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.     

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.     

Norm-overlap formula for Hartree-Fock-Bogoliubov states with odd number parity

A formula to calculate the norm overlap between Hartree-Fock-Bogoliubov (HFB) states with odd number parity (one quasi-particle excited states) is derived with the help of Grassmann numbers and Fermion coherent states. The final formula is expressed in terms of a product of the Pfaffian for a neighboring even-even system (the zero quasi-particle state), and an extra factor consisting of the Bogoliubov transformation matrix and the anti-symmetric matrix in Thouless? HFB ansatz for the even-even system.     

Pfaffian Expressions for Random Matrix Correlation Functions

It is well known that Pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices. Moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of Pfaffians. In this article, we review the formulations and applications of Pfaffian formulas. For that purpose, we first present the general Pfaffian expressions in terms of the corresponding skew orthogonal polynomials. Then we clarify the relation to Eynard and Mehta’s determinant formula for hermitian matrix models and explain how the evaluation is simplified in the cases related to the classical orthogonal polynomials. Applications of Pfaffian formulas to random matrix theory and other fields are also mentioned.     

Understanding the 5/2 fractional quantum Hall effect without the Pfaffian wave function

It is demonstrated that an understanding of the 5/2 fractional quantum Hall effect can be achieved within the composite fermion theory without appealing to the Pfaffian wave function. The residual interaction between composite fermions plays a crucial role in establishing incompressibility at this filling factor. This approach has the advantage of being amenable to systematic perturbative improvements, and produces ground as well as excited states. It, however, does not relate to non-Abelian statistics in any obvious manner.     

拓扑绝缘体简介

拓扑绝缘体是最近几年发现的一种全新的物质形态,由于其独特的能带结构,具有零质量的狄拉克费米子及其相关的奇妙物理特性,近些年来引起了人们的广泛关注.同时,它还展现出在自旋电子学和量子计算等领域巨大的应用前景.     

Index theorem for the zero modes of Majorana fermion vortices in chiral p-wave superconductors

We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D (p(x)+ip(y))-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion field theory where the first and second components are related by parity reversal and Hermitian conjugation.     

Fractional Josephson current through a Luttinger liquid with topological excitations

Recently, the Majorana fermion has received great attentions due to its promising application in the fault-tolerant quantum computation. This application requires more accessible methods to detect the motion and braiding of the Majorana fermions. We use a Luttinger liquid ring to achieve this goal, where the ring geometry is nontrivial in the sense that it leads to fermion-parity-dependent topological excitations. First, we briefly review the essential physics of the Luttinger liquid and the Majorana fermion, in order to give an introduction of the general framework used in the following main work. Then, we theoretically investigated the DC Josephson effect between two topological superconductors via a Luttinger liquid ring. A low-energy effective Hamiltonian is derived to show the existence of the fractional Josephson current. Also, we find that the amplitude of the Josephson current, which is determined by the correlation function of Luttinger liquid, exhibits different behaviors in terms of the parity of Luttinger liquid due to the topological excitations. Our results suggest a possible method to detect the Majorana fermions and their tunneling process.     

无相互作用费米量子信道直积态容量研究

用费米线性光学方法,提出无相互作用费米量子信道物理模型.用平稳量子高斯态协方差矩阵性质及Majorization不等式理论,推导出在平稳高斯输入态下费米量子信道最小输出熵的表达式.利用在n模费米系统添加一个额外模的方法,得到平稳高斯态和高斯态输出熵的关系|利用此关系式,借助在高斯输入态下费米信道最小输出熵值是可达的猜测,推导出无相互作用费米信道直积态容量的表达式.最后,用最小输出熵的迭代算法验证已推出的费米信道最小输出熵表达式正确性,数值计算结果表明:对于带噪声的无相互作用费米量子信道,已推出最小输出熵与数值计算结果的吻合度可以达到10e-9.     

Axial anomalies of Lifshitz fermions

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z = 3 which is minimally coupled to geometry in 3+1 space‐time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the η‐invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non‐relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Hořava–Lifshitz theory and find that the index is non‐zero provided that the space‐time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2) × U(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Hořava–Lifshitz theory arising at λ = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non‐relativistic quantum field theories are also discussed.     

无相互作用费米量子信道直积态容量研究

用费米线性光学方法,提出无相互作用费米量子信道物理模型.用平稳量子高斯态协方差矩阵性质及Majorization不等式理论,推导出在平稳高斯输入态下费米量子信道最小输出熵的表达式.利用在n模费米系统添加一个额外模的方法,得到平稳高斯态和高斯态输出熵的关系;利用此关系式,借助在高斯输入态下费米信道最小输出熵值是可达的猜测...     

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.     

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.     

Contributed report: Flavor anarchy for Majorana neutrinos

We argue that neutrino flavor parameters may exhibit features that are very different from those of quarks and charged leptons. Specifically, within the Proggatt-Nielsen (FN) framework, charged fermion parameters depend on the ratio between two scales, while for neutrinos a third scale — that of lepton number breaking — is involved. Consequently, the selection rules for neutrinos may be different. In particular, if the scale of lepton number breaking is similar to the scale of horizontal symmetry breaking, neutrinos may become flavor-blind even if they carry different horizontal charges. This provides an attractive mechanism for neutrino flavor anarchy.     

Empirical investigation of a field theory formula and Black's formula for the price of an interest-rate caplet

The industry standard for pricing an interest-rate caplet is Black's formula. Another distinct price of the same caplet can be derived using a quantum field theory model of the forward interest rates. An empirical study is carried out to compare the two caplet pricing formulae. Historical volatility and correlation of forward interest rates are used to generate the field theory caplet price; another approach is to fit a parametric formula for the effective volatility using market caplet price. The study shows that the field theory model generates the price of a caplet and cap fairly accurately. Black's formula for a caplet is compared with field theory pricing formula. It is seen that the field theory formula for caplet price has many advantages over Black's formula.     

A Chern-Simons effective field theory for the Pfaffian quantum Hall state

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)₂ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.     

Non-Abelian statistics of half-quantum vortices in p-wave superconductors

Excitation spectrum of a half-quantum vortex in a p-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core we derive the non-Abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.