Uniform Exchange Field Research Articles

Reentrant quantum spin Hall effect in the presence of an exchange field

Driven by various physical origins, the interesting reentrant phenomena in quantum Hall effect (QHE), quantum anomalous Hall effect (QAHE), and non-Hermitian systems have been discussed recently. Here, we present that the reentrant phenomena of the quantum spin Hall effect (QSHE) can be achieved by introducing a uniform exchange field into a topological insulator with a four-band model Hamiltonian. Furthermore, it is found that both time-reversal (TR) symmetry broken QSHE and spin-polarized QAHE can simultaneously be generated in the system with proper exchange field strength by inspecting the corresponding edge states. Through analyzing the energy-dependent spin-Chern number ${\ensuremath{\nu}}_{s}$ and transmission in the presence of random disorders, we verify the topological protection and the robustness of induced QSHE and QAHE. Finally, the theoretical realization of reentrant QSHE in a topolectrical circuit is demonstrated. Our work not only extends the reentrant phenomena into the QSHE but also stimulates interest in their realization in different systems.

Suppression of superconducting parameters by correlated quasi-two-dimensional magnetic fluctuations

We consider a clean layered magnetic superconductor in which a continuous magnetic transition takes place inside superconducting state and the exchange interaction between superconducting and magnetic subsystems is weak so that superconductivity is not destroyed at the magnetic transition. An example of such material is RbEuFe$_{4}$As$_{4}$. We investigate the suppression of the superconducting gap and superfluid density by correlated magnetic fluctuations in the vicinity of the magnetic transition. The influence of nonuniform exchange field on superconducting parameters is sensitive to the relation between the magnetic correlation length, $\xi_{h}$, and superconducting coherence length $\xi_{s}$ defining the 'scattering' ($\xi_{h}<\xi_{s}$) and 'smooth' ($\xi_{h}>\xi_{s}$) regimes. As a small uniform exchange field does not affect the superconducting gap and superfluid density at zero temperature, smoothening of the spatial variations of the exchange field reduces its effects on these parameters. We develop a quantitative description of this 'scattering-to-smooth' crossover for the case of quasi-two-dimensional magnetic fluctuations. Since the magnetic-scattering probability varies at the energy scale comparable with the gap, the quasiclassical approximation is not applicable in the crossover region and microscopic treatment is required. We find that the corrections to both the gap and superfluid density grow proportionally to $\xi_{h}$ until it remains much smaller than $\xi_{s}$. When $\xi_{h}$ exceeds $\xi_{s}$, both parameters have much weaker dependence on $\xi_{h}$. Moreover, the gap correction may decrease with increasing of $\xi_{h}$ in the vicinity of the magnetic transition. We also find that the crossover is unexpectedly broad: the standard scattering approximation becomes sufficient only when $\xi_{h}$ is substantially smaller than $\xi_{s}$.

Time-reversal-symmetry broken quantum spin Hall in Lieb lattice

In this paper, the time-reversal (TR) symmetry broken quantum spin Hall (QSH) in Lieb lattice is investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, and it has three different sites in each unit cell. The most distinctive feature of this model is that it contains only one Dirac-cone in the first Brillouin zone, where the upper dispersive band and the lower dispersive band touch the middle zero-energy band at M point and form a cone-like dispersion. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. When the intrinsic SOC is nonzero, all the band structures are separated everywhere in the Brillouin zone and can be characterized by some topological invariants. The exact QSH first put forward by Kane and Mele in 2005 is characterized by the z2 number. The protection from the TR symmetry ensures the gapless crossing in the surface state in the bulk gap. In our model, the presence of the exchange field breaks the TR symmetry, which results in opening a small gap in the crossing point and the z2 topological order is not suitable for the system. This kind of state is a TR symmetry broken QSH, which is characterized by the spin Chern numbers. The spin Chern numbers have a much wider scope of application than z2 index. It is suitable for both TR symmetry system and the TR symmetry broken system. For Lieb lattice ribbons, the spin polarization and the wave-function distributions are obtained numerically. There exists a weak scattering between the counter-propagating states in the TR symmetry broken QSH, and the spin transport along the boundary with a low dissipation replaces the dissipationless spin current in a TR symmetry system. In experiment, such a system can be realized by the two-dimensional Fermi gases in optical lattice with Lieb symmetry. The above conclusions are expected to give theoretical guidance in the spin device and the quantum information.

Phase transition and spin-resolved transport inMoS2nanoribbons

The electronic structure and transport properties of monolayer ${\mathrm{MoS}}_{2}$ are studied using a tight-binding approach coupled with the nonequilibrium Green's function method. A zigzag nanoribbon of ${\mathrm{MoS}}_{2}$ is conducting due to the intersection of the edge states with the Fermi level that is located within the bulk gap. We show that applying a transverse electric field results in the disappearance of this intersection and turns the material into a semiconductor. By increasing the electric field the band gap undergoes a two stage linear increase after which it decreases and ultimately closes. It is shown that in the presence of a uniform exchange field, this electric field tuning of the gap can be exploited to open low energy domains where only one of the spin states contributes to the electronic conductance. This introduces possibilities in designing spin filters for spintronic applications.

The topological quantum phase transitions in Lieb lattice driven by the Rashba SOC and exchange field

The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieb lattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, which is characterized by the single Dirac-cone per Brillouin zone and the middle flat band in the band structure. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. The QSH effect could survive even in the presence of the exchange field. In terms of the first Chern number and the spin Chern number, we study the topological nature and the topological phase transition from the time-reversal symmetry broken QSH effect to the QAH effect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributions are obtained numerically, where the helical edge states and the chiral edge states reveal the non-trivial topological QSH and QAH properties, respectively.

Chiral Surface Modes in Three-Dimensional Topological Insulators

Where chiral modes should appear is an essential question for the quantum anomalous Hall (QAH) effect in three-dimensional topological insulators (3DTIs). In this Letter, we show that in a slab of ferromagnetic 3DTI subjected to a uniform exchange field normal to its top and bottom surfaces, the QAH effect creates a single chiral surface mode delocalized on the side faces. In a nonmagnetic 3DTI, analogously, delocalized helical modes consisting of a pair of oppositely propagating chiral surface modes are produced by the quantum spin Hall effect.

The Effect of Planar Magnetic Inhomogeneities on the Critical Temperature of Ferromagnet–Superconductor Systems

We study superconducting systems with the inhomogeneous effective exchange field background. A model of magnetic superconductor which takes into account the collectivized electrons interaction with the inhomogeneous effective exchange field is used. With local unitary rotation in spinor space we rewrite the Hamiltonian in a new basis where this interaction is diagonal. The problem is reduced to the one with a uniform exchange field but the effective tensor field appears. This method allows us to simplify the Gor’kov, Eilenberger, and Usadel equations in many symmetric cases. We calculate the critical temperature of the superconductor/ferromagnet proximity system in the dirty limit where the ferromagnet has periodic domain structure with planar domain walls.

Spin-polarized Wannier functions for the two-dimensional topological insulators

We propose that the topological properties of the two-dimensional topological insulators can be classified by the evolution of the centers of the spin-polarized Wannier functions. Numerical results are obtained based upon a modified Kane-Mele model with next-nearest-neighbor hopping terms and a uniform exchange field. The centers of the spin-polarized Wannier functions are shown to display different spectral flow patterns in different quantum phases, characterizing the topological structures of the bulk energy bands.

Effect of partial magnetic order on resistivity and thermopower of Ho(Co1−x Al x )2 alloys

The electrical resistivity ρ and the thermopower S of Ho(Co1−xAlx)2 alloys (x = 0 to 0.2) were measured at temperatures from 2 K to 300 K in magnetic fields up to 10 T. While ρ(T) and S(T) of pure HoCo2 reveal abrupt changes at the magnetic ordering temperature TC, indicating a firstorder transition, the temperature variations of both properties across the ordering temperature in Ho(Co1−xAlx)2 alloys clearly show that the type of magnetic transition changes under substitution of Al for Co from first order to second order around x ≈ 0.06. ρ(T) of the Al-substituted samples (x = 0.15 and 0.2) has a very unusual variation at temperatures below TC: in contrast to the expected and usually-observed decrease of ρ(T), the resistivity of Ho(Co1−xAlx)2 alloys (x = 0.15 and 0.2) increases at temperatures below TC. Moreover, the magnetoresistance of these alloys is positive around TC; this is also in a sharp contrast to the usually observed negative magnetoresistance. We show that the anomalous resistivity and magnetoresistance in these alloys are related to the metamagnetic instability of the Co 3d subsystem and to the fluctuating local magnetic susceptibility due to atomic substitution. Due to this fluctuating local magnetic susceptibility, the uniform exchange field of 4f moments induces a non-uniform polarization of the 3d system, with static spatial fluctuations of the local magnetization. This static magnetic disorder gives an additional contribution (ρm) to the electrical resistance in the alloys at temperatures below TC. The degree of this disorder changes with decreasing temperature, resulting in specific variation of ρm with temperature.

Classical Mechanical Analogies in Wide Dirty SFS Junctions

The Usadel equation in a bulk superconductor and a ferromagnet is noticed to be mathematically similar to the equation of motion of a pendulum. A solution technique developed to solve the classic pendulum is applied to analytically determine the order parameter of the singlet state in a superconductor-ferromagnet-superconductor (SFS) trilayer with a constant, uniform exchange field.

Critical velocity of a clean one-dimensional superconductor

We revisit the problem of critical velocity of a clean one-dimensional superconductor. At the level of mean-field theory, we find that the zero-temperature value of the critical velocity\char22{}the uniform velocity of the superfluid condensate at which the superconducting state becomes unstable\char22{}is a factor of $\sqrt{2}$ smaller than the Landau critical velocity. This is in contrast to a prior finding, which held that the critical velocity is equal to the Landau critical velocity. The smaller value of the critical velocity, which our analysis yields, is the result of a pre-emptive Clogston-Chandrasekhar-type discontinuous phase transition, and is an analog of the threshold value of the uniform exchange field of a superconductor previously investigated by Sarma [J. Phys. Chem. Solids 24, 1029 (1963)] and by Maki and Tsuneto [Prog. Theor. Phys. 31, 945 (1964)]. We also consider the impact of nonzero temperature, study critical currents, and examine metastability and its limits in the temperature versus flow-velocity phase diagram. In addition, we comment on the effects of electron scattering by impurities.

Superconductivity in a Strong Spin-Exchange Field

A strong exchange field, such as produced by ferromagnetically aligned impurities in a metal, will tend to polarize the conduction electron spins. If the metal is a superconductor, this will happen only if the spin-exchange field is sufficiently strong compared to the energy gap. When the field is strong enough to break many electron pairs, the self-consistent gap equation is modified and a new type of depaired superconducting ground state occurs. In the idealization of a spatially uniform exchange field with no scattering, it is found that the depaired state has a spatially dependent complex Gorkov field, corresponding to a nonzero pairing momentum in the BCS model. The presence of the electrons from the broken pairs reduces the total current to zero, gives the depaired state some spin polarization, and results in almost normal Sommerfeld specific heat and single-electron tunneling characteristics. The nonzero value of the pairing momentum also gives rise to an unusual anisotropic electrodynamic behavior of the superconductor, as well as to a degenerate ground state and low-lying collective excitations, in accordance with Goldstone's theorem. The effects of scattering in an actual superconducting ferromagnetic alloy have not been studied and may interfere with experimental investigation of the theoretical results found in this paper for the idealized model.

On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor

The effect of a uniform exchange field acting on the spins of the conduction electrons is treated within the framework of the B.C.S. theory of superconductivity. The transition from the superconducting to the normal state is shown to be of the first or second order according to the values of the field.