Non-Hermitian Moiré Valley Filter.

A valley filter capable of generating a valley-polarized current is a crucial element in valleytronics, yet its implementation remains challenging. Here, we propose a valley filter made of a graphene bilayer which exhibits a 1D moiré pattern in the overlapping region of the two layers controlled by heterostrain. In the presence of a lattice modulation between layers, electrons propagating in one layer can have valley-dependent dissipation due to valley asymmetric interlayer coupling, thus giving rise to a valley-polarized current. Such a process can be described by an effective non-Hermitian theory, in which the valley filter is driven by a valley-resolved non-Hermitian skin effect. Nearly 100% valley polarization can be achieved within a wide parameter range and the functionality of the valley filter is electrically tunable. The non-Hermitian topological scenario of the valley filter ensures high tolerance against imperfections such as disorder and edge defects. Our work opens a new route for efficient and robust valley filters while significantly relaxing the stringent implementation requirements.

Tomasch Oscillations as Above-Gap Signature of Topological Superconductivity.

The identification of topological superconductors usually involves searching for in-gap modes that are protected by topology. However, in current experimental settings, the smoking-gun evidence of these in-gap modes is still lacking. In this Letter, we propose to support the distinction between two-dimensional conventional s-wave and topological p-wave superconductors by above-gap transport signatures. Our method utilizes the emergence of Tomasch oscillations of quasiparticles in a junction consisting of a superconductor sandwiched between two metallic leads. We demonstrate that the behavior of the oscillations in conductance as a function of the interface barriers provides a distinctive signature for s-wave and p-wave superconductors. Specifically, the oscillations become weaker as the barrier strength increases in s-wave superconductors, while they become more pronounced in p-wave superconductors, which we prove to be a direct manifestation of the pairing symmetries. Our method can serve as a complimentary probe for identifying some classes of topological superconductors through the above-gap transport.

Entanglement of Nambu Spinors and Bell Inequality Test without Beam Splitters.

The identification of electronic entanglement in solids remains elusive so far, which is owed to the difficulty of implementing spinor-selective beam splitters with tunable polarization direction. Here, we propose to overcome this obstacle by producing and detecting a particular type of entanglement encoded in the Nambu spinor or electron-hole components of quasiparticles excited in quantum Hall edge states. Because of the opposite charge of electrons and holes, the detection of the Nambu spinor translates into a charge-current measurement, which eliminates the need for beam splitters and assures a high detection rate. Conveniently, the spinor correlation function at fixed effective polarizations derives from a single current-noise measurement, with the polarization directions of the detector easily adjusted by coupling the edge states to a voltage gate and a superconductor, both having been realized in experiments. We show that the violation of Bell inequality occurs in a large parameter region. Our Letter opens a new route for probing quasiparticle entanglement in solid-state physics exempt from traditional beam splitters.

Photon-Induced Weyl Half-Metal Phase and Spin Filter Effect from Topological Dirac Semimetals.

Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as Na_{3}Bi and Cd_{2}As_{3}, are regarded as carrying the Z_{2} topological charge in addition to the chiral charge. We study the Floquet phase transition of Z_{2} topological DSMs subjected to a beam of circularly polarized light. Owing to the resulting interplay of the chiral and Z_{2} charges, the Weyl nodes are not only chirality dependent but also spin dependent, which constrains the behavior in creation and annihilation of the pair of Weyl nodes. Interestingly, we find a novel phase: One spin band is in the Weyl semimetal phase while the other is in the insulator phase, and we dub it the Weyl half-metal (WHM) phase. We further study the spin-dependent transport in a Dirac-Weyl semimetal junction and find a spin filter effect as a fingerprint of the existence of the WHM phase. The proposed spin filter effect, based on the WHM bulk band, is highly tunable in a broad parameter regime and robust against magnetic disorder, which is expected to overcome the shortcomings of the previously proposed spin filter based on the topological edge or surface states. Our results offer a unique opportunity to explore the potential applications of topological DSMs in spintronics.

Quantum Oscillations of the Positive Longitudinal Magnetoconductivity: A Fingerprint for Identifying Weyl Semimetals.

Weyl semimetals (WSMs) host charged Weyl fermions as emergent quasiparticles. We develop a unified analytical theory for the anomalous positive longitudinal magnetoconductivity (LMC) in a WSM, which bridges the gap between the classical and ultraquantum approaches. More interestingly, the LMC is found to exhibit periodic-in-1/B quantum oscillations, originating from the oscillations of the nonequilibrium chiral chemical potential. The quantum oscillations, superposed on the positive LMC, are a remarkable fingerprint of a WSM phase with a chiral anomaly, whose observation is a valid criteria for identifying a WSM material. In fact, such quantum oscillations were already observed by several experiments.

Prediction of a topological p + ip excitonic insulator with parity anomaly.

Excitonic insulators are insulating states formed by the coherent condensation of electron and hole pairs into BCS-like states. Isotropic spatial wave functions are commonly considered for excitonic condensates since the attractive interaction among the electrons and the holes in semiconductors usually leads to s-wave excitons. Here, we propose a new type of excitonic insulator that exhibits order parameter with p + ip symmetry and is characterized by a chiral Chern number Cc = 1/2. This state displays the parity anomaly, which results in two novel topological properties: fractionalized excitations with e/2 charge at defects and a spontaneous in-plane magnetization. The topological insulator surface state is a promising platform to realize the topological excitonic insulator. With the spin-momentum locking, the interband optical pumping can renormalize the surface electrons and drive the system towards the proposed p + ip instability.

Time-reversal invariant resonant backscattering on a topological insulator surface driven by a time-periodic gate voltage.

We study the scattering of the Dirac electrons by a point-like nonmagnetic impurity on the surface of a topological insulator, driven by a time-periodic gate voltage. It is found that, due to the doublet degenerate crossing points of different Floquet sidebands, resonant backscattering can happen for the surface electrons, even without breaking the time-reversal (TR) symmetry of the topological surface states (TSSs). The energy spectrum is reshuffled in a way quite different from that for the circularly polarized light, so that new features are exhibited in the Friedel oscillations of the local charge and spin density of states. Although the electron scattering is dramatically modified by the driving voltage, the 1/ρ scale law of the spin precession persists for the TSSs. The TR invariant backscattering provides a possible way to engineer the Dirac electronic spectrum of the TSSs, without destroying the unique property of spin-momentum interlocking of the TSSs.

Analytical theory and possible detection of the ac quantum spin Hall effect.

We develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means.

Theory of Inverse Edelstein Effect of The Surface States of A Topological Insulator.

The surface states of three-dimensional topological insulators possess the unique property of spin-momentum interlocking. This property gives rise to the interesting inverse Edelstein effect (IEE), in which an applied spin bias µ is converted to a measurable charge voltage difference V. We develop a semiclassical theory for the IEE of the surface states of Bi2Se3 thin films, which is applicable from the ballistic regime to diffusive regime. We find that the efficiency of the spin-charge conversion, defined as γ = V/µ, exhibits a universal dependence on the ratio between sample size and electron mean free path. The efficiency increases from γ = π/4 in the ballistic limit to γ = π in the diffusive limit, suggesting that sufficient strength of impurity scattering is favorable for the IEE.

Topological phases of the kicked Harper-Kitaev model with ultracold atoms.

We propose using ultracold atoms trapped in a one-dimensional periodically driven optical lattice to realize the Harper-Kitaev model, where the on-site energies are periodically kicked. Such a system provides a natural platform to study both Chern insulators and Majorana fermions. Based on calculating the quasienergy spectra, we find that both Floquet Majorana modes and Hall chiral edge modes could appear at the sample boundary in the gaps between the quasienergy bands. We also study the competition of topological superconductor and Chern insulator states in the model. We calculate the [Formula: see text] index and Floquet Chern number to characterize the above two different topological states, including the topological phase transitions in the kicked Harper-Kitaev model with the increase in the strength of the kick.

Topological spin and valley pumping in silicene.

We propose to realize adiabatic topological spin and valley pumping by using silicene, subject to the modulation of an in-plane ac electric field with amplitude Ey and a vertical electric field consisting of an electrostatic component and an ac component with amplitudes and . By tuning and , topological valley pumping or spin-valley pumping can be achieved. The low-noise valley and spin currents generated can be useful in valleytronic and spintronic applications. Our work also demonstrates that bulk topological spin or valley pumping is a general characteristic effect of two-dimensional topological insulators, irrelevant to the edge state physics.

π Spin Berry Phase in a Quantum-Spin-Hall-Insulator-Based Interferometer: Evidence for the Helical Spin Texture of the Edge States.

The quantum spin Hall insulator is characterized by helical edge states, with the spin polarization of the electron being locked to its direction of motion. Although the edge-state conduction has been observed, unambiguous evidence of the helical spin texture is still lacking. Here, we investigate the coherent edge-state transport in an interference loop pinched by two point contacts. Because of the helical character, the forward interedge scattering enforces a π spin rotation. Two successive processes can only produce a nontrivial 2π or trivial 0 spin rotation, which can be controlled by the Rashba spin-orbit coupling. The nontrivial spin rotation results in a geometric π Berry phase, which can be detected by a π phase shift of the conductance oscillation relative to the trivial case. Our results provide smoking gun evidence for the helical spin texture of the edge states. Moreover, it also provides the opportunity to all electrically explore the trajectory-dependent spin Berry phase in condensed matter.

Zeeman-Field-Tuned Topological Phase Transitions in a Two-Dimensional Class-DIII Superconductor.

We investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field. Based on the spin Chern number theory, we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field, including a quantum spin Hall-like phase, quantum anomalous Hall-like phases with total Chern number C = -2, -1, 1 and 2, and a topologically trivial superconductor phase. The BdG band gap closes at each boundary of the phase transitions. Furthermore, we demonstrate that the zero bias conductance provides clear transport signatures of the different topological phases, which are robust against symmetry-breaking perturbations.

Universal anyons at the irradiated surface of topological insulator.

Anyons have recently received great attention due to their promising application in topological quantum computation. The best validated system that enjoys the anyonic excitations are the Laughlin states. The quasi-particles in Laughlin states are neither fermions nor bosons but possess the discrete statistical angle θ = π/m, with m being an integer. Here we report a possible realization of the universal Abelian anyons, whose statistical angle can be tuned continuously by external parameters and can take any arbitrary values interpolating θ = 0 and θ = π. The proposed setup is the surface state of a three dimensional topological insulator driven by an amplitude-modulated circularly-polarized light. It is found that the external field leads to a particular Floquet phase, which is a two-spatial-dimensional analogy of the Weyl semimetal phase in the Floquet first Brillouin zone. The chiral anomaly of this phase results in a U(1) Chern-Simons gauge theory with a tunable Floquet Chern number. Owing to this underlying gauge field theory, the irradiated surface of topological insulator constitutes a promising platform for the observation of the universal anyons.

Long-range Cooper pair splitter with high entanglement production rate.

Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.

Entanglement, subsystem particle numbers and topology in free fermion systems.

We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from other states, and can be used to establish a new topological index for the system. Furthermore, we apply the new topological invariant to a disordered system and show that a topological phase transition occurs when the disorder strength is increased beyond a critical value. It is also shown that the subsystem particle number fluctuation displays behavior very similar to that of the entanglement entropy. This provides a lower-bound estimation for the entanglement entropy, which can be utilized to obtain an estimate of the entanglement entropy experimentally.

Stabilization of the quantum spin Hall effect by designed removal of time-reversal symmetry of edge states.

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the ferromagnetic region and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes," the QSH effect becomes robust against symmetry-breaking perturbations.

Kosterlitz-Thouless transition in disordered two-dimensional topological insulators.

The disorder-driven metal-insulator transition in the quantum spin Hall systems is studied by scaling analysis of the Thouless conductance g. Below a critical disorder strength, the conductance is independent of the sample size M, an indication of critically delocalized electron states. The calculated beta function ß = d ln g/d ln M indicates that the metal-insulator transition is of Kosterlitz-Thouless (KT) type, which is characterized by binding and unbinding of vortex-antivortex pairs of the local currents. The KT-like metal-insulator transition is a basic characteristic of the quantum spin Hall state, being independent of the time-reversal symmetry.

Connection of edge states to bulk topological invariance in a quantum spin Hall state.

We propose a topological understanding of general characteristics of edge states in a quantum spin Hall phase without considering any symmetries. It follows from the requirement of gauge invariance that either the energy gap or the gap in the spectrum of the projected spin operator needs to close on the sample edges. Based upon the Kane-Mele model with a uniform Zeeman field and a smooth confining potential near the sample boundaries, we demonstrate the existence of gapless edge states in the absence of time-reversal symmetry and their robust properties against impurities. These gapless edge states are protected by the band topology alone, rather than any symmetries.

Electron entanglement detected by quantum spin Hall systems.

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell's inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell's inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.