Trivial State Research Articles

Gate-tunable spin-galvanic effect in graphene-topological insulator van der Waals heterostructures at room temperature

Unique electronic spin textures in topological states of matter are promising for emerging spin-orbit driven memory and logic technologies. However, there are several challenges related to the enhancement of their performance, electrical gate-tunability, interference from trivial bulk states, and heterostructure interfaces. We address these challenges by integrating two-dimensional graphene with a three-dimensional topological insulator (TI) in van der Waals heterostructures to take advantage of their remarkable spintronic properties and engineer proximity-induced spin-charge conversion phenomena. In these heterostructures, we experimentally demonstrate a gate-tunable spin-galvanic effect (SGE) at room temperature, allowing for efficient conversion of a non-equilibrium spin polarization into a transverse charge current. Systematic measurements of SGE in various device geometries via a spin switch, spin precession, and magnetization rotation experiments establish the robustness of spin-charge conversion in the Gr-TI heterostructures. Importantly, using a gate voltage, we reveal a strong electric field tunability of both amplitude and sign of the spin-galvanic signal. These findings provide an efficient route for realizing all-electrical and gate-tunable spin-orbit technology using TIs and graphene in heterostructures, which can enhance the performance and reduce power dissipation in spintronic circuits.

Isolas of multi-pulse solutions to lattice dynamical systems

This work investigates the existence and bifurcation structure of multi-pulse steady-state solutions to bistable lattice dynamical systems. Such solutions are characterized by multiple compact disconnected regions where the solution resembles one of the bistable states and resembles another trivial bistable state outside of these compact sets. It is shown that the bifurcation curves of these multi-pulse solutions lie along closed and bounded curves (isolas), even when single-pulse solutions lie along unbounded curves. These results are applied to a discrete Nagumo differential equation and we show that the hypotheses of this work can be confirmed analytically near the anti-continuum limit. Results are demonstrated with a number of numerical investigations.

Dual topological insulator device with disorder robustness

Two-dimensional ${\mathrm{Na}}_{3}\mathrm{Bi}$ is a dual topological insulator protected by time-reversal and mirror symmetry, resulting in a promising platform for device design. However, in reality, the design of topological devices is hindered by a sensitivity against disorder and temperature. We study the topological properties of ${\mathrm{Na}}_{3}\mathrm{Bi}$ in the presence of intrinsic defects, investigating the robustness of the edge states and the resulting transport properties. We apply a recursive Green's function technique enabling the study of disordered systems with lengths comparable to experimentally synthesized materials, in the order of micrometers. We combine our findings to propose a topological insulator device, where intrinsic defects are used to filter the response of trivial bulk states. This results in a stable conductance throughout a large range of electronic temperatures, and controllable by a perpendicular electric field. Our proposal is general, enabling the design of various dual topological insulator devices.

Emerging Superconductivity and the Origin of Its Enhancement in Pressurized Topological Nodal‐Line Semimetal SrAs3

AbstractTopological nodal‐line semimetal SrAs3 hosts a simple nodal loop on the verge of Fermi level without distracting trivial states, providing a good platform for further investigations of electronic quantum states. Here, a report on pressure‐driven superconductivity in SrAs3 single crystal is provided and the interplay between the crystal structure, electronic state, and superconductivity is clarified therein. The comprehensive high‐pressure experiments, i.e., synchrotron X‐ray diffraction, electrical transport, and Raman spectroscopy, consistently reveal a critical pressure Pc ≈ 25 GPa. Around Pc, a superconducting transition appears, concomitant with the formation of high‐pressure cubic Pm‐3m phase. Meanwhile, the superconducting transition temperature Tc and hole carrier density increase synchronously above Pc. This finding demonstrates that the emerging superconductivity in SrAs3 stems from the high‐pressure cubic phase on the one hand, and shows that the evolution of Tc(P) is intimately correlated with the enhanced density of states near the Fermi level on the other hand.

Toy model of boundary states with spurious topological entanglement entropy

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates topological entanglement entropy. We show that if the state at the boundary of a subregion is a stabilizer state, then it has a non-zero spurious contribution to the region if and only if, the state is in a non-trivial one-dimensional $G_1\times G_2$ symmetry-protected-topological (SPT) phase. However, we provide a candidate of a boundary state that has a non-zero spurious contribution but does not belong to any such SPT phase.

Bifurcation analysis in a discrete time square root response function of predator-prey system with fractional order

Stability and bifurcation analysis for a two spices discrete fractional order system by introducing square root response function of the form is examined in the closed first quadrant . The model parameters h, α, β, μ, σ, η are biologically feasible positive real numbers. Piecewise constant arguments method is applied to obtain the discrete fractional order system, particularly to study the rich dynamical behavior of the proposed system. Because the system has square root response function, the variation matrix of trivial and axial equilibrium states are in-determinant. In order to study the stability of the trivial and semi trivial equilibrium states, the change of variables x(j) = X 2(j) and y(j) = Y 2 (j) is considered. Moreover, we determine the criteria for stability of the interior equilibrium state using jury conditions. The numerical performance is shown for various parameter values and the time series and phase line diagrams are obtained. Bifurcation theory is applied to check whether the system undergoes periodic doubling bifurcations at its semi trivial and interior equilibrium states. Also we explore the periodic halving bifurcation which occurs for the fractional order as a bifurcation parameter. Numerical examples are presented to show the validity and feasibility of the obtained stability criterion in both species, including periodic doubling, periodic - 2, 4, 8, 16, periodic windows and Non periodic orbit (i.e., chaos).

Topological Phase Transition in the Non-Hermitian Coupled Resonator Array.

In a two-dimensional non-Hermitian topological photonic system, the physics of topological states is complicated, which brings great challenges for clarifying the topological phase transitions and achieving precise active control. Here, we prove the topological phase transition exists in a two-dimensional parity-time-symmetric coupled-resonator optical waveguide system. We reveal the inherent condition of the appearance of topological phase transition, which is described by the analytical algebraic relation of coupling strength and the quantity of gain-loss. In this framework, the system can be switched between the topological and trivial states by pumping the site rings. This work provides a new degree of freedom to control topological states and offers a scheme for studying non-Hermitian topological photonics.

Magnetic-Field-Independent Subgap States in Hybrid Rashba Nanowires.

Subgap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically nontrivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete subgap states in a long nanowire segment. In addition to subgap states with a standard magnetic field dependence, we find topologically trivial subgap states that are independent of the external magnetic field, i.e., that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates. This result constitutes an important step forward in the research on superconducting subgap states in nanowires, such as Majorana bound states.

Coupling and protection effects of Jackiw-Rebbi states and trivial states in interfaced binary waveguide arrays

We systematically study different scenarios of interaction between two localized structures which were both found recently in interfaced binary waveguide arrays with alternating signs of the Dirac mass in the linear and nonlinear regimes of Kerr type. The first localized structure is the optical analog of the famous Jackiw-Rebbi state emerging from the Dirac equation in quantum field theory, and the second one is the trivial state. We show that two localized states of different types practically do not interact at all; thus, they can be protected from each other in a reliable way. Meanwhile, two localized states of the same type can couple efficiently with each other and show the nonlinear switching effect like in well-known symmetric fiber couplers.

Impurity bound states as detectors of topological band structures revisited

Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126 (2015)] has argued, based on theoretical results for a particular class of models, that insulators with topologically trivial and non-trivial band structures in two space dimensions display a qualitatively different response to point-like impurities. Here we present a comprehensive investigation of the impurity response of a large set of models of non-interacting electrons on the honeycomb lattice, driven insulating by either broken inversion, broken time reversal, broken $C_3$, or broken translation symmetry. These cases include Hofstadter bands, strain-induced pseudo-Landau levels and higher-order topological insulators. Our results confirm that for hopping models respecting the lattice symmetries, the response to a single impurity can indeed distinguish between trivial and non-trivial band topology. However, for modulated or inhomogeneous host systems we find that trivial states of matter can display an impurity response akin to that of topologically non-trivial states, and thus the diagnostic fails.

Jackiw-Rebbi states and trivial states in interfaced binary waveguide arrays with cubic-quintic nonlinearity.

We systematically investigate two types of localized states-one is the optical analog of the quantum relativistic Jackiw-Rebbi states and the other is the trivial localized state-in interfaced binary waveguide arrays in the presence of cubic-quintic nonlinearity. By using the shooting method, we can exactly calculate the profiles of these nonlinear localized states. Like in the case with Kerr nonlinearity, we demonstrate that these localized states with cubic-quintic nonlinearity also have an extraordinary property, which completely differs from many well-known nonlinear localized structures in other media. Specifically, both the peak amplitude and transverse dimension of these nonlinear localized states can increase at the same time. Apart from that, we show that high values of the saturation nonlinearity parameter can help to generate and stabilize the intense localized states during propagation, especially in the case with a negative coefficient for the cubic nonlinearity term.

From the pseudogap metal to the Fermi liquid using ancilla qubits

We propose a new parton theory of the hole-doped cuprates, describing the evolution from the pseudogap metal with small Fermi surfaces to the conventional Fermi liquid with a large Fermi surface. We introduce 2 ancilla qubits per square lattice site, and employ them to obtain a variational wavefunction of a fractionalized Fermi liquid for the pseudogap metal state. We propose a multi-layer Hamiltonion for the cuprates, with the electrons residing in the 'physical' layer, and the ancilla qubits in two 'hidden' layers: the hidden layers can be decoupled from the physical layer by a canonical transformation which leaves the hidden layers in a trivial gapped state. This Hamiltonian yields an emergent gauge theory which describes not only the fractionalized Fermi liquid, but also the conventional Fermi liquid, and possible exotic intermediate phases and critical points. The fractionalized Fermi liquid has hole pockets with quasiparticle weight which is large only on "Fermi arcs", and fermionic spinon excitations which carry charges of the emergent gauge fields.

Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires

In the topological phase of spin-orbit coupled nanowires Majorana bound states are known to localize at the nanowire edges and to exhibit a spin density orthogonal to both the magnetic field and the spin-orbit field. By investigating a nanowire exposed to a uniform magnetic field with an interface between regions with different spin-orbit couplings, we find that the orthogonal spin density is pinned at the interface even when both interface sides are in the topologically trivial phase, and even when no bound state is present at all. A trivial bound state may additionally appear at the interface, especially if the spin-orbit coupling takes opposite signs across the interface. However, it can be destroyed by a smoothening of the spin-orbit profile or by a magnetic field component parallel to the spin-orbit field. In contrast, the orthogonal spin density persists in various and realistic parameter ranges. We also show that, while the measurement of bulk equilibrium spin currents has been elusive so far, such robust orthogonal spin density peak may provide a way to detect spin current variations across interfaces.

High-temperature Majorana fermions in magnet-superconductor hybrid systems

Magnet-superconductor hybrid (MSH) structures represent one of the most promising platforms to realize, control and manipulate Majorana modes using scanning tunneling methods. By depositing either chains or islands of magnetic atoms on the surface of a conventional, elemental superconductor such as Pb or Re, topological superconducting phases can emerge. They feature either localised Majorana bound states at the chain ends or dispersing chiral Majorana modes at the island's boundary. Yet some of these experiments have not reached the spectral resolution to clearly distinguish between topological Majorana and trivial Shiba states due to very small superconducting gap sizes and experiments performed at sub-Kelvin temperatures. Here we consider superconducting substrates with unconventional spin-singlet pairing, including high-temperature d-wave and extended s-wave superconductors. We derive topological phase diagrams and compute edge states for cylinder and island geometries and discuss their properties. Several time-reversal invariant topological superconducting phases of the Zhang-Kane-Mele type are found and discussed. Moreover, we study one-dimensional MSH structures and show that parameters to realize topologically non-trivial magnetic chains embedded into a larger, two-dimensional substrate differ from the purely one-dimensional case. Quite generally we find that unconventional superconducting substrates work as well as the conventional s-wave substrates to realize topological phases. In particular, iron-based pnictide and chalcogenide superconductors are the most promising class of substrates for future high-temperature MSH systems.

Analytical and numerical detection of traveling wave and wave-train solutions in a prey–predator model with weak Allee effect

The traveling wave and wave-train fronts correspond to the transition zones from a trivial steady state to a coexistence steady state and a limit cycle around the coexistence steady state, respectively. In this study, we establish the existence of both types of fronts for a reaction–diffusion system of prey–predator interactions with weak additive Allee effect in prey growth, Holling type II functional response and density-dependent death rate for predators. For analytical simplicity, we consider immobile prey population. Under this consideration, the existence of both the traveling fronts is mathematically equivalent to the existence of point-to-point and point-to-cycle heteroclinic connections in $$\mathbb {R}^{3}$$. The proof for the existence of traveling fronts relies on the construction of an unbounded wedged region, a shooting argument and an appropriate Lyapunov function. Also, by employing the Hopf bifurcation theorem we show the existence of traveling wave-train solution. In both the cases, we find successful invasion by the predator species. Further, we provide adequate numerical illustrations in order to corroborate our theoretical predictions. Our numerical simulations also suggest that the theoretically obtained minimum wave speed serves as an asymptotic speed of traveling wave propagation.

Topological Invariants for Quantum Quench Dynamics from Unitary Evolution.

Recent experiments began to explore the topological properties of quench dynamics, i.e., the time evolution following a sudden change in the Hamiltonian, via tomography of quantum gases in optical lattices. In contrast to the well-established theory for static band insulators or periodically driven systems, at present it is not clear whether, and how, topological invariants can be defined for a general quench of band insulators. Previous work solved a special case of this problem beautifully using Hopf mapping of two-band Hamiltonians in two dimensions. However, it only works for a topologically trivial initial state and is hard to generalize to multiband systems or other dimensions. Here we introduce the concept of loop unitary constructed from the unitary time-evolution operator and show its homotopy invariant fully characterizes the dynamical topology. For two-band systems in two dimensions, we prove that the invariant is precisely equal to the change in the Chern number across the quench, regardless of the initial state. We further show that the nontrivial dynamical topology manifests as hedgehog defects in the loop unitary and also as winding and linking of its eigenvectors along a curve where dynamical quantum phase transition occurs. This opens up a systematic route to classify and characterize quantum quench dynamics.

Conductance of quantum spin Hall edge states from first principles: The critical role of magnetic impurities and inter-edge scattering

The outstanding transport properties expected at the edge of two-dimensional time-reversal invariant topological insulators have proven to be challenging to realize experimentally, and have so far only been demonstrated in very short devices. In search for an explanation to this puzzling observation, we here report a full first-principles calculation of topologically protected transport at the edge of novel quantum spin Hall insulators - specifically, Bismuth and Antimony halides - based on the non-equilibrium Green's functions formalism. Our calculations unravel two different scattering mechanisms that may affect two-dimensional topological insulators, namely time-reversal symmetry breaking at vacancy defects and inter-edge scattering mediated by multiple co-operating impurities, possibly non-magnetic. We discuss their drastic consequences for typical non-local transport measurements as well as strategies to mitigate their negative impact. Finally, we provide an instructive comparison of the transport properties of topologically protected edge states to those of the trivial edge states in MoS$_2$ ribbons. Although we focus on a few specific cases (in terms of materials and defect types) our results should be representative for the general case and thus have significance beyond the systems studied here.

Pressure Induced Topological Quantum Phase Transition in Weyl Semimetal Td-MoTe2

We report the pressure (p_max = 1.5 GPa) evolution of the crystal structure of the Weyl semimetal T_d-MoTe_2 by means of neutron diffraction experiments. We find that the fundamental non-centrosymmetric structure T_d is fully suppressed and transforms into a centrosymmertic 1T' structure at a critical pressure of p_cr = 1.2 GPa. This is strong evidence for a pressure induced quantum phase transition (QPT) between topological to a trivial electronic state. Although the topological QPT has strong effect on magnetoresistance, it is interesting that the superconducting critical temperature T_c, the superfluid density, and the SC gap all change smoothly and continuously across p_cr and no sudden effects are seen concomitantly with the suppression of the T_d structure. This implies that the T_c, and thus the SC pairing strength, is unaffected by the topological QPT. However, the QPT requires the change in the SC gap symmetry from non-trivial s+- to a trivial s++ state, which we discuss in this work. Our systematic characterizations of the structure and superconducting properties associated with the topological QPT provide deep insight into the pressure induced phase diagram in this topological quantum material.

Stacking-dependent topological phase in bilayer MBi2Te4(M=Ge,Sn,Pb)

Inspired by the breakthroughs of twisted bilayer graphene, stacking-dependent phenomena are recently emerging as fascinating objects of condensed matter research, harboring a variety of new physics. However, current studies are restricted to electronic, superconducting and magnetic properties. Here, using first-principles calculations, we reveal the connection between stacking order and topological property in bilayer $M\mathrm{B}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{4}(M=\mathrm{Ge},\mathrm{Sn},\mathrm{Pb})$. We show the stacking order determines the topological property. Upon changing the stacking order, one can achieve topological phase transition between trivial and nontrivial states. We unveil that this stacking-dependent topological property is attributed to the interlayer $\mathrm{Te}\ensuremath{-}{p}_{z}$ orbitals coupling, which is closely related to the stacking order. Our work not only expands the scope of stacking-dependent properties but also provides a promising experimental platform to study this novel stacking-dependent topological property.

Phase diagram and thermal Hall conductivity of the spin-liquid Kekulé-Kitaev model

In this work we study the phase diagram of Kekul\'{e}-Kitaev model. The model is defined on a honeycomb lattice with bond dependent anisotropic exchange interactions making it exactly solvable in terms of Majorana representation of spins in close analogy to the Kitaev model. However, the energy spectrum of Majorana fermions has a multi-band structure characterized by Chern numbers 0, $\pm$1, and $\pm2$. We obtained the phase diagram of the model in the plane of exchange couplings and in the presence of a magnetic field and found chiral topological and trivial spin-liquid ground states. In the absence of magnetic field most part of the phase diagram is a trivial gapped phase continuously connected to an Abelian phase, while in the presence of the magnetic field a topological phase arises. Furthermore, motivated by recent thermal measurements on the spin-liquid candidate $\alpha$-RuCl$_{3}$, we calculated the thermal Hall conductivity at different regimes of parameters and temperatures and found the latter is quantized over a wide range of temperatures.