Two-dimensional Topological Systems Research Articles

Distribution of Fisher zeros in dynamical quantum phase transitions of two-dimensional topological systems

Distribution of Fisher zeros in dynamical quantum phase transitions of two-dimensional topological systems

Classifying phases protected by matrix product operator symmetries using matrix product states

We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry. This characterization yields a set of quantities satisfying the coupled pentagon equations, associated with a module category over the fusion category that describes the MPO symmetry. Equivalence classes of these quantities provide complete invariants for an MPO symmetry protected phase: they are robust under continuous deformations of the MPS tensor, and two phases with the same equivalence class can be connected by a symmetric gapped path. Our techniques match and extend the known renormalization fixed point classifications and facilitate the numerical study of these systems. For MPO symmetries described by a group, we recover the symmetry protected topological order classification for unique and degenerate ground states. Moreover, we study the interplay between time reversal symmetry and an MPO symmetry and we also provide examples of our classification, together with explicit constructions based on groups. Finally, we elaborate on the connection between our setup and gapped boundaries of two-dimensional topological systems, where MPO symmetries also play a key role.

Engineering Floquet topological phases using elliptically polarized light

We study a two-dimensional topological system driven out of equilibrium by the application of elliptically polarized light. In particular, we analyze the Bernevig-Hughes-Zhang model when it is perturbed using an elliptically polarized light of frequency $\mathrm{\ensuremath{\Omega}}$ described in general by a vector potential $\mathbf{A}(t)=({A}_{0x}cos(\mathrm{\ensuremath{\Omega}}t),{A}_{0y}cos(\mathrm{\ensuremath{\Omega}}t+{\ensuremath{\phi}}_{0}))$. Even for a fixed value of ${\ensuremath{\phi}}_{0}$, we can change the topological character of the system by changing the $x$ and $y$ amplitudes of the drive. We therefore find a rich topological phase diagram as a function of ${A}_{0x}$, ${A}_{0y}$, and ${\ensuremath{\phi}}_{0}$. In each of these phases, the topological invariant given by the Chern number is consistent with the number of spin-polarized states present at the edges of a nanoribbon.

Local equilibrium charge and spin currents in two-dimensional topological systems

We study the equilibrium and nonequilibrium electronic transport properties of multiprobe topological systems using a combination of the Landauer-B\"uttiker approach and nonequilibrium Green's functions techniques. We obtain general expressions for both nonequilibrium and equilibrium local electronic currents that, by suitable projections, allow one to compute charge, spin, valley, and orbital currents. We show that external magnetic fields give rise to equilibrium charge currents in mesoscopic system and study the latter in the quantum Hall regime. Likewise, a spin-orbit interaction leads to local equilibrium spin currents, that we analyze in the quantum spin Hall regime. We show that an accurate theoretical assessment of the equilibrium currents is quite challenging and propose a two-measurement protocol that facilitates a comparison between experiment and theory.

Regularly multiple double Dirac cones in photonic bands and topological transitions of all-dielectric photonic crystals

Research on the remarkable characteristics of topological phases and topological phase transitions in various topological systems has been performed. In this paper, we propose a two-dimensional topological system composed of triangle photonic crystals (PCs) with ${C}_{3}$ point group symmetry, which hosts both regularly multiple fourfold-degenerate double Dirac cones and topological transitions in all-dielectric PC systems. By applying the tight-binding model to our system, we reveal the mechanism for topological transitions in the present configuration manufactured of conventional silicon material. Topological edge states at the common boundary of two different topological regions are demonstrated, which indicates that electromagnetic wave can propagate unidirectionally and robustly along the boundary with eximious transmission performance. Further, we manifest that topological edge states characterized by pseudospin-dependent unidirectional edge transport and have robustness against commonly minor defects. This flexible topological system demonstrates more abundant physics principles compared with previous research, which can be used to explore different topological phenomena and be implemented in integrated optical devices.

Living on the edge: Topology, electrostatics, and disorder

We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function describing the band inversion and the band bending due to electrostatic effects between the bulk of the quantum well and the vacuum. Within this minimal model we identify distinct parameter sets that can lead to the co-existence of the two types of edge states, and that determine their number and characteristics. We propose several experimental setups that could demonstrate their presence in two-dimensional topological systems, as well as ways to regulate or tune the contribution of the massive edge states to the conductance of associated electronic devices. Our results suggest that such states may also be present in novel two-dimensional Van der Waals topological materials.

Theory of chiral edge state lasing in a two-dimensional topological system

We theoretically study topological laser operation in a bosonic Harper-Hofstadter model featuring a saturable optical gain. Crucial consequences of the chirality of the lasing edge modes are highlighted, such as a sharp dependence of the lasing threshold on the geometrical shape of the amplifying region and the possibility of ultraslow relaxation times and of convectively unstable regimes. The different unstable regimes are characterized in terms of spatio-temporal structures sustained by noise and a strong amplification of a propagating probe beam is anticipated to occur in between the convective and the absolute (lasing) thresholds. The robustness of topological laser operation against static disorder is assessed.

Efficient quantum simulation for thermodynamics of infinite-size many-body systems in arbitrary dimensions

In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show that the QES can, for instance, accurately simulate varieties of many-body phenomena, including finite-temperature crossover and algebraic excitations of the one-dimensional spin liquid, the phase transitions and low-temperature physics of the two- and three-dimensional antiferromagnets, and the crossovers of the two-dimensional topological system. Our work provides an efficient way to explore the thermodynamics of intractable quantum many-body systems with easily accessible systems.

Long range intrinsic ferromagnetism in two dimensional materials and dissipationless future technologies

The inherent susceptibility of low-dimensional materials to thermal fluctuations has long been expected to pose a major challenge to achieve intrinsic long-range ferromagnetic order in two-dimensional materials. The recent explosion of interest in atomically thin materials and their assembly into van der Waals heterostructures has renewed interest in two-dimensional ferromagnetism, which is interesting from a fundamental scientific point of view and also offers a missing ingredient necessary for the realization of spintronic functionality in van der Waals heterostructures. Recently, several atomically thin materials have been shown to be robust ferromagnets. Such ferromagnetism is thought to be enabled by magnetocrystalline anisotropy which suppresses thermal fluctuations. In this article, we review recent progress in two-dimensional ferromagnetism in detail and predict new possible two-dimensional ferromagnetic materials. We also discuss the prospects for applications of atomically thin ferromagnets in novel dissipationless electronics, spintronics, and other conventional magnetic technologies. Particularly, atomically thin ferromagnets are promising to realize time reversal symmetry breaking in two-dimensional topological systems, providing a platform for electronic devices based on the quantum anomalous Hall effect showing dissipationless transport. Our proposed directions will assist the scientific community to explore novel two-dimensional ferromagnetic families which can spawn new technologies and further improve the fundamental understanding of this fascinating area.

Dynamical topological invariants and reduced rate functions for dynamical quantum phase transitions in two dimensions

We show that dynamical quantum phase transitions (DQPTs) in the quench dynamics of two-dimensional topological systems can be characterized by a dynamical topological invariant defined along an appropriately chosen closed contour in momentum space. Such a dynamical topological invariant reflects the vorticity of dynamical vortices responsible for the DQPTs, and thus serves as a dynamical topological order parameter in two dimensions. We demonstrate that when the contour crosses topologically protected fixed points in the quench dynamics, an intimate connection can be established between the dynamical topological order parameter in two dimensions and those in one dimension. We further define a reduced rate function of the Loschmidt echo on the contour, which features non-analyticities at critical times and is sufficient to characterize DQPTs in two dimensions. We illustrate our results using the Haldane honeycomb model and the quantum anomalous Hall model as concrete examples, both of which have been experimentally realized using cold atoms.

Quantum Hall Edge Magnetoplasmons Probed by Novel Experimental Techniques

Edge magnetoplasmons (EMPs) are collective charge-density excitations along the edge of a two-dimensional topological system. Unique radio-frequency transmission and thermoelectric measurements rep...

Noise and current correlations in tunnel junctions of quantum spin Hall edge states

The edge channels of two-dimensional topological systems are protected from elastic reflection and are noiseless at low temperature. Yet, noise and cross-correlations can be induced when electron waves partly transmit to the opposite edge via tunneling through a constriction. In particular, in a quantum spin Hall (QSH) system tunnelling occurs via both spin-preserving ($p$) and spin-flipping ($f$) processes, each fulfilling time-reversal symmetry. We investigate the current correlations of a four-terminal QSH setup in the presence of a tunneling region, both at equilibrium and out-of-equilibrium. We find that, although $p$ and $f$ processes do not commute and the generic current correlation depends on both, under appropriate conditions a direct detection of two types of partition noise is possible. In particular, while the spin-preserving partitioning can be probed for any arbitrary tunnel junction with a specific configuration of terminal biases, the spin-flipping partitioning can be directly detected only under suitably designed setups and conditions. We describe two setups where these conditions can be fulfilled, and both types of partitioning can be detected and controlled.