Majorana fermions induced fast-and slow-light in a hybrid semiconducting nanowire/superconductor device

We investigate theoretically Rabi-like splitting and Fano resonance in absorption spectra of quantum dots(QDs)based on a hybrid QD-semiconducting nanowire/superconductor(SNW/SC)device mediated by Majorana fermions(MFs).Under the condition of pump on-resonance and off-resonance,the absorption spectrum experiences the conversion from Fano resonance to Rabi-like splitting in different parametric regimes.In addition,the Fano resonances are accompanied by the rapid normal phase dispersion,which will indicate the coherent optical propagation.The results indicate that the group velocity index is tunable with controlling the interaction between the QD and MFs,which can reach the conversion between the fast-and slow-light.Fano resonance will be another method to detect MFs and our research may indicate prospective applications in quantum information processing based on the hybrid QD-SNW/SC devices.

Dissipative Quantum Computing with Majorana Fermions

We describe a scheme for universal quantum computation with Majorana fermions. We investigate two possible dissipative couplings of Majorana fermions to external systems, including metallic leads and local phonons. While the dissipation when coupling to metallic leads to uninteresting states for the Majorana fermions, we show that coupling the Majorana fermions to local phonons allows to generate arbitrary dissipations and therefore universal quantum operations on a single QuBit that can be enhanced by additional two-QuBit operations.

Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions

Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform any unitary transformation with arbitrary accuracy.Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions.Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures,which enable the braiding operation and the partial exchange operation.After defining a qubit by four chiral Majorana fermions,the singlequbit T and H quantum gates are realized via one partial exchange operation and three braiding operations,respectively.The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions.Besides,we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device.Thus,our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.

Controlling Fusion of Majorana Fermions in One-Dimensional Systems by Zeeman Field

We propose the realization of Majorana fermions （MFs） on the edges of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h. It is shown that there appear a pair of MFs localized at two junctions and that a reverse in the direction of h can lead to permutation of two MFs. With decreasing h, the MF states can either be fused or form one Dirac fermion on the π-junctions, exhibiting a topological phase transition. This characteristic can be used to detect physical states of MFs when they are transformed into Dirac fermions MFs is also given. localized on the π-junction. A condition of decoupling two

Detection of Majorana fermions in an Aharonov-Bohm interferometer

By using the non-equilibrium Green＇s function technique, we investigate the electronic transport properties in an Aharonov-Bohm interferometer coupling with Majorana fermions. We find a fixed unit conductance peak which is in-dependent of the other factors when the topological superconductor is grounded. Especially, an additional phase appears when the topological superconductor is in the strong Coulomb regime, which induces a new conductance resonant peak compared with the structure of replacing the topological superconductor by a quantum dot, and the conductance oscillation with the magnetic flux reveals a 2π phase shift by raising （lowering） a charge on the capacitor.

Robustness of coherence between two quantum dots mediated by Majorana fermions

We study three important measurements used to identify the quantum correlations between two quantum dots （QDs） mediated by a pair of Majorana fermions （MFs） in a superconducting quantum wire. We find that, in addition to the quantum discord, the robustness of coherence （ROC） can also be considered as a quantity to measure the quantum correlation for the special case where the quantum entanglement is vanishing. For comparison, we study the quantum correlation between two QDs mediated by other fermions, i.e., regular fermions and superconducting fermions. We find that, when the quantum entanglement is not vanishing, i.e., the concurrence is finite, the detailed difference between the concurrence and ROC can be considered as an important implication for the existence of MFs.

Nonexistence of Majorana fermions in Kerr-Newman type spacetimes with nontrivial charge

We show that the Dirac equation is separated into four differential equations for time-periodic Majorana fermions in Kerr-Newman and Kerr-Newman-(A)dS spacetimes.Although they cannot be transformed into radial and angular equations,the four differential equations yield two algebraic identities.When the electric or magnetic charge is nonzero,they conclude that there is no differentiable time-periodic Majorana fermions outside the event horizon in Kerr-Newman and Kerr-Newman-AdS spacetimes,or between the event horizon and the cosmological horizon in Kerr-Newman-dS spacetime.

Majorana tunneling in a one-dimensional wire with non-Hermitian double quantum dots

The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneling and interdot tunneling in a non-Hermitian double quantum dots system. It is found that in the weak-coupling regime the Majorana tunneling has pronounced effects on the transport properties of such a system, manifested as splitting of the single peak into three and a reduced 1/4 peak in the transmission function. In the presence of the PT-symmetric complex potentials and interdot tunneling, the 1/4 central peak is robust against them, while the two side peaks are tuned by them. The interdot tunneling only induces asymmetry, instead of moving the conductance peak, due to the robustness of the Majorana modes. There is an exceptional point induced by the union of Majorana tunneling and interdot tunneling. With increased PT-symmetric complex potentials, the two side peaks will move towards each other. When the exceptional point is passed through, these two side peaks will disappear. In the strong-coupling regime, the Majorana fermion induces a 1/4 conductance dip instead of the three-peak structure. PT-symmetric complex potentials induce two conductance dips pinned at the exceptional point. These effects should be accessible in experiments.

Negative tunnel magnetoresistance in a quantum dot induced by interplay of a Majorana fermion and thermal-driven ferromagnetic leads

We investigate the spin-related currents and tunnel magnetoresistance through a quantum dot,which is side-coupled with a Majorana fermion zero mode and two thermal-driven ferromagnetic electrodes.It is found that the interplay of Majorana fermion and electrodes'spin polarization can induce a nonlinear thermal-bias spin current.This interplay also decreases the total magnitude of spin or charge current,in either parallel or antiparallel configuration.In addition,a thermal-driven negative tunnel magnetoresistance is found,which is an unique feature to characterize Majorana fermion.With large temperature difference,a step phenomenon is observed in gate tuned spin-up current.When the coupling between quantum dot and topological superconductor is strong enough,this step will evolve into a linear relation,revealing Majorana fermion's robustness.

Realizing Majorana fermion modes in the Kitaev model

We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work.To achieve this we first apply a uniform[111]magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p+ip topological superconductor of spinons.We then study possible vortex binding in such system to a topologically trivial spot in the ground state.We consider two cases in the system:one is a vacancy and the other is a fully polarized spin.We show that in both cases,the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform[111]magnetic field.The distribution and asymptotic behavior of these Majorana zero modes are studied.The Majorana zero modes in both cases decay exponentially in space,and are robust against local perturbations and other Majorana zero modes far away,which makes them promising candidates for braiding in topological quantum computing.

Majorana fermion realization and relevant transport processes in a triple-quantum dot system

Nonequilibrium electronic transports through a system hosting three quantum dots hybridized with superconductors are investigated. By tuning the relative positions of the dot levels, we illustrate the existence of Majorana fermions and show that the Majorana feimions will either survive separately on single dots or distribute themselves among different dots with tunable probabilities. As a result, different physical mechanisms appear, including local Andreev reflection（LAR）,cross Andreev reflection（CAR）, and cross resonant tunneling（CRT）. The resulting characteristics may be used to reveal the unique properties of Majorana fermions. In addition, we discuss the spin-polarized transports and find a pure spin current and a spin filter effect due to the joint effect of CRT and CAR, which is important for designing spintronic devices.

The stability of Majorana fermion in correlated quantum wire

In this paper, we investigate the effect of the Coulomb interaction between electrons on the stability of Majorana fermion in a heterostructure of s-wave superconductor and quantum wire. In particular, by using the bosonization method and the renormalization group technique, we show that interplay between the so-called umklapp electron–electron scattering process and the superconducting proximity effect plays an extremely important role in determining the phase diagram of the system. We find that, at half-filling, the strong umklapp scattering process suppresses not only the superconducting pairing interaction and hence, destabilizes Majorana fermion in the quantum wire, but aslo results in a Mott insulating state.However, if the proximity effect is sufficiently strong, the topological superconducting phase can still survive and support Majorana fermion in the heterostructure. Furthermore, the existence of a critical Luttinger liquid phase is also found in a narrow region of parameters.

Chiral p-wave pairing of ultracold fermionic atoms due to a quadratic band touching

We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Instead of pairing between spin states, here we focus on pairing interactions between different orbital states. We find that our systems have only odd-parity （orbital） pairing instability while the singlet （orbital） pairing instability vanishes thanks to the quadratic band touching. In the mean field level, the ground state is found to be a chiral p-wave pairing superfluid （mixed with finite f-wave pairing order-parameters） which supports Majorana fermions.

Hinge Majorana flat band in type-Ⅱ Dirac semimetals

Type-Ⅱ Dirac semimetals exhibit a unique Fermi surface topology,which allows them to host novel topological superconductivity(TSC).We reveal a novel inter-orbital superconducting state,corresponding to the B_(1u) and B_(2u) pairings under the D_(4h) point group.Intriguingly,we find that both first-and second-order TSC coexist in this novel state.It is induced by a dominant inter-orbital attraction and possesses surface helical Majorana cones and hinge Majorana flat bands,spanning the entire z-directed hinge Brillouin zone.Further investigation uncovers that these higher-order hinge modes are robust against the C_(4z) symmetry-breaking perturbation.

Topological phase transitions driven by next-nearest-neighbor hopping in noncentrosymmetric cold Fermi gases

We investigate the topological phase marked by the Thouless–Kohmoto–Nightingale–Nijs（TKNN） number and the phase transitions driven by the next nearest neighbor（NNN） hopping in noncentrosymmetric cold Fermi gases, both spinsinglet pairing and spin-triplet pairing are considered. There exists a critical t＇c for the NNN hopping, at which the quantum phase transition occurs, and the system changes from an Abelian（non-Abelian） phase to a non-Abelian（Abelian） one. By numerically diagonalizing the Hamiltonian in the real space, the energy spectra with edge states for different topological phases and the Majorana zero modes are discussed. Although the spin-triplet pairing does not contribute to the gap closing and the phase diagram, it induces gapless states in the presence of a magnetic field, and the TKNN number in this region is still zero.

All-electrically reading out and initializing topological qubits with quantum dots

We analyze the reading and initialization of a topological qubit encoded by Majorana fermions in one-dimensional semiconducting nanowires, weakly coupled to a single level quantum dot （QD）. It is shown that when the Majorana fermions are fused by tuning gate voltage, the topological qubit can be read out directly through the occupation of the QD in an energy window. The initialization of the qubit can also be realized via adjusting the gate voltage on the QD, with the total fermion parity conserved. As a result, both reading and initialization processes can be achieved in an all-electrical way.

Solid-state quantum computation station

Solid-state quantum computation station belongs to the group 2 of manipulation of quantum state in the Synergetic Extreme Condition User Facility. Here we will first outline the research background, aspects, and objectives of the station, followed by a discussion of the recent scientific as well as technological progress in this field based on similar experimental facilities to be constructed in the station. Finally, a brief summary and research perspective will be presented.

Phase Diagram and Edge States of Surface States of Topological Superconductors

Majorana fermions in two-dimensional systems satisfy non-Abelian statistics. They are possible to exist in topological superconductors as quasi particles, which is of great significance for topological quantum computing. In this paper, we study a new promising system of superconducting topological surface state topological insulator thin films. We also study the phase diagrams of the model by plotting the Majorana edge states and the density of states in different regions of the phase diagram. Due to the mirror symmetry of the topological surface states, the Hamiltonian can be block diagonalized into two spin-triplet p-wave superconductors, which are also confirmed by the phase diagrams. The chiral Majorana edge modes may provide a new route for realizing topological quantum computation.

All-optical scheme for detecting the possible Majorana signature based on QD and nanomechanical resonator systems

Majorana fermions(MFs) are exotic particles that are their own anti-particles. Currently, the search for MFs occurring as quasiparticle excitations in condensed matter systems has attracted widespread interest, because of their importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Motivated by recent experimental progress towards the detection and manipulation of MFs in hybrid semiconductor/superconductor heterostructures, in this review, we present a novel proposal to probe MFs in all-optical domain. We introduce a single quantum dot(QD), a hybrid quantum dot-nanomechanical resonators(QD-NR) system, and a carbon nanotube(CNT) resonator implanted in a single electron spin system with optical pump-probe technology to detect MFs, respectively. With this scheme, a possible Majorana signature is investigated via the probe absorption spectrum and nonlinear optical Kerr effect, and the coupling strength between MFs and the QD or the single electron spin is also determined. In the hybrid QD-NR system, vibration of the NR will enhance the nonlinear optical effect, which makes the MFs more sensitive for detection. In the CNT resonator with a single electron, the single electron spin can be considered as a sensitive probe, and the CNT resonator behaved as a phonon cavity is robust for detecting of MFs. This optical scheme will provide another method for the detection MFs and will open the door for new applications ranging from robust manipulation of MFs to quantum information processing based on MFs.

Majorana zero mode in the vortex of an artificial topological superconductor

Majorana fermion （MF）, an exotic particle that is identical to its own antiparticle, was recently found in solid matter as a quasiparticle excitation, the Majorana zero mode （MZM）, in the vortex of an artificial topological superconductor （TSC）. This artificial TSC, first proposed by Fu and Kane in 2008, is a heterostructure made of a topological insulator BiETe3 and an s-wave superconductor NbSe2. This paper will briefly review the experimental progresses based on the Bi2Te3/NbSe2 heterostructure. All evidences are self-consistent and reveal that the MZM exists in the center of vortex. Those experimental results are also supported by theory. This finding is a milestone in the research ofMajorana fermions in solid state physics and a starting point of MZM＇s application in topological quantum computation.