Topological Distillation by Principal Component Analysis in Disordered Fractional Quantum Hall States

We study the behavior of two-dimensional electron gas in the fractional quantum Hall(FQH) regime in the presence of disorder potential. The principal component analysis is applied to a set of disordered Laughlin ground state model wave function to enable us to distill the model wave function of the pure Laughlin state.With increasing the disorder strength, the ground state wave function is expected to deviate from the Laughlin state and eventually leave the FQH phase. We investigate the phase transition from the Laughlin state to a topologically trivial state by analyzing the overlap between the random sample wave functions and the distilled ground state wave function. It is proposed that the cross point of the principal component amplitude and its counterpart is the critical disorder strength, which marks the collapse of the FQH regime.     

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.     

Narrowing of topological bands due to electronic orbital degrees of freedom

The fractional quantum Hall effect has been predicted to occur in the absence of magnetic fields and at high temperature in lattice systems that have flat bands with a nonzero Chern number. We demonstrate that orbital degrees of freedom in frustrated lattice systems lead to a narrowing of topologically nontrivial bands. This robust effect does not rely on fine-tuned long-range hopping parameters and is directly relevant to a wide class of transition-metal compounds.     

Helical Luttinger liquid in topological insulator nanowires

We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.     

Topological surface States in three-dimensional magnetic insulators

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the three-sphere to the two-sphere. This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.     

Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime.We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su-Schrieffer Heeger(SSH)model via designing the effective optomechanical coupling.Especially,the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the opto mechanical coupling.We stress that the to pological phase transition is mainly induced by the decay of the cavity field,which is counter-intuitive since the dissipation is usually detrimental to the system.Also,we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice.We find that the quantum st ate transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields.Our scheme provides the fundamental and the insightful explanations towards the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform.     

Existence of Majorana fermions and topological order in nodal superconductors with spin-orbit interactions in external magnetic fields

We demonstrate that Majorana fermions exist in edges of systems and in a vortex core even for superconductors with nodal excitations such as the d-wave pairing state under a particular but realistic condition in the case with an antisymmetric spin-orbit interaction and a nonzero magnetic field below the upper critical field. We clarify that the Majorana fermion state is topologically protected in spite of the presence of bulk gapless nodal excitations, because of the existence of a nontrivial topological number. Our finding drastically enlarges target systems where we can explore the Majorana fermion state.     

Topological order at nonzero temperature

We propose a definition for topological order at nonzero temperature in analogy to the usual zero temperature definition that a state is topologically ordered, or "nontrivial", if it cannot be transformed into a product state (or a state close to a product state) using a local (or approximately local) quantum circuit. We prove that any two-dimensional Hamiltonian which is a sum of commuting local terms is not topologically ordered at T > 0. We show that such trivial states cannot be used to store quantum information using certain stringlike operators. This definition is not too restrictive, however, as the four dimensional toric code does have a nontrivial phase at nonzero temperature.     

Thickness-induced violation of de Haas-van Alphen effect through exact analytical solutions at a one-electron and a one-composite fermion level

A systematic study of the energetics of electrons in an interface in a magnetic field is reported with exact analytical calculations based on a Landau level (LL) picture, by serious consideration of the finite thickness of the quantum well (QW). The approach is physically transparent and subtly different in its line of reasoning from standard methods avoiding any semi-classical approximation. We find “internal” phase transitions (at partial LL filling) for magnetisation and susceptibility that are not captured by other approaches and that give rise to nontrivial violations of the standard de Haas-van Alphen periods, in a manner that reproduces the exact quantal astrophysical behaviours in the limit of full three-dimensional (3D) space. Upon inclusion of Zeeman splitting, additional features are also found, such as global energy minima originating from the interplay of QW, Zeeman and LL Physics, while a corresponding calculation in a composite fermion picture with Λ-levels, leads to new predictions on magnetic properties of an interacting electron liquid. By pursuing the same line of reasoning for a topologically nontrivial system with a relativistic spectrum, we find evidence that similar effects might be operative in the dimensionality crossover of 3D strong topological insulators to 2D topological insulator quantum wells.     

Control of topological phase transitions in Dirac semimetal films by exchange fields

The exchange field effects on topological Dirac semimetal(DSM) films are discussed in this article. A topological phase transition can be controlled by tuning the exchange field together with the quantum confinement effects. What is more interesting is that the system can transit into the quantum anomalous Hall(QAH) state from the topologically trivial state(Z_2 = 0) or from the topologically nontrivial state(Z_2 = 1), depending on the thickness of the DSM films. This provides a useful mechanism to realize the QAH state from the DSM.     

Topological phases and phase transitions on the honeycomb lattice

We investigate possible phase transitions among the different topological insulators in a honeycomb lattice under the combined influence of spin-orbit couplings and staggered magnetic flux. We observe a series of topological phase transitions when tuning the flux amplitude, and find topologically nontrivial phases with high Chern number or spin-Chern number. Through tuning the exchange field, we also find a new quantum state which exhibits the electronic properties of both the quantum spin Hall state and quantum anomalous Hall state. The topological characterization based on the Chern number and the spin-Chern number are in good agreement with the edge-state picture of various topological phases.     

二维声子晶体中简单旋转操作导致的拓扑相变

构建了一种简单的二维声子晶体:由两个横截面为三角形的钢柱所组成的复式元胞按三角点阵的形式排列在空气中,等效地形成了一个蜂巢点阵结构.当三角形钢柱的取向与三角点阵的高对称方向一致时,整个体系具有C_(6v)对称性.研究发现:在保持钢柱填充率不变的条件下,只需要将所有三角柱绕着自己的中心旋转180°,就可实现二重简并的p态和d态在布里渊区中心Γ点处的频率反转,且该能带反转过程实质上是一个拓扑相变过程.通过利用Γ点的P态和d态的空间旋转对称性,构造了一个赝时反演对称性,并在声学系统中实现了类似于电子系统中量子自旋霍尔效应的赝自旋态.随后通过k·p微扰法导出了Γ点附近的有效哈密顿量,并分别计算了拓扑平庸和非平庸系统的自旋陈数,揭示了能带反转和拓扑相变的内在联系.最后通过数值模拟演示了受到拓扑不变量保护的声波边界态的单向传输行为和对缺陷的背向散射抑制.文中所研究的声波体系,尽管材料普通常见,但其拓扑带隙的相对宽度超过21%,比已报道的类似体系的带隙都要宽,且工作原理涵盖从次声波到超声波的很大频率范围,从而在实际应用上具有较大的优势和潜力.     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

The lattices with the continuous vorticity as a model for fractional quantum hall effect

It was shown that the including spin of 2d electrons at high magnetic field is possible to remove the divergences in the cores of the vortex lattice and construct the topologically stable states. These states can be considered as the lattices of skyrmions where the unit cell is mapped on the whole sphere of spin directions. That gives the gapped ground state for electrons and can be used as a model for fractional quantum Hall effect.     

Exact chiral spin liquid with non-Abelian anyons

We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle. This CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSL's separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number +/-1) CSL obey non-Abelian statistics.     

Chern-Simons term by spontaneous symmetry breaking in an abelian Higgs model

We show that the Chern-Simons terms can be generated by spontaneous symmetry breaking in a generalized abelian Higgs model in 2+1 dimensions. We analyze this model in some detail and show the existence of two (neutral) vortices of finite energy in each topologically nontrivial sector.     

Additional acceleration and collimation of relativistic electron beams by magnetic field resonance at very high intensity laser interaction

For the interpretation of experiments for acceleration of electrons at interaction up to nearly GeV energy in laser produced plasmas, we present a new model using interaction magnetic fields. In addition to the ponderomotive acceleration of highly relativistic electrons at the interaction of very short and very intense laser pulses, a further acceleration is derived from the interaction of these electron beams with the spontaneous magnetic fields of about 100 MG. This additional acceleration is the result of a laser-magnetic resonance acceleration (LMRA) around the peak of the azimuthal magnetic field. This causes the electrons to gain energy within a laser period. Using a Gaussian laser pulse, the LMRA acceleration of the electrons depends on the laser polarization. Since this is in the resonance regime, the strong magnetic fields affect the electron acceleration considerably. The mechanism results in good collimated high energetic electrons propagating along the center axis of the laser beam as has been observed by experiments and is reproduced by our numerical simulations. PACS 41.75.Jv; 52.38.Kd; 52.65.Cc     

Pressure-Induced Topological and Structural Phase Transitions in an Antiferromagnetic Topological Insulator

Recently,natural van der Waals heterostructures of(MnBi_2 Te_4)_m(Bi_2 Te_3)_n have been theoretically predicted and experimentally shown to host tunable magnetic properties and topologically nontrivial surface states.We systematically investigate both the structural and electronic responses of MnBi_2 Te_4 and MnBi_4 Te_7 to external pressure.In addition to the suppression of antiferromagnetic order,MnBi_2 Te_4 is found to undergo a metalsemiconductor-metal transition upon compression.The resistivity of MnBi_4 Te_7 changes dramatically under high pressure and a non-monotonic evolution of p(T) is observed.The nontrivial topology is proved to persist before the structural phase transition observed in the high-pressure regime.We find that the bulk and surface states respond differently to pressure,which is consistent with the non-monotonic change of the resistivity.Interestingly,a pressure-induced amorphous state is observed in MnBi_2 Te_4,while two high-pressure phase transitions are revealed in MnBi_4 Te_7.Our combined theoretical and experimental research establishes MnBi_2 Te_4 and MnBi_4 Te_7 as highly tunable magnetic topological insulators,in which phase transitions and new ground states emerge upon compression.     

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.