Topological d-wave superconductor

The hypothetical topologically nontrivial superconducting state of a two-dimensional electron system is discussed in connection with the problem of high-temperature superconductivity of cuprates. Direct numerical solution of the self-consistency equation exhibits two nearly degenerate order parameters which can be formally referred to $d_{x^2 - y^2 }$ and d _xy orbital symmetry. Spontaneous breaking of the time-reversal symmetry can mix these states and form fully gapped chiral d + id superconducting state.     

Alloying and magnetic disordering effects on phase stability of Co2 YGa (Y=Cr,V, and Ni) alloys: A first-principles study

The alloying and magnetic disordering effects on site occupation, elastic property, and phase stability of Co$_{2}Y$Ga ($Y={\rm Cr}$, V, and Ni) shape memory alloys are systematically investigated using the first-principles exact muffin-tin orbitals method. It is shown that with the increasing magnetic disordering degree $y$, their tetragonal shear elastic constant $C'$ (i.e., $(C_{11}-C_{12})/2$) of the $L2_{1}$ phase decreases whereas the elastic anisotropy $A$ increases, and upon tetragonal distortions the cubic phase gets more and more unstable. Co$_{2}$CrGa and Co$_{2}$VGa alloys with $y\geq0.2$ thus can show the martensitic transformation (MT) from $L2_{1}$ to $D0_{22}$ as well as Co$_{2}$NiGa. In off-stoichiometric alloys, the site preference is controlled by both the alloying and magnetic effects. At the ferromagnetism state, the excessive Ga atoms always tend to take the $Y$ sublattices, whereas the excessive Co atom favor the $Y$ sites when $Y={\rm Cr}$, and the excessive $Y$ atoms prefer the Co sites when $Y={\rm Ni}$. The Ga-deficient $Y={\rm V}$ alloys can also occur the MT at the ferromagnetism state by means of Co or V doping, and the MT temperature $T_{\rm M}$ should increase with their addition. In the corresponding ferromagnetism $Y={\rm Cr}$ alloys, nevertheless, with Co or Cr substituting for Ga, the reentrant MT (RMT) from $D0_{22}$ to $L2_{1}$ is promoted and then $T_{\rm M}$ for the RMT should decrease. The alloying effect on the MT of these alloys is finally well explained by means of the Jahn-Teller effect at the paramagnetic state. At the ferromagnetism state, it may originate from the competition between the austenite and martensite about their strength of the covalent banding between Co and Ga as well as $Y$ and Ga.     

Nodal d + id pairing and topological phases on the triangular lattice of Na(x)CoO(2).yH(2)O: evidence for an unconventional superconducting state

We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density x(c) where the normal state Fermi surface crosses the isolated zeros. For spin-singlet pairing, we show that the second-nearest-neighbor (d+id)-wave pairing can be the dominant pairing channel. The gapless critical state at x (c) approximately 0.25 has six Dirac points and is topologically nontrivial with a T3 spin relaxation rate below T(c). This picture provides a possible explanation for the unconventional superconducting state of Na(x)Co O(2). yH(2)O. Analyzing a pairing model with strong correlation using the Gutzwiller projection and symmetry arguments, we study these topological phases and phase transitions as a function of Na doping.     

Magnetic properties and magnetocaloric effect in RE55Co30Al10Si5 (RE = Er and Tm) amorphous ribbons

The magnetic and magnetocaloric effects (MCE) of the amorphous $RE_{55}$Co$_{30}$Al$_{10}$Si$_{5}$ ($RE={\rm Er}$ and Tm) ribbons were systematically investigated in this paper. Compounds with $R ={\rm Er}$ and Tm undergo a second-order magnetic phase transition from ferromagnetic (FM) to paramagnetic (PM) around Curie temperature $T_{\rm C} \sim 9.3$ K and 3 K, respectively. For Er$_{55}$Co$_{30}$Al$_{10}$Si$_{5}$ compound, an obvious magnetic hysteresis and thermal hysteresis were observed at low field below 6 K, possibly due to spin-glass behavior. Under the field change of 0 T-5 T, the maximum values of magnetic entropy change ($-\Delta S_{\rm M}^{\rm max}$) reach as high as 15.6 J/kg$\cdot$K and 15.7 J/kg$\cdot$K for Er$_{55}$Co$_{30}$Al$_{10}$Si$_{5}$ and Tm$_{55}$Co$_{30}$Al$_{10}$Si$_{5}$ compounds, corresponding refrigerant capacity (RC) values are estimated as 303 J/kg and 189 J/kg, respectively. The large MCE makes amorphous $RE_{55}$Co$_{30}$Al$_{10}$Si$_{5 }$ ($RE={\rm Er}$ and Tm) alloys become very attractive magnetic refrigeration materials in the low-temperature region.     

Manipulation of intrinsic quantum anomalous Hall effect in two-dimensional MoYN2CSCl MXene

Quantum anomalous Hall effect (QAHE) is an innovative topological spintronic phenomenon with dissipationless chiral edge states and attracts rapidly increasing attention. However, it has only been observed in few materials in experiments. Here, according to the first-principles calculations, we report that the MXene MoYN$_{2}$CSCl shows a topologically nontrivial band gap of 37.3~meV, possessing QAHE with a Chern number of $C = 1$, which is induced by band inversion between $ {\rm d}_{xz}$ and ${\rm d}_{yz}$ orbitals. Also, the topological phase transition for the MoYN$_{2}$CSCl can be realized via strain or by turning the magnetization direction. Remarkably, MoYN$_{2}$CSCl shows the nodal-line semimetal state dependent on the electron correlation $U$. Our findings add an experimentally accessible and tunable member to the QAHE family, which stands a chance of enriching the applications in spintronics.     

Theoretical study of M6X2 and M6XX' structure (M = Au,Ag; X,X' = S,Se): Electronic and optical properties,ability of photocatalytic water splitting,and tunable properties under biaxial strain

MoS$_{2}$, a transition metal dichalcogenide (TMDC), has attracted significant amount of attention due to its direct bandgap, tunability and optical properties. Recently, a novel structure consisting of MoS$_{2}$ and noble metal nanoclusters has been reported. Inspired by this, first principle calculations are implemented to predict the structures of $M_{6}X_{2}$ and $M_{6}XX'$ ($M= {\rm Au}$, Ag; $X$, $X' ={\rm S}$, Se). The calculated bandgap, band edge position, and optical absorption of these structures prove that the silver compounds (Ag$_{6}X_{2 }$ and Ag$_{6}XX'$) have great potential for catalytic water splitting. In addition, biaxial strain (tensile strain and compressive strain) is applied to adjust the properties of these materials. The bandgap presents a quasi-linear trend with the increase of the applied strain. Moreover, the transition between the direct and indirect bandgap is found. The outstanding electronic and optical properties of these materials provide strong evidence for their application in microelectronic devices, photoelectric devices, and photocatalytic materials.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

Superconductivity with broken time-reversal symmetry

This presentation gives an overview over phenomena occurring in unconventional superconductors with broken time-reversal symmetry. The best-known effect related with broken time-reversal symmetry is intrinsic magnetism observable by μSR. In many cases this magnetism is connected to the appearance of chiral quasiparticle edge states which originate from topological properties of the superconducting order parameter. Time-reversal symmetry can also be broken only locally and has then strong influence of the local quasiparticle spectrum. The existence of vortices with fractional flux pinned strongly on domain walls in time-reversal symmetry breaking superconductors leads to unusual flux flow behavior.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Persistence of Spin Edge Currents in Disordered Quantum Spin Hall Systems

For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance and time-reversal symmetry breaking terms (such as a Rashba spin-orbit coupling and a Zeeman term), it is proved that the spin edge currents persist provided there is a spectral gap and the spin Chern numbers are well-defined and non-trivial. These are sufficient conditions for being in the quantum spin Hall phase. The result materializes the general philosophy that topological insulators are topologically non-trivial bulk systems with persistent edge or surface currents.     

Potential energy curves and analytical potential energy functions of the metastable states of B2^＋＋

The multi-reference configuration interaction method and aug-cc-pvqz （AVQZ） have been used to calculate potential energy curves （PECs） of the singlet and triplet states of the riu and rig symmetry of B2＋＋. All of the four states （^l∏u, ^1∏g, ^3∏u and ^3∏g） are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions （APEFs） of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.     

${ \mathcal P }{ \mathcal T }$-symmetry berry phases,topology and ${ \mathcal P }{ \mathcal T }$-symmetry breaking

We study the complex Berry phases in non-Hermitian systems with parity- and time-reversal $\left({ \mathcal P }{ \mathcal T }\right)$ symmetry. We investigate a kind of two-level system with ${ \mathcal P }{ \mathcal T }$ symmetry. We find that the real part of the the complex Berry phases have two quantized values and they are equal to either 0 or π, which originates from the topology of the Hermitian eigenstates. We also find that if we change the relative parameters of the Hamiltonian from the unbroken-${ \mathcal P }{ \mathcal T }$-symmetry phase to the broken-${ \mathcal P }{ \mathcal T }$-symmetry phase, the imaginary part of the complex Berry phases are divergent at the exceptional points. We exhibit two concrete examples in this work, one is a two-level toys model, which has nontrivial Berry phases; the other is the generalized Su–Schrieffer–Heeger (SSH) model that has physical loss and gain in every sublattice. Our results explicitly demonstrate the relation between complex Berry phases, topology and ${ \mathcal P }{ \mathcal T }$-symmetry breaking and enrich the field of the non-Hermitian physics.     

Pairing symmetry in monolayer of orthorhombic CoSb

Ferromagnetism and superconductivity are generally considered to be antagonistic phenomena in condensed matter physics. Here, we theoretically study the interplay between the ferromagnetic and superconducting orders in a recent discovered monolayered CoSb superconductor with an orthorhombic symmetry and net magnetization, and demonstrate the pairing symmetry of CoSb as a candidate of non-unitary superconductor with time-reversal symmetry breaking. By performing the group theory analysis and the first-principles calculations, the superconducting order parameter is suggested to be a triplet pairing with the irreducible representation of ³B_2u, which displays intriguing nodal points and non-zero periodic modulation of Cooper pair spin polarization on the Fermi surface topologies. These findings not only provide a significant theoretical insight into the coexistence of superconductivity and ferromagnetism, but also reveal the exotic spin polarized Cooper pairing driven by ferromagnetic spin fluctuations in a triplet superconductor.     

Orbital magnetization in semiconductors

This paper theoretically investigates the orbital magnetization of electron-doped (n-type) semiconductor heterostructures and of hole-doped (p-type) bulk semiconductors, which are respectively described by a two-dimensional electron/hole Hamiltonian with both the included Rashba spin--orbit coupling and Zeeman splitting terms. It is the Zeeman splitting, rather than the Rashba spin--orbit coupling, that destroys the time-reversal symmetry of the semiconductor systems and results in nontrivial orbital magnetization. The results show that the magnitude of the orbital magnetization per hole and the Hall conductance in the p-type bulk semiconductors are about 10^-2--10^-1 effective Bohr magneton and 10^-1--1 e²/h, respectively. However, the orbital magnetization per electron and the Hall conductance in the n-type semiconductor heterostructures are too small to be easily observed in experiment.     

Cascade of Quantum Transitions and Magnetocaloric Anomalies in an Open Nanowire

A sequence of magnetocaloric anomalies occurring with the change in a magnetic field H is predicted for an open nanowire with the Rashba spin–orbit coupling and the induced superconducting pairing potential. The nature of such anomalies is due to the cascade of quantum transitions related to the successive changes in the fermion parity of the nanowire ground state with the growth of the magnetic field. It is shown that the critical H_c values fall within the parameter range corresponding to the nontrivial values of the Z₂ topological invariant of the corresponding 1D band Hamiltonian characteristic of the D symmetry class. It is demonstrated that such features in the behavior of the open nanowire are retained even in the presence of Coulomb interactions.     

Surface Majorana flat bands in j=3/2 superconductors with singlet-quintet mixing

Recent experiments [Science Advances 4 eaao4513(2018)] have revealed the evidence of nodal-line superconductivity in half-Heusler superconductors, e.g., YPt Bi. Theories have suggested the topological nature of such nodal-line superconductivity and proposed the existence of surface Majorana flat bands on the(111) surface of half-Heusler superconductors.Due to the divergent density of states of the surface Majorana flat bands, the surface order parameter and the surface impurity play essential roles in determining the surface properties. We study the effect of the surface order parameter and the surface impurity on the surface Majorana flat bands of half-Heusler superconductors based on the Luttinger model. To be specific, we consider the topological nodal-line superconducting phase induced by the singlet-quintet pairing mixing, classify all the possible translationally invariant order parameters for the surface states according to irreducible representations of C_(3v)point group, and demonstrate that any energetically favorable order parameter needs to break the time-reversal symmetry. We further discuss the energy splitting in the energy spectrum of surface Majorana flat bands induced by different order parameters and non-magnetic or magnetic impurities. We propose that the splitting in the energy spectrum can serve as the fingerprint of the pairing symmetry and mean-field order parameters. Our theoretical prediction can be examined in the future scanning tunneling microscopy experiments.     

Accurate calculation of the elastic scattering properties of ^7Li atoms at ultralow temperatures

The elastic scattering properties for collisions between two ^7Li atoms are investigated in the cold and ultracold regimes separately. Based on recent theoretical and experimental results, we present the improved hybrid potentials for the singlet X^1 ∑g^＋ and triplet a^3 ∑u^＋ ground states of the Li2, Our calculated values for the scattering lengths α and the effective ranges re are compared with previous ones, and found them to be in good agreement. The scattering lengths are 34.6α0 for the singlet state and -27.6α0 for the triplet state. Shape resonances occur in the collisions at low energies. We also calculate the total cross sections and the energy positions of shape resonances for both X^1 ∑g^＋ and a^3 ∑u^＋ states.     

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.     

铁基超导中拓扑量子态研究进展

铁基超导体和拓扑量子材料是近年来凝聚态物理两个重要的前沿研究方向.铁基超导体中是否能衍生出非平庸的拓扑现象是一个非常有意义的问题.本文从晶体对称性、布里渊区高对称点附近的有效模型以及自旋轨道耦合相互作用三个方面具体分析了铁基超导的电子结构的基本特点.在此基础上,重点阐述铁基超导的正常态、临近超导的长程有序态以及超导态中非平庸的拓扑量子态是如何衍生的;具体介绍了相关的理论模型以及结果,回顾了相关的实验进展,展望了该领域的发展前景.