Josephson current through a quantum dot molecule with a Majorana zero mode and Andreev bound states

Based on the Green's function method, we investigate the interplay between Majorana zero mode (MZM) and Andreev bound states (ABSs) in a quantum dot molecule side coupled to a topological superconducting nanowire with a pair of MZMs forming a Josephson junction. Since the strong electron–hole asymmetry induced by the nanowire with a topologically non-trivial phase, the MZM suppress the ABSs. The suppression induced by the MZM is robust against the Coulomb repulsion. The interplay between the MZM and the ABSs in Josephson junction presents a feasible experimental means for distinguish between the presence of MZM and ABSs.     

Topological superconductivity and the fractional Josephson effect in quasi-one dimensional wires on a plane

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one-dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin–orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of the Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle–hole symmetry. Tunneling of Majorana quasiparticle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with 4π-periodicity.     

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.     

Topological Fulde–Ferrell and Larkin–Ovchinnikov states in spin-orbit-coupled lattice system

The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde–Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin–Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number (C=−1) (tFF₁) and topological LO state with C= 2 (tLO₂) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with C=−1 (tBCS₁) far from half filling and C= 2 (tBCS₂) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF₁ and tLO_1,2 states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.     

Kondo screening cloud in a superconductor with mixed s-wave and p-wave pairing states

We study the Kondo screening of a spin-1/2 magnetic impurity coupled to a superconductor, which is fabricated by combination of an s-wave superconductor, a ferromagnet and a semiconductor with Rashba spin—orbit coupling (RSOC). The proximity induced superconducting states include the s-wave and p-wave pairing components with the aids of RSOC, and the ferromagnet induces a Zeeman field which removes the spin degeneracy of the quasiparticles in the triplet states. Thus, the Kondo screening of magnetic impurity involves the orbital degrees of freedom, and is also affected by the Zeeman field. Using the variational method, we calculate the binding energy and the spin—spin correlation between the magnetic impurity and the electrons in the coexisting s-wave and p-wave pairing states. We find that Kondo singlet forms more easily with stronger RSOC, but Zeeman field in general decreases the binding energy. The spin—spin correlation decays fast in the vicinity of the magnetic impurity. Due to the RSOC, the spatial spin—spin correlation becomes highly anisotropic, and the Zeeman field can induce extra asymmetry to the off-diagonal components of the spin—spin correlation. Our study can offer some insights into the studies of extrinsic topological superconductors fabricated from the hybrid structures containing chains of magnetic impurities.     

Superconducting quantum interference devices made of Sb-doped Bi2Se3 topological insulator nanoribbons

We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) made of Sb-doped Bi₂Se₃ topological insulator (TI) nanoribbon (NR) contacted with PbIn superconducting electrodes. When an external magnetic field was applied along the NR axis, the TI NR exhibited periodic magneto-conductance oscillations, the so-called Aharonov-Bohm oscillations, owing to one-dimensional subbands. Below the superconducting transition temperature of PbIn electrodes, we observed supercurrent flow through TI NR-based SQUID. The critical current periodically modulates with a magnetic field perpendicular to the SQUID loop, revealing that the periodicity corresponds to the superconducting flux quantum. Our experimental observations can be useful to explore Majorana bound states (MBS) in TI NR, promising for developing topological quantum information devices.     

BCS-BEC crossover and topological phase transition in 3D spin-orbit coupled degenerate Fermi gases

We investigate the BCS-BEC crossover in three-dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a nontopological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum-resolved photoemission spectroscopy.     

铁磁绝缘体间的极薄Bi2Se3薄膜的相变研究

研究一个极薄三维拓扑绝缘体Bi₂Se₃薄膜处于两个铁磁绝缘体层之间, 其铁磁层的磁化方向都处于竖直平面, 系统拓扑性质随磁化方向夹角的变化. 从表面态电子低能有效哈密顿量出发计算系统的Chern 数, 和运用一个具有Armchair边界的单层六角晶格带的紧束缚模型模拟系统的体能带和边缘态, 来确定系统所处的拓扑相. 发现两个铁磁层的磁化方式从平行转到反平行的某一临界角度, 系统经历从反常量子霍尔相到普通绝缘相的转变.     

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid.In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines,which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.     

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.     

Transport induced dimer state from topological corner states

Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise at the corners with obtuse angles of an isolated diamond-shaped flake. To probe the corner states, we study their transport properties by attaching two leads to the system. Dressed by incoming electrons, the dynamic corner state is very different from its static counterpart.Resonant tunneling through the dressed corner state can occur by tuning the in-plane Zeeman field. At the resonance, the pair of spatially well separated and highly localized corner states can form a dimer state, whose wavefunction extends almost the entire bulk of the diamond-shaped flake. By varying the Zeeman field strength, multiple resonant tunneling events are mediated by the same dimer state. This re-entrance effect can be understood by a simple model. These findings extend our understanding of dynamic aspects of the second-order topological corner states.     

塞曼效应对正常金属/d波超导结中微分电导的影响

通过外加塞曼磁场在d波超导中,研究磁场对d波超导及其正常金属/d波超导结中隧道谱的影响。研究表明(1)塞曼磁场能使能隙变小,且随着磁场变大,超导态会变为正常态,产生一级相变;(2)塞曼磁场可导致零偏压电导峰劈裂,劈裂宽度为2h0(h0为塞曼能)。     

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.     

Nonequilibrium Josephson effect through helical edge states

We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4π periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that his effect is absent in the average current. However, clear signatures can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestations of the Majorana bound states forming at the edges of the superconductors.     

Quench dynamics of edge states in 2-D topological insulator ribbons

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Lochschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.     

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.     

Transport features of topological corner states in honeycomb lattice with multihollow structure

Higher-order topological phase in 2-dimensional (2D) systems is characterized by in-gap corner states, which are hard to detect and utilize. We numerically investigate transport properties of topological corner states in 2D honeycomb lattice, where the second-order topological phase is induced by an in-plane Zeeman field in the conventional Kane–Mele model. Through engineering multihollow structures with appropriate boundaries in honeycomb lattice, multiple corner states emerge, which greatly increases the probability to observe them. A typical two-probe setup is built to study the transport features of a diamond-shaped system with multihollow structures. Numerical results reveal the existence of global resonant states in bulk insulator, which corresponds to the resonant tunneling of multiple corner states and occupies the entire scattering region. Furthermore, based on the well separated energy levels of multiple corner states, a single-electron source is constructed.     

Origin of excess low-energy states in a disordered superconductor in a Zeeman field

Tunneling density of states measurements of disordered superconducting Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The disordered Larkin-Ovchinnikov superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states that lead to distinct spectral signatures at low energy.     

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman energy difference between the two splitting peaks in the conductance spectrum is equal to2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks,however, neither of them can influence the Zeeman effect.