applying it firstly to the thermal data generated from a given spin model, and then to realistic experimental data measured in the spin-chain compound copper nitrate and triangular-lattice magnet TmMgGaO$_4$. The present automatic approach constitutes a unified framework of many-body thermal data analysis in the studies of quantum magnets and strongly correlated materials in general.

The development of high-fidelity two-qubit quantum gates is essential for digital quantum computing. Here, we propose and realize an all-microwave parametric controlled-Z (CZ) gates by coupling strength modulation in a superconducting Transmon qubit system with tunable couplers. After optimizing the design of the tunable coupler together with the control pulse numerically, we experimentally realized a 100 ns CZ gate with high fidelity of 99.38%$ \pm 0.34$% and the control error being 0.1%. We note that our CZ gates are not affected by pulse distortion and do not need pulse correction, providing a solution for the real-time pulse generation in a dynamic quantum feedback circuit. With the expectation of utilizing our all-microwave control scheme to reduce the number of control lines through frequency multiplexing in the future, our scheme draws a blueprint for the high-integrable quantum hardware design.

Realization of Kondo lattice in superconducting van der Waals materials not only provides a unique opportunity for tuning the Kondo lattice behavior by electrical gating or intercalation, but also is helpful for further understanding the heavy fermion superconductivity. Here we report a low-temperature and vector-magnetic-field scanning tunneling microscopy and spectroscopy study on a superconducting compound (4Hb-TaS$_{2})$ with alternate stacking of 1T-TaS$_{2}$ and 1H-TaS$_{2}$ layers. We observe the quasi-two-dimensional superconductivity in the 1H-TaS$_{2}$ layer with anisotropic response to the in-plane and out-of-plane magnetic fields. In the 1T-TaS$_{2}$ layer, we detect the Kondo resonance peak that results from the Kondo screening of the unpaired electrons in the Star-of-David clusters. We also find that the intensity of the Kondo resonance peak is sensitive to its relative position with the Fermi level, and it can be significantly enhanced when it is further shifted towards the Fermi level by evaporating Pb atoms onto the 1T-TaS$_{2}$ surface. Our results not only are important for fully understanding the electronic properties of 4Hb-TaS$_{2}$, but also pave the way for creating tunable Kondo lattice in the superconducting van der Waals materials.

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.

Megabar pressures are of crucial importance for cutting-edge studies of condensed matter physics and geophysics. With the development of diamond anvil cell (DAC), laboratory studies of high pressure have entered the megabar era for decades. However, it is still challenging to implement in situ magnetic sensing under ultrahigh pressures. In this work, we demonstrate optically detected magnetic resonance and coherent quantum control of diamond nitrogen-vacancy (NV) center, a promising quantum sensor inside the DAC, up to 1.4 Mbar. The pressure dependence of optical and spin properties of NV centers in diamond are quantified, and the evolution of an external magnetic field has been successfully tracked at about 80 GPa. These results shed new light on our understanding of diamond NV centers and pave the way for quantum sensing under extreme conditions.

In iron-based superconductors, the ($0, \pi$) or ($\pi, 0$) nematicity, which describes an electronic anisotropy with a four-fold symmetry breaking, is well established and believed to be important for understanding the superconducting mechanism. However, how exactly such a nematic order observed in the normal state can be related to the superconducting pairing is still elusive. Here, by performing angular-dependent in-plane magnetoresistivity using ultra-thin flakes in the steep superconducting transition region, we unveil a nematic superconducting order along the ($\pi, \pi$) direction in electron-doped BaFe$_{2-x}$Ni$_x$As$_2$ from under-doped to heavily overdoped regimes with $x=0.065$–0.18. It shows superconducting gap maxima along the ($\pi, \pi$) direction rotated by 45$^\circ$ from the nematicity along ($0, \pi$) or ($\pi, 0$) direction observed in the normal state. A similar ($\pi, \pi$)-type nematicity is also observed in the under-doped and optimally doped hole-type Ba$_{1-y}$K$_y$Fe$_2$As$_2$, with $y = 0.2$–0.5. These results suggest that the ($\pi, \pi$) nematic superconducting order is a universal feature that needs to be taken into account in the superconducting pairing mechanism in iron-based superconductors.

The recent observation of superconductivity in thin films of infinite-layer nickelate Nd$ _{0.8}$Sr$ _{0.2}$NiO$ _{2}$ has received considerable attention. Despite the many efforts to understand the superconductivity in infinite-layer nickelates, a consensus on the underlying mechanism for the superconductivity has yet to be reached, partly owing to the challenges with the material synthesis. Here, we report the successful growth of superconducting infinite-layer Nd$ _{0.8}$Sr$ _{0.2}$NiO$ _{2}$ films by pulsed laser deposition and soft chemical reduction. The details on the growth process are discussed.

We studied anomalous Josephson effect (AJE) in Josephson trijunctions fabricated on Bi$_2$Se$_3$, and found that the AJE in T-shaped trijunctions significantly alters the Majorana phase diagram of the trijunctions, when an in-plane magnetic field is applied parallel to two of the three single junctions. Such a phenomenon in topological insulator-based Josephson trijunction provides unambiguous evidence for the existence of AJE in the system, and may provide an additional knob for controlling the Majorana bound states in the Fu–Kane scheme of topological quantum computation.