Majorana modes in time-reversal invariant s-wave topological superconductors

We present a time-reversal invariant s-wave superconductor supporting Majorana edge modes. The multiband character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the s-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.     

Spin-Orbit Coupled s-Wave Superconductor in One-Dimensional Optical Lattice

We study the topological properties of spin-orbit coupled s-wave superconductor in one-dimensional optical lattice. Compared to its corresponding continuum model, the single particle spectrum is modified by the optical lattice and the topological phase which is characterized by the Majorana edge modes can survive in two regions of the singleparticle spectrum. With the help of the self-consistent Bogoliubov-de Gennes calculation in the harmonic trap, we find that the existence of an upper critical magnetic field removes the topological superconductor phase to the trap wings.We also study the effects of nonmagnetic and magnetic impurity on the topological properties, and find the universal behavior of the mid-gap state induced by impurity in the topological superconductor phase in strong scattering limit.     

Search for Majorana fermions in multiband semiconducting nanowires

We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor. We show that, when an odd number of subbands are occupied, the system realizes a nontrivial topological state supporting Majorana modes. We study the topological quantum phase transition in this system and calculate the phase diagram as a function of the chemical potential and magnetic field. Our key finding is that multiband occupancy not only lifts the stringent constraint of one-dimensionality but also allows one to have higher carrier density in the nanowire, and as such multisubband nanowires are better suited for observing the Majorana particle. We study the robustness of the topological phase by including the effects of the short- and long-range disorder. We show that there is an optimal regime in the phase diagram ("sweet spot") where the topological state is to a large extent insensitive to the presence of disorder.     

Helical liquids and Majorana bound states in quantum wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.     

Proposal for direct measuring of the Majorana number in a topological superconductor using a quantum dot

We propose to directly measure the Majorana number for one-dimensional topological superconductors using a quantum dot. The setup consists of two topological superconducting wires with four Majorana zero modes, which are coupled to an external quantum dot. The measurement is achieved by utilizing the definition of the Majorana number, which is the charge-parity flipping when changing the boundary condition for the topological superconductor. We consider a control of the boundary condition with voltage gates. When the voltage on the gate are modulated sequentially, the boundary conditions changes and the parity of the superconducting state flips. We demonstrate that this parity flipping will change the electron occupation probability of the quantum dot, which reflects the value of the Majorana number.     

梯度磁场中自旋-轨道耦合旋转两分量玻色-爱因斯坦凝聚体的基态研究

利用准二维Gross-Pitaevskii方程,研究了在梯度磁场中具有自旋-轨道耦合的旋转两分量玻色-爱因斯坦凝聚体的基态结构.探索了自旋-轨道耦合作用和梯度磁场对基态的影响.结果发现,在梯度磁场下,随着自旋-轨道耦合强度增大,基态结构由skyrmion格子逐渐过渡为skyrmion列.对于弱自旋-轨道耦合和小旋转频率情况,增大磁场梯度强度可导致基态由平面波相转变为half-skyrmion;对于强自旋-轨道耦合和大旋转频率情况,梯度磁场可诱导hidden涡旋的产生.梯度磁场、自旋-轨道耦合和旋转作为体系的调控参数,可用于控制不同基态相间的转化.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

从高质量半导体/超导体纳米线到马约拉纳零能模

作为马约拉纳费米子的"凝聚态版本",马约拉纳零能模是当前凝聚态物理领域的研究热点.马约拉纳零能模满足非阿贝尔统计,可以构建受拓扑保护的量子比特.这种由空间上分离的马约拉纳零能模构建的拓扑量子比特不易受局域噪声的干扰,具有长的退相干时间,在容错量子计算中具有重要的应用前景.半导体/超导体纳米线是研究马约拉纳零能模和拓扑量...     

Floquet topological phase transition in two-dimensional quadratic band crossing system

We investigate the Hall effects of quadratic band crossing(QBC) fermions in a square optical lattice with spin–orbit coupling and orbital Zeeman term. We find that the orbital Zeeman term and shaking play critical roles in the systems,which can drive a topological transition from spin Hall phases to anomalous Hall phase with nonvanishing(spin) Chern numbers. Due to the interplay among the orbital Zeeman term, spin–orbit coupling, and the shaking, the phase diagram of the system exhibits rich phases, which are characterized by Chern number.     

Majorana零模式的电导与低压振荡散粒噪声

Majorana零能量模式是自身的反粒子,在拓扑量子计算中有重要应用.本文研究量子点与拓扑超导纳米线混合结构,通过量子点的输运电荷检测Majorana零模式.利用量子主方程方法,发现有无Majorana零模式的电流与散粒噪声存在明显差别.零模式导致稳态电流差呈反对称,在零偏压处显示反常电导峰.电流差随零模式分裂能的增大而减小,随量子点与零模式耦合的增强而增大.另一方面,零模式导致低压散粒噪声相干振荡,零频噪声显著增强.分裂能导致相干振荡愈加明显且零频噪声减小,而量子点与零模式的耦合使零频噪声增强.当量子点与电极非对称耦合时,零模式使电子由反聚束到聚束输运,亚泊松噪声增强为超泊松噪声.稳态电流差结合低压振荡的散粒噪声能够揭示Majorana零模式是否存在.     

Finite length effect on supercurrents between trivial and topological superconductors

We numerically analyze the effect of finite length of the superconducting regions on the low-energy spectrum, current-phase curves, and critical currents in junctions between trivial and topological superconductors. Such junctions are assumed to arise in nanowires with strong spin-orbit coupling under external magnetic fields and proximity-induced superconductivity. We show that all these quantities exhibit a strong dependence on the length of the topological sector in the topological phase and serve as indicators of the topological phase and thus the emergence of Majorana bound states at the end of the topological superconductor.     

Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin-orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.     

Evolution of edge states and critical phenomena in the Rashba superconductor with magnetization

We study Andreev bound states (ABS) and the resulting charge transport of a Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures are sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode in the topological phase (TP). We clarify two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether or not ABS exists at QCP. In the former type, ABS has an energy gap and does not cross at zero energy in the nontopological phase. These complex properties can be detected by tunneling conductance between normal metal-RSC junctions.     

Majorana fermions in equilibrium and in driven cold-atom quantum wires

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.     

两体相互作用费米系统在自旋轨道耦合和塞曼场中的基态转变

在超冷费米系统中实现人造规范势的突破,吸引了许多新问题的研究,展现了许多新奇的物理现象.本文研究了在环阱中,具有自旋轨道耦合和塞曼作用的两体相互作用费米模型.通过平面波展开的方法,解析求解了两体费米系统的本征能态.系统的总动量为守恒量,可以在不同总动量空间中研究能谱.研究发现:随着塞曼相互作用增大,在不同总动量空间,两体费米系统的本征能量均逐渐降低,系统基态从总动量为零空间转变到有限值空间.从吸引到排斥相互作用,无塞曼相互作用时,基态总动量始终为零,有塞曼相互作用时,基态总动量从零转变为有限值.通过单粒子和基态动量分布研究,本文直观地揭示了由塞曼能级劈裂引起的基态转变.     

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.     

Pairing and density-wave phases in boson-fermion mixtures at fixed filling

We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two isospin states and the bosons have Bose-Einstein condensed. Number density fluctuations of the condensate form delocalized bosonic modes which couple to the fermionic atoms similarly to the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site. We find that tuning of the lattice parameters and interaction strengths drives the system to undergo antiferromagnetic ordering, s-wave and d-wave pairing superconductivity, or a charge density-wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem.     

The Josephson effect in superconductors with heavy Fermions

The Josephson effect between a usual superconductor with even-parity pairing and a heavy-Fermion superconductor with odd-parity pairing would not be zero. Instead, due to spin-orbit coupling it would be of relative magnitude a/Ξ_o compared to the effect between two even-parity superconductors. a/Ξ_o, the ratio of lattice constant to pair size, is comparable to 0.1 for heavy-Fermion superconductors. Recent claims, that with strong spin-orbit coupling the even-parity to odd-parity Josephson effect should be of order unity times the even-even effect, are shown to be incorrect.     

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.