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.     

Resonant Andreev reflection in a normal-metal/quantum-dot/superconductor system with coupled Majorana bound states

Andreev reflection(AR) in a normal-metal/quantum-dot/superconductor(N–QD–S) system with coupled Majorana bound states(MBSs) is investigated theoretically. We find that in the N–QD–S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD–MBS coupling or MBS–MBS coupling. The AR conductance is always e~2/2h at the zero Fermi energy point when only QD–MBSs coupling is considered. In addition, the resonant AR occurs when the MBS–MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD–MBS coupling and the MBS–MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.     

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.     

Quantum transport through a multi-quantum-dot-pair chain side-coupled with Majorana bound states

We investigate the quantum transport properties through a special kind of quantum dot(QD) system composed of a serially coupled multi-QD-pair(multi-QDP) chain and side-coupled Majorana bound states(MBSs) by using the Green functions method,where the conductance can be classified into two kinds:the electron tunneling(ET) conductance and the Andreev reflection(AR) one.First we find that for the nonzero MBS-QDP coupling a sharp AR-induced zero-bias conductance peak with the height of e~2/h is present(or absent) when the MBS is coupled to the far left(or the other) QDP.Moreover,the MBS-QDP coupling can suppress the ET conductance and strengthen the AR one,and further split into two sub-peaks each of the total conductance peaks of the isolated multi-QDPs,indicating that the MBS will make obvious influences on the competition between the ET and AR processes.Then we find that the tunneling rate ΓLis able to affect the conductances of leads L and R in different ways,demonstrating that there exists a ΓL-related competition between the AR and ET processes.Finally we consider the effect of the inter-MBS coupling on the conductances of the multi-QDP chains and it is shown that the inter-MBS coupling will split the zero-bias conductance peak with the height of e~2/h into two sub-peaks.As the inter-MBS coupling becomes stronger,the two sub-peaks are pushed away from each other and simultaneously become lower,which is opposite to that of the single QDP chain where the two sub-peaks with the height of about e~2/2h become higher.Also,the decay of the conductance sub-peaks with the increase of the MBS-QDP coupling becomes slower as the number of the QDPs becomes larger.This research should be an important extension in studying the transport properties in the kind of QD systems coupled with the side MBSs,which is helpful for understanding the nature of the MBSs,as well as the MBS-related QD transport properties.     

Quantum Transport through a Triple Quantum Dot System in the Presence of Majorana Bound States

We study the electron transport through a special quantum-dot(QD)structure composed of three QDs and two Majorana bound states(MBSs)using the nonequilibrium Green’s function technique.This QD-MBS ring structure includes two channels with the two coupled MBSs being Channel 1 and one QD being Channel 2,and three types of transport processes such as the electron transmission(ET),the Andreev reflection(AR),and the crossed Andreev reflection(CAR).By comparing the ET,AR,and CAR processes through Channels 1 and 2,we make a systematic study on the transport properties of the QD-MBS ring.It is shown that there appear two kinds of characteristic transport patterns for Channels 1 and 2,as well as the interplay between the two patterns.Of particular interest is that there exists an AR-assisted ET process in Channel 2,which is different from that in Channel 1.Thus a clear"X"pattern due to the ET and AR processes appears in the ET,AR,and CAR transmission coefficients.Moreover,we study how Channel 2 affects the three transport processes when Channel 1 is tuned in the ET and CAR regimes.It is shown that the transport properties of the ET,AR and CAR processes can be adjusted by tuning the energy level of the QD embedded in Channel 2.We believe this research should be a helpful reference for understanding the transport properties in the QD-MBS coupled systems.     

Kondo-assistant Aharonov-Bohm transport in a quantum dot-Majorana wire system

We investigate the Kondo-assistant Aharonov-Bohm (AB) transport in a Quantum dot (QD) coupled with a topological Majorana wire. We noted that the conductance exhibits sensitive dependence on the phase factor of AB ring when the wire-QD coupling strength changes. The DOS resonance split when the coupling strength changes from small to large. The current is determined by the Kondo transport characteristics presented by the quantum dots (QDs). Also, the transport results show different p-dependence properties under parallel and anti-parallel leads alignment. We believe that these results can be helpful for understanding the Majorana-QD coupling properties as well as the detection of the Majorana bound states.     

Bound states in the continuum in metal—dielectric photonic crystal with a birefringent defect

By using the difference of the band structure for the TE and TM waves in the metal—dielectric photonic crystals beyond the light cone and the birefringence of the anisotropic crystal, a one-dimensional photonic system is constructed to realize the bound states in the continuum (BICs). In addition to the BICs arising from the polarization incompatibility, the Friedrich—Wintgen BICs are also achieved when the leaking TM wave is eliminated due to the destructive interference of its ordinary and extraordinary wave components in the anisotropic crystal. A modified scheme favorable for practical application is also proposed. This scheme for BICs may help to suppress the radiation loss in the metal—dielectric photonic crystal systems.     

Majorana fermion modulated nonequilibrium transport through double quantum dots

Nonequilibrium electronic transports through a double-QD-Majorana coupling system are studied with a purpose to extract the information to identify Majorana bound states (MBSs). It is found that MBSs can help form various transport processes, including the nonlocal crossed Andreev reflection, local resonant Andreev reflection, and cotunneling, depending on the relative position of two dot levels. These processes enrich the signature of average currents and noise correlations to probe the nature of MBSs. We further demonstrate the switching between the current peaks of crossed Andreev reflection and cotunneling, which is closely related to the nonlocal nature of Majorana fermions. We also propose effective physical pictures to understand these Majorana-assisted transports.     

Topological nature of in‐gap bound states in disordered large‐gap monolayer transition metal dichalcogenides

We propose a physical model based on disordered (a hole punched inside a material) monolayer transition metal dichalcogenides (TMDs) to demonstrate a large‐gap quantum valley Hall insulator. We find an emergence of bound states lying inside the bulk gap of the TMDs. They are strongly affected by spin–valley coupling, rest‐ and kinetic‐mass terms and the hole size. In addition, in the whole range of the hole size, at least two in‐gap bound states with opposite angular momentum, circulating around the edge of the hole, exist.Their topological insulator (TI) feature is analyzed by the Chern number, characterized by spacial distribution of their probabilities and confirmed by energy dispersion curves (energy vs. angular momentum). It not only sheds light on overcoming low‐temperature operating limitation of existing narrow‐gap TIs, but also opens an opportunity to realize valley‐ and spin‐qubits. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

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.     

Ab Initio Simulation of Charge Transfer at the Semiconductor Quantum Dot/TiO2 Interface in Quantum Dot‐Sensitized Solar Cells

Quantum dot‐sensitized solar cells (QDSSCs) have emerged as a promising solar architecture for next‐generation solar cells. The QDSSCs exhibit a remarkably fast electron transfer from the quantum dot (QD) donor to the TiO₂ acceptor with size quantization properties of QDs that allows for the modulation of band energies to control photoresponse and photoconversion efficiency of solar cells. To understand the mechanisms that underpin this rapid charge transfer, the electronic properties of CdSe and PbSe QDs with different sizes on the TiO₂ substrate are simulated using a rigorous ab initio density functional method. This method capitalizes on localized orbital basis set, which is computationally less intensive. Quite intriguingly, a remarkable set of electron bridging states between QDs and TiO₂ occurring via the strong bonding between the conduction bands of QDs and TiO₂ is revealed. Such bridging states account for the fast adiabatic charge transfer from the QD donor to the TiO₂ acceptor, and may be a general feature for strongly coupled donor/acceptor systems. All the QDs/TiO₂ systems exhibit type II band alignments, with conduction band offsets that increase with the decrease in QD size. This facilitates the charge transfer from QDs donors to TiO₂ acceptors and explains the dependence of the increased charge transfer rate with the decreased QD size.     

Universal transport properties of a quantum dot system with a laterally-coupled Majorana zero mode

We present a comprehensive analysis about the transport properties of a quantum dot (QD) system with a side-coupled Majorana zero mode. Our calculation result shows that when the coupling manners between the two leads and QDs are identical, the local Andreev reflection and the interlead normal tunneling have the same magnitude at the zero-bias limit. Accordingly, the zero-bias conductance value is always equal to e²/2h, which is exactly one half of the resonant-tunneling conductance. This result is independent of the level number and the level distribution in the single-QD case, and in the coupled-QD case it is irrelevant to the geometry of the QD molecule. The universal transport property is a powerful evidence for the feasibility to detect the MBSs based on a QD circuit. This result also means that the QD condition is not a key factor to achieve the detection. On the other hand, if the decoupling phenomenon appears, the Majorana zero mode may play a trivial role in contributing to the conductance property.     

Multicolor Light‐Emitting Diodes with MoS2 Quantum Dots

Molybdenum disulfide (MoS₂) quantum dots (QDs) are known for their excitation‐wavelength‐dependent photoluminescent (PL) properties. However, the mechanism of this phenomenon is still unclear. Here, small size MoS₂ QDs with a narrow size distribution are synthesized. Based on the decay study and PL dynamics, a reasonable radiation model is presented to understand the special PL properties, i.e., the carrier recombination in the localized surface defect states generated the PL. Accordingly, this optical property is used to fabricate multicolor light‐emitting devices with the same MoS₂ QDs. The emission color covers the full visible spectrum from blue to red, only by adjusting the thickness of the down‐conversion QD layers.     

Bound States in Coulomb Systems ‐ Old Problems and New Solutions

We analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 10⁴K < T < 10⁵K and not too high densities n < 10²⁴ protons per cm³, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms: (i) formation of bound states occurring by increasing the density from low to moderate values, (ii) the destruction of bound states in the high density region, modelled here by Pauli‐Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T‐p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density‐dependent energy levels, and find the pressure in Hartree‐Fock‐Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aharonov-Bohm Interferometer in a T-Shaped Quantum Dot Embedded in Majorana Bound States *

We theoretically study the spin-dependent transport properties of anAharonov-Bohm (AB) interferometer composed by a T-shaped quantum dot (QD)embedded in Majorana bound states (MBS). We use the equation of motion method tocalculate the conductance across the interferometer. We note that the conductance exhibitssensitive dependence on the MBS-QD coupling strength as well as the polarization strengthof the leads when the phase factor of AB ring changes periodically. The conductance shows a transitionfrom resonance to anti-resonance when the MBS-QD coupling strength changes from small to large. Also, there is different p-dependence conductance when the leads alignment changesfrom parallel to anti-parallel. These findings suggest that such a model could be used for a sensitivedetection of MBS interactions, exploiting the high sensitivity of conductance to the AB phase in theinterferometer.     

Lower‐ and Higher‐Order Nonclassical Properties of Photon Added and Subtracted Displaced Fock States

Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower‐ and higher‐order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower‐ and higher‐order antibunching and sub‐Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel $Q_M$ parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.     

Non‐magnetic defects in the bulk of two‐dimensional topological insulators

We found that non‐magnetic defects in two‐dimensional topological insulators induce bound states of two kinds for each spin orientation: electron‐ and hole‐like states. Depending on the sign of the defect potential these states can be also of two kinds with different distribution of the electron density. The density has a maximum or minimum in the center. A surprising effect caused by the topological order is a singular dependence of the bound‐state energy on the defect potential.

     

Suppression of leakage effect of Majorana bound states in the T-shaped quantum-dot structure

We theoretically study the transport properties in the T-shaped double-quantum-dot structure, by considering the dot in the main channel to be coupled to the Majorana bound state(MBS) at one end of the topological superconducting nanowire.It is found that the side-coupled dot governs the effect of the MBS on the transport behavior. When its level is consistent with the energy zero point, the MBS contributes little to the conductance spectrum. Otherwise, the linear conductance exhibits notable changes according to the inter-MBS coupling manners. In the absence of inter-MBS coupling, the linear conductance value keeps equal to e~2/2 h when the level of the side-coupled dot departs from the energy zero point. However,the linear conductance is always analogous to the MBS-absent case once the inter-MBS coupling comes into play. These findings provide new information about the leakage effect of MBSs in quantum-dot structures.     

Evolution of polarization singularities accompanied by avoided crossing in plasmonic system

The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied. The lateral inversion symmetry of the system, which breaks the in-plane inversion symmetry and up-down mirror symmetry simultaneously, yields abundant polarization states. A complete evolution process with geometry for the polarization states is traced. In the evolution, circularly polarized points (C points) can stem from 3 different processes. In addition to the previously reported processes occurring in an isolated band, a new type of C point appearing in two bands simultaneously due to the avoided band crossing, is observed. Unlike the dielectric system with a similar structure which only supports at-$\varGamma$ bound states in the continuum (BICs), accidental BICs off the $\varGamma$ point are realized in this plasmonic system. This work provides a new scheme of polarization manipulation for the plasmonic systems.