Effective Time-reversal Symmetry Research Articles

Giant X-Ray Circular Dichroism in a Time-Reversal Invariant Antiferromagnet.

X-ray circular dichroism, arising from the contrast in X-ray absorption between opposite photon helicities, serves as a spectroscopic tool to measure the magnetization of ferromagnetic materials and identify the handedness of chiral crystals. Antiferromagnets with crystallographic chirality typically lack X-ray magnetic circular dichroism because of time-reversal symmetry, yet exhibit weak X-ray natural circular dichroism. Here, the observation of giant natural circular dichroism in the Ni L3-edge X-ray absorption of Ni3TeO6 is reported, a polar and chiral antiferromagnet with effective time-reversal symmetry. To unravel this intriguing phenomenon, a phenomenological model is proposed that classifies the movement of photons in a chiral crystal within the same symmetry class as that of a magnetic field. The coupling of X-ray polarization with the induced magnetization yields giant X-ray natural circular dichroism, revealing typical ferromagnetic behaviors allowed by the symmetry in an antiferromagnet, i.e., the altermagnetism of Ni3TeO6. The findings provide evidence for the interplay between magnetism and crystal chirality in natural optical activity. Additionally, the first example of a new class of magnetic materials exhibiting circular dichroism is established with time-reversalsymmetry.

Ferromagnetic insulating substrate for magnetic proximity studies: LaCoO3thin film.

Ferromagnetic insulators (FMIs) are intriguing not only due to their rare nature, but also due to their potential applications in spintronics and various electronic devices. One of its key promising applications is based on an FMI-induced magnetic proximity effect, which can impose an effective time-reversal symmetry breaking on the target ultrathin layer to realize novel emergent phenomena. Here, we conduct systematic studies on thin film LaCoO3, an insulator known to be ferromagnet under tensile strain, with varying thicknesses, to establish it as an FMI platform to be integrated in heterostructures. The optimal thickness of the LaCoO3layer, providing a smooth surface and robust ferromagnetism with large remanence, is determined. A heterostructure consisting of an ultrathin target layer (2 uc SrRuO3), the LaCoO3FMI layer, and the La0.5Sr0.5CoO3conducting layer has been fabricated and the angle-resolved photoemission spectroscopy measurement on the multi-layer system demonstrates a sharp Fermi edge and a well-defined Fermi surface without the charging effect. This demonstrates the feasibility of the proposed heterostructure using LaCoO3thin film as the FMI layer, and further lays a groundwork to investigate the magnetic proximity induced phases in quantum materials.

Majorana edge states in Kitaev chains of the BDI symmetry class

Majorana edge states in Kitaev chains possessing an effective time reversal symmetry with one fermionic site per unit cell are studied. For a semi-infinite chain the equations for the wave functions of Majorana zero modes can be reduced to a single Wiener-Hopf equation, which has an exact analytical solution. We use this solution to determine the asymptotic behaviors of the Majorana wave functions at large distances from the edge of the chain for several infinite-range models described in the literature with focus on a model with slow power-law falloff of pairing and hopping amplitudes. For these models we also determine the asymptotic behavior of the energy of the fermionic state composed of two Majorana modes in the limit of long (finite) Kitaev chains.

Magnon Hall effect in antiferromagnetic lattices

Topology applied to condensed matter is an important area of research and technology, and topological magnetic excitations have recently become an active field of study. This paper presents a general discussion of magnon Hall transport in two-dimensional antiferromagnets. Although the Chern number is zero for a collinear antiferromagnet, we offer a general discussion that can be used in the more general case. First, we study the Union Jack lattice, where an effective time-reversal symmetry is broken, making the system display the magnon Hall effect. Then, we investigate the brick-wall lattice where such symmetry is present. Consequently, we have a phenomenon similar to the quantum spin Hall effect in electronic systems. Both lattices have not yet been studied from the topological point of view. The coexistence of opposite spin polarization in an antiferromagnet resembles the electron spin in various transport phenomena. We study magnon transport in the lattices mentioned above with Dzyaloshinskii-Moriya interaction and easy-axis single-ion anisotropy. We calculate the Berry curvature from the eigenvalues of the Hamiltonian. From that, we plot the spin Hall and thermal Hall conductivities, as well as the spin Nernst coefficient, as functions of the temperature. In the Union Jack lattice, we treat the effect of anharmonic interactions using a mean-field spin wave theory where the Hamiltonian becomes implicitly temperature-dependent. We determine self-consistently the renormalized dispersion and the staggered magnetization as a function of temperature. Our calculations can be applied to other antiferromagnetic lattices.

Quantum anomalous Hall effect in an antiferromagnetic monolayer of MoO

The quantum anomalous Hall (QAH) effect is rarely predicted in antiferromagnetic (AFM) materials. Here, by first-principles calculations, we propose that the monolayer of MoO is AFM and can be tuned to be a QAH insulator with a band gap of 50 meV. The MoO monolayer is a tetragonal lattice and we have checked its stability by the phonon spectrum and molecular dynamical simulation. It has a collinear AFM order with magnetic moments larger than $2\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$ on each Mo atom. In the absence of strain, it is an AFM metal with a direct gap if spin-orbital coupling is considered. Tensile strain results in a metal-insulator phase transition, but it is still topologically trivial protected by an effective time-reversal symmetry. Shear strain breaks this symmetry and leads to the expected nontrivial electronic bands with Chern number $C=\ensuremath{-}1$. In addition, its N\'eel temperature could be larger than room temperature, providing another platform for the application of AFM materials in spintronic devices.

Thermal transport of helical Majorana edge modes in a superconducting antiferromagnetic quantum spin Hall insulator

In the system composed of a two-dimensional antiferromagnetic quantum spin Hall insulator (AFQSHI) nanoribbon covered by s -wave superconductors, possessing helical Majorana edge mode (HMEM), and preserving effective time-reversal symmetry. Based on such the AFQSHI-SC hybrid system, we investigate the band structure and thermal transport properties. The two-terminal thermal conductance κ e l and electric conductance G are calculated by using the Landauer-Büttiker formula and the nonequilibrium Green’s function method. When a pair of intersecting edge states exists in the bulk band gap, a helical topological superconductor with Z 2 invariant ν = ± 1 is formed, which has a pair of Majorana edge states with opposite chirality, that is Majorana Kramer pairs, leading to a integer quantized thermal conductance plateau. We find that the quantized thermal conductance plateau is well preserved in a certain range of temperature. The presence and number of Majorana Kramer pairs in helical topological superconductor can be confirmed with the help of the quantized thermal conduction plateau, which is promising for the experimental detection of helical Majorana fermions. • In this manuscript, based on the Landauer-Buttiker formula and the nonequilibrium Green’s function method, we investigate the properties of helical Majorana fermions edge states thermal transport in a hybrid AFQSHI-SC structure. • When a pair of Majorana edge states with opposite chirality residing at the edge of the central topological superconductor region, a integer quantized thermal conductance plateau is discovered. • This quantized plateau can be used as strong evidence for the experimental detection of helical topological superconductors.

Floquet topological insulators with hybrid edges

Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice terminations, for example, at zigzag or bearded edges in honeycomb lattices. Here we show that unconventional topological edge states may exist in Floquet insulators based on arrays of helical waveguides with hybrid edges involving alternating zigzag and armchair segments, even if the latter are long. Such edge states appear in the largest part of the first Brillouin zone and show topological protection upon passage through the defects. Topological states at hybrid edges persist in the presence of focusing nonlinearity of the material. Our results can be extended to other lattice types and physical systems, they lift some of the constraints connected with lattice terminations that may not support edge states in the absence of effects breaking time-reversal symmetry of the system and expand the variety of geometrical shapes in which topological insulators can be constructed.

Floquet topological systems with flat bands: Edge modes, Berry curvature, and orbital magnetization

Results are presented for Floquet systems in two spatial dimensions where the Floquet driving breaks an effective time-reversal symmetry. The driving protocol also induces flat bands that correspond to anomalous Floquet phases where the Chern number is zero and yet chiral edge modes exist. Analytic expressions for the edge modes, Berry curvature, and orbital magnetization are derived for the flat bands. Results are also presented for the static Haldane model for parameters when the bands are flat. Floquet driving of the same model is shown to give rise to Chern insulators as well as anomalous Floquet phases. The orbital magnetization for these different topological phases are presented and are found to be enhanced at half filling by the broken particle-hole symmetry of the Haldane model.

Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model

We introduce a spinful variant of the Sachdev-Ye-Kitaev model with an effective time-reversal symmetry, which can be solved exactly in the limit of a large number $N$ of degrees of freedom. At low temperature, its phase diagram includes a compressible non-Fermi liquid and a strongly correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. These two phases are separated by a first-order transition, in the vicinity of which a gapless superconducting phase, characterized by a nonzero magnetization, is stabilized upon applying a Zeeman field. We study equilibrium transport properties of such superconductors using a lattice construction and propose a physical platform based on topological insulator flakes where they may arise from repulsive electronic interactions.

Interaction-Stabilized Topological Magnon Insulator in Ferromagnets

Condensed matter systems admit topological collective excitations above a trivial ground state, an example being Chern insulators formed by Dirac bosons with a gap at finite energies. However, in contrast to electrons, there is no particle-number conservation law for collective excitations. This gives rise to particle number-nonconserving many-body interactions whose influence on single-particle topology is an open issue of fundamental interest in the field of topological quantum materials. Taking magnons in ferromagnets as an example, we uncover topological magnon insulators that are stabilized by interactions through opening Chern-insulating gaps in the magnon spectrum. This can be traced back to the fact that the particle-number nonconserving interactions break the effective time-reversal symmetry of the harmonic theory. Hence, magnon-magnon interactions are a source of topology that can introduce chiral edge states, whose chirality depends on the magnetization direction. Importantly, interactions do not necessarily cause detrimental damping but can give rise to topological magnons with exceptionally long lifetimes. We identify two mechanisms of interaction-induced topological phase transitions---one driven by an external field, the other by temperature---and show that they cause unconventional sign reversals of transverse transport signals, in particular of the thermal Hall conductivity. We identify candidate materials where this many-body mechanism is expected to occur, such as the metal-organic kagome-lattice magnet Cu(1,3-benzenedicarboxylate), the van der Waals honeycomb-lattice magnet CrI$_3$, and the multiferroic kamiokite (Fe$_2$Mo$_3$O$_8$). Our results demonstrate that interactions can play an important role in generating nontrivial topology.

Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals.

We propose a route to achieve odd-parity spin-triplet (OPST) superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfaces constrain the electrons to form spin-triplet Cooper pairs with odd parity. Interestingly, all the odd-parity superconducting ground states we obtained host nontrivial band topologies manifested as chiral topological superconductors, second-order topological superconductors, and nodal superconductors. We propose that double perovskite oxides with collinear antiferromagnetic or ferrimagnetic ordering, such as SrLaVMoO_{6}, are promising candidate systems where our theoretical ideas can be applied to.

Theory of topological spin Josephson junctions

We study the spin transport through a 1D quantum Ising-XY-Ising spin link that emulates a topological superconducting-normal-superconducting structure via Jordan-Wigner (JW) transformation. We calculate, both analytically and numerically, the spectrum of spin Andreev bound states and the resulting $\mathbb{Z}_2$ fractional spin Josephson effect (JE) pertaining to the emerging Majorana JW fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to $\mathbb{Z}_4$ fractional spin JE in the $\textit{presence}$ of interactions within the junction. Moreover, we uncover a hidden inversion time-reversal symmetry that protects the $\mathbb{Z}_4$ periodicity in chains with an odd number of spins, even in the $\textit{absence}$ of interactions. We also analyze the entanglement between pairs of spins by evaluating the concurrence in the presence of spin current and highlight the effects of the JW Majorana states. We propose to use a microwave cavity setup for detecting the aforementioned JEs by dispersive readout methods and show that, surprisingly, the $\mathbb{Z}_2$ periodicity is immune to $\textit{any}$ local magnetic perturbations. Our results are relevant for a plethora of spin systems, such as trapped ions, photonic lattices, electron spins in quantum dots, or magnetic impurities on surfaces.

Floquet second-order topological superconductor driven via ferromagnetic resonance

We consider a Floquet triple-layer setup composed of a two-dimensional electron gas with spin-orbit interactions, proximity coupled to an s-wave superconductor and to a ferromagnet driven at resonance. The ferromagnetic layer generates a time-oscillating Zeeman field which competes with the induced superconducting gap and leads to a topological phase transition. The resulting Floquet states support a second-order topological superconducting phase with a pair of localized zero-energy Floquet Majorana corner states. Moreover, the phase diagram comprises a Floquet helical topological superconductor, hosting a Kramers pair of Majorana edge modes protected by an effective time-reversal symmetry, as well as a gapless Floquet Weyl phase. The topological phases are stable against disorder and parameter variations and are within experimental reach.

Thermal Hall effect in noncollinear coplanar insulating antiferromagnets

We establish theoretically a thermal Hall effect of collective magnetic excitations in noncollinear but coplanar antiferromagnets. In agreement with superordinate symmetry arguments for linear transport tensors, our findings demonstrate that neither a ferromagnetic moment, nor a magnetic field, nor a scalar spin chirality are indispensable for a magnon thermal Hall effect. Similar to the electronic anomalous Hall effect, the two necessary requirements are broken effective time-reversal symmetry and a magnetic point group compatible with ferromagnetism. As an example, we construct a minimal model for an antiferromagnet on the kagome lattice with the coplanar negative vector chiral order. In the presence of in-plane Dzyaloshinskii-Moriya interactions, the coplanar order stays intact but both magnon band gaps and a nonzero Berry curvature develop. This coplanar magnet realizes an antiferromagnetic magnon Chern insulator with a nonzero thermal Hall effect. We propose cadmium kapellasite ${\mathrm{CdCu}}_{3}{(\mathrm{OH})}_{6}{({\mathrm{NO}}_{3})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$ as an approximate material realization.

Tunable band topology in gyroscopic lattices

Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables their topological behavior emerges directly from the lattice geometry. Here we show that variations in the lattice geometry can therefore give rise to more complex band topology than has been previously described. A `spindle' lattice (or truncated hexagonal tiling) of gyroscopes possesses both clockwise and counterclockwise edge modes distributed across several band gaps. Tuning the interaction strength or twisting the lattice structure along a Guest mode opens and closes these gaps and yields bands with Chern numbers of $|C| > 1$ without introducing next-nearest-neighbor interactions or staggered potentials. A deformable honeycomb structure provides a simple model for understanding the role of lattice geometry in constraining the effects of time reversal symmetry and inversion symmetry breaking. Lastly, we find that topological band structure generically arises in gyroscopic networks, and a simple protocol generates lattices with topological excitations.

Helical Majorana edge mode in a superconducting antiferromagnetic quantum spin Hall insulator

A two-dimensional time-reversal symmetric topological superconductor is a fully gapped system possessing a helical Majorana mode on the edges. This helical Majorana edge mode (HMEM), which is a Kramer's pair of two chiral Majorana edge modes in the opposite propagating directions, is robust under time-reversal symmetry protection. We propose a feasible setup and accessible measurement to provide the preliminary step of the HMEM realization by studying superconducting antiferromagnetic quantum spin Hall insulators. Since this antiferromagnetic topological insulator hosts a helical electron edge mode and preserves effective time-reversal symmetry, which is the combination of time-reversal symmetry and crystalline symmetry, the proximity effect of the conventional s-wave superconducting pairing can directly induce a single HMEM. We further show the HMEM leads to the observation of an $e^2/h$ conductance, and this quantized conductance survives even in the presence of small symmetry-breaking disorders.

Synthetic-gauge-field-induced Dirac semimetal state in an acoustic resonator system

Recently, a proposal of synthetic gauge field in reduced two-dimensional (2D) system from three-dimensional (3D) acoustic structure shows an analogue of the gapped Haldane model with fixed kz, and achieves the gapless Weyl semimetal phase in 3D momentum space. Here, extending this approach of synthetic gauge flux, we propose a reduced square lattice of acoustic resonators, which exhibits Dirac nodes with broken effective time-reversal symmetry. Protected by an additional hidden symmetry, these Dirac nodes with quantized values of topological charge are characterized by nonzero winding number and the finite structure exhibits flat edge modes that cannot be destroyed by perturbations.

Transport signatures of interacting fermions in quasi-one-dimensional topological superconductors

A topological superconducting wire with an effective time reversal symmetry is known to have a $\mathbb{Z}_8$ topological classification in the presence of interactions. The topological index $|n| \le 4$ counts the number of Majorana end states, negative $n$ corresponding to end states that are odd under time reversal. If such a wire is weakly coupled to a normal-metal lead, interactions induce a Kondo-like correlated state if $|n| = 4$. We show that the Kondo-like state manifests itself in an anomalous temperature dependence of the zero-bias conductance and by an anomalous Fano factor for the zero-temperature normally-reflected current at finite bias. We also consider the splitting of the effective Kondo resonance for weak symmetry-breaking perturbations.

Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors.

We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time-reversal symmetry in the presence of interactions. For an isolated system, Fidkowski and Kitaev have shown that such systems have a Z_{8} topological classification. We here show that these systems have a unitary scattering matrix at zero temperature when weakly coupled to a normal-metal lead, with a topological index given by the trace of the Andreev-reflection matrix, trr_{he}. With interactions, trr_{he} generically takes on the finite set of values 0, ±1, ±2, ±3, and ±4. We show that the two topologically equivalent phases with trr_{he}=±4 support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-Fermi-liquid fixed point where a multiple-channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.

Quantum phase transitions of a disordered antiferromagnetic topological insulator

We study the effect of electrostatic disorder on the conductivity of a three-dimensional antiferromagnetic insulator (a stack of quantum anomalous Hall layers with staggered magnetization). The phase diagram contains regions where the increase of disorder first causes the appearance of surface conduction (via a topological phase transition), followed by the appearance of bulk conduction (via a metal-insulator transition). The conducting surface states are stabilized by an effective time-reversal symmetry that is broken locally by the disorder but restored on long length scales. A simple self-consistent Born approximation reliably locates the boundaries of this socalled "statistical" topological phase.