电子型FeSe基高温超导体的磁通束缚态与Majorana零能模

作为凝聚态物理中一类新奇准粒子态,Majorana零能模(Majorana zero mode)由于可用来实现拓扑量子计算而成为当前的研究热点.理论预言,Majorana零能模可作为特殊的束缚态出现在一些拓扑超导体的磁通涡旋中.但实际超导体磁通中还可能存在其他低能束缚态或杂质态,这给Majorana零能模的辨别和具体应用带来了困难.目前实验上寻找合适的拓扑超导体系、分辨出清晰的Majorana零能模仍然是十分迫切的.本文主要介绍最近利用高能量分辨的扫描隧道显微镜,对电子掺杂铁硒类超导体(Li,Fe)OHFeSe和单层FeSe/SrTiO3磁通态进行的研究.实验上在前者的自由磁通中观测到清晰的零能模,并进一步测量到Majorana零能模的重要特征—量子化电导.而在后者磁通中只发现常规Caroli-de Gennes-Matricon(CdGM)束缚态,反映出s波对称性的特征.这系列实验既为Majorana零能模物性的进一步研究提供了合适平台,也为澄清铁基超导体中拓扑超导电性的来源提供了线索.     

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and nontopological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing spin-triplet superfluid ³He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where the Green’s function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green’s function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

We investigate electronic transport through a parallel double quantum dot （DQD） system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit （2e^2/h） due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.     

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.     

耦合Majorana束缚态T形双量子点中的Andreev反射

研究了连接在正常金属电极和超导电极之间的耦合Majorana束缚态(MBSs)T形双量子点结构中的Andreev反射.研究发现,对于T形双量子点结构,当入射能量等于边耦合量子点能级时Andreev反射电导出现Fano振荡,连接MBSs之后,零费米能附近出现一对新的Fano型振荡峰.如果忽略两个MBSs之间的相互作用,零费米能点的Andreev反射电导为定值1/2G_0(G_0=2e~2/h),不受量子点能级、双量子点之间耦合强度以及量子点与MBSs之间的耦合强度的影响.此外,在没有耦合MBSs的T形双量子点结构中,调节双量子点间的耦合强度可以使零费米能附近的Andreev反射电导出现由共振带向反共振带的转变,而耦合MBSs之后,又可以使反共振消失转而出现新的共振峰.     

Majorana–Kondo interplay in a Majorana wire-quantum dot system with ferromagnetic contacts*

We consider a single-level quantum dot(QD)and a topological superconducting wire hosting Majorana bound states at its ends.By the equation of motion method,we give the analytical Green’s function of the QD in the noninteracting and the infinite interacting case.We study the effects of QD energy level and the spin polarization on the density of states(DOS)and linear conductance of the system.In the noninteracting case,the DOS resonance shifts with the change of energy level and it shows bimodal structure at large spin polarization strength.In the infinite interacting case,the up-spin linear conductance first increases and then decreases with the increase of spin polarization strength,but the down-spin is stable.However,the DOS shows a splitting phenomenon in the large energy level with the increase of spin polarization strength.This provides an interesting way to explore the physical properties of such spin dependent effect in the hybrid Majorana QD systems.     

Detection of spin current through a quantum dot with Majorana bound states

The spin transport properties are theoretically investigated when a quantum dot(QD) is side-coupled to Majorana bound states(MBSs) driven by a symmetric dipolar spin battery. It is found that MBSs have a great effect on spin transport properties. The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases. Moreover, a non-zero charge current with two resonance peaks appears in the system. In the extreme case where the dot–MBS coupling strength is strong enough, the spin current and the charge current are both constants in the non-resonance peak range. When considering the effect of the Zeeman energy, it is interesting that the resonance peak at the higher energy appears one shoulder. And the shoulder turns into a peak when the Zeeman energy is big enough. In addition, the coupling strength between the two MBSs weakens their effects on the currents of the system. These results are helpful for understanding the MBSs signature in the transport spectra.     

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.     

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.     

Topological insulator: Spintronics and quantum computations

Topological insulators are emergent states of quantum matter that are gapped in the bulk with timereversal symmetry-preserved gapless edge/surface states, adiabatically distinct from conventional materials. By proximity to various magnets and superconductors, topological insulators show novel physics at the interfaces, which give rise to two new areas named topological spintronics and topological quantum computation. Effects in the former such as the spin torques, spin-charge conversion, topological antiferromagnetic spintronics, and skyrmions realized in topological systems will be addressed. In the latter, a superconducting pairing gap leads to a state that supports Majorana fermions states, which may provide a new path for realizing topological quantum computation. Various signatures of Majorana zero modes/edge mode in topological superconductors will be discussed. The review ends by outlooks and potential applications of topological insulators. Topological superconductors that are fabricated using topological insulators with superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.     

Interplay of Rashba spin orbit coupling and disorder in the conductance properties of a four terminal junction device

We report a thorough theoretical investigation on the quantum transport of a disordered four terminal device in the presence of Rashba spin orbit coupling (RSOC) in two dimensions. Specifically we compute the behaviour of the longitudinal (charge) conductance, spin Hall conductance and spin Hall conductance fluctuation as a function of the strength of disorder and Rashba spin orbit interaction using the Landauer Büttiker formalism via Green’s function technique. Our numerical calculations reveal that both the conductances diminish with disorder. At smaller values of the RSOC parameter, the longitudinal and spin Hall conductances increase, while both vanish in the strong RSOC limit. The spin current is more drastically affected by both disorder and RSOC than its charge counterpart. The spin Hall conductance fluctuation does not show any universality in terms of its value and it depends on both disorder as well as on the RSOC strength. Thus the spin Hall conductance fluctuation has a distinct character compared to the fluctuation in the longitudinal conductance. Further one parameter scaling theory is studied to assess the transition to a metallic regime as claimed in literature and we find no confirmation about the emergence of a metallic state induced by RSOC.     

Spin-polarized transport induced by photoirradiation in zigzag silicene nanosystem

We study the spin-polarized transport induced by photoirradiation in zigzag silicene nanosystem, based on tight-binding approach, Green's function method and Landauer–Büttiker formula. By applying strong circular polarized light, silicene nanosystem can be transformed into a quantum Hall insulator, where the spin-down subband is gapped while the spin-up subband persists gapless edge state. Therefore, the dc conductance is dominated by the spin-up electrons, and the spin polarization can reach almost 100% around the Fermi energy. The spatial-resolved local density of states confirm that the spin-up electrons transport at two edges of the nanosystem in opposite current directions. Furthermore, because of the topological origin of the edge state, the spin-polarized transport is very robust against the size change of the nanosystem.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

Quantum spin Hall effect in inverted type-II semiconductors

The quantum spin Hall (QSH) state is a topologically nontrivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells and in this Letter we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. The quantum well exhibits an "inverted" phase similar to HgTe/CdTe quantum wells, which is a QSH state when the Fermi level lies inside the gap. Due to the asymmetric structure of this quantum well, the effects of inversion symmetry breaking are essential. Remarkably, the topological quantum phase transition between the conventional insulating state and the quantum spin Hall state can be continuously tuned by the gate voltage, enabling quantitative investigation of this novel phase transition.     

Influence of Majorana Bound States in Quantum Rings

A quantum ring coupled to a 1D topological superconductor hosting Majorana bound states (MBSs) is investigated. The MBSs effects over the spectrum and persistent current along the quantum ring are studied. The spectra of the system are obtained by an exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian in the Majorana representation. In addition, Green's function formalism is implemented for analytical calculations and obtained a switching condition in the MBSs fermionic parity. Three different patterns that could be obtained for the spatial separation of the MBSs, named: bowtie, diamond, and asymmetric, are reported here, which are present only in odd parity in the quantum ring, while only a single pattern (bowtie) is obtained for even parity. Those patterns are subject strictly to the switching condition for the MBSs. Besides, quantum ring with the presence of a Majorana zero mode presents gapped/gapless spectra in odd/even parity showing in the even case a subtle signature in the persistent current.     

Nondissipative spin Hall effect via quantized edge transport

The spin Hall effect in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings is studied numerically. Integer quantized spin Hall conductance is obtained at the zero Rashba coupling limit when electron Fermi energy lies in the energy gap created by the intrinsic spin-orbit coupling, in agreement with recent theoretical prediction. While nonzero Rashba coupling destroys electron spin conservation, the spin Hall conductance is found to remain near the quantized value, being insensitive to disorder scattering, until the energy gap collapses with increasing the Rashba coupling. We further show that the charge transport through counterpropagating spin-polarized edge channels is well quantized, which is associated with a topological invariant of the system.     

Topological Knots in Quantum Spin Systems

Knot theory provides a powerful tool for understanding topological matters in biology, chemistry, and physics.Here knot theory is introduced to describe topological phases in a quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other, forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.     

Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.