Distinct Topological States Research Articles

Bi2:Bi2Te3 stacking influence on the surface electronic response of the topological insulator Bi4Te3

We report on the successful synthesis of a crystal of the strong topological insulator Bi4Te3 and the study of its surface electronic response. A combination of theoretical and experimental techniques allowed for a systematic study of the composition and electronic properties of the sample. These techniques include density functional theory (DFT), scanning tunneling microscopy and spectroscopy (STM-STS). DFT predicts that distinct surface topological states exist for the two surface terminations of Bi4Te3, i.e. Bi2 and Bi2Te3. These terminations are also clearly distinguished in STS measurements, which allow choosing the main conducting channel through a combination of topography and electronic response. We find that the density of states are similar to those of their parent crystals Bi2 and Bi2Te3, albeit shifted in energy.

One compound with two distinct topological states.

Two distinct topological states that are closely tied to the spin configurations of a layered compound, here MnBi2Te4, have been demonstrated. Such control of the topological state should enable new opportunities to realize quantum and spintronic devices.

Topological phase transition between distinct Weyl semimetal states in MoTe2

We present experimental evidence of an intriguing phase transition between distinct topological states in the type-II Weyl semimetal MoTe2. We observe anomalies in the Raman phonon frequencies and linewidths as well as electronic quasielastic peaks around 70 K, which, together with structural, thermodynamic measurements, and electron-phonon coupling calculations, demonstrate a temperature-induced transition between two topological phases previously identified by contrasting spectroscopic measurements. An analysis of experimental data suggests electron-phonon coupling as the main driving mechanism for the change of key topological characters in the electronic structure of MoTe2.We also find the phase transition to be sensitive to sample conditions distinguished by synthesis methods. These discoveries of temperature and material condition-dependent topological phase evolutions and transitions in MoTe2 advance the fundamental understanding of the underlying physics and enable an effective approach to tuning Weyl semimetal states for technological applications.

Spin and spin-valley Hall effects in a honeycomb lattice with antiferromagnetism and spin-orbit couplings

We study linear response to a longitudinal electric field on an antiferromagnetic honeycomb lattice with intrinsic and Rashba spin-orbit couplings (SOCs). It is found that the spin-valley Hall effect could emerge alone or coexist with the spin Hall effect. The spin and spin-valley Hall conductivities exhibit some peculiarities that depend on the distinct topological states of the graphene lattice. Furthermore, the spin and spin-valley Hall conductivities could be remarkably modulated by changing the Fermi level. Our findings suggest that the antiferromagnetic honeycomb lattice with SOCs is an excellent platform for potential applications of spintronics and valleytronics.

Dynamic interplay between enhancer-promoter topology and gene activity.

A long-standing question in gene regulation is how remote enhancers communicate with their target promoters, and specifically how chromatin topology dynamically relates to gene activation. Here, we combine genome editing and multi-color live imaging to simultaneously visualize physical enhancer–promoter interaction and transcription at the single cell level in Drosophila embryos. Examining transcriptional activation of a reporter by the endogenous even-skipped enhancers 150 kb away, we identify three distinct topological conformation states and measure their transition kinetics. We show that sustained proximity of the enhancer to its target is required for activation. Transcription in turn affects the 3D topology, as it enhances the temporal stability of the proximal conformation and is associated with further spatial compaction. Furthermore, the facilitated long-range activation results in transcriptional competition at the locus, causing corresponding developmental defects. Our approach thus offers quantitative insight into the spatial and temporal determinants of long-range gene regulation and their implications for cellular fates.

Spontaneous breaking of time-reversal symmetry in topological insulators

The system of spinless fermions on a hexagonal lattice is studied. We have considered tight-binding model with the hopping integrals between the nearest-neighbor and next-nearest-neighbor lattice sites, that depend on the direction of the link. The links are divided on three types depending on the direction, the hopping integrals are defined by different phases along the links. The energy of the system depends on the phase differences, the solutions for the phases, that correspond to the minimums of the energy, lead to a topological insulator state with the nontrivial Chern numbers. We have analyzed distinct topological states and phase transitions, the behavior of the chiral gapless edge modes, have defined the Chern numbers. The band structure of topological insulator (TI) is calculated, the ground-state phase diagram in the parameter space is obtained. We propose a novel mechanism of realization of TI, when the TI state is result of spontaneous breaking of time-reversal symmetry due to nontrivial stable solutions for the phases that determine the hopping integrals along the links and show that the Haldane model [1] can be implemented in real compounds of the condensed matter physics.

Superconducting dome and crossover to an insulating state in [Tl4]Tl1−xSnxTe3

The structural, superconducting, and electronic phase diagram of [Tl4]Tl1−xSnxTe3 is reported. Magnetization and specific heat measurements show bulk superconductivity exists for 0 ≤ x ≤ 0.4. Resistivity measurements indicate a crossover from a metallic state at x = 0 to a doped insulator at x = 1. Universally, there is a large non-Debye specific heat contribution, characterized by an Einstein temperature of θE ≈ 35 K. Density functional theory calculations predict x = 0 to be a topological metal, while x = 1 is a topological crystalline insulator. The disappearance of superconductivity correlates with the transition between these distinct topological states.

Knotted defects in nematic liquid crystals.

We show that the number of distinct topological states associated with a given knotted defect, L, in a nematic liquid crystal is equal to the determinant of the link L. We give an interpretation of these states, demonstrate how they may be identified in experiments, and describe the consequences for material behavior and interactions between multiple knots. We show that stable knots can be created in a bulk cholesteric and illustrate the topology by classifying a simulated Hopf link. In addition, we give a topological heuristic for the resolution of strand crossings in defect coarsening processes which allows us to distinguish topological classes of a given link and to make predictions about defect crossings in nematic liquid crystals.

Interaction-driven transition between topological states in a Kondo insulator

Heavy fermion materials naturally combine strong spin-orbit interactions and electronic correlations. When there is precisely one conduction electron per impurity spin, the coherent heavy fermion state is insulating. This Kondo insulating state has recently been argued to belong to the class of quantum spin Hall states. Motivated by this conjecture and a very recent experimental realization of this state, we investigate a model for Kondo insulators with spin-orbit coupling. Using dynamical mean-field theory we observe an interaction-driven transition between two distinct topological states, indicated by a closing of the bulk gap and a simultaneous change of topological invariants as obtained in a classification which takes into account lattice symmetries. At large interaction strength we find a topological heavy fermion state, characterized by strongly renormalized heavy bulk bands, hosting a pair of zero-energy edge modes. The model allows a detailed understanding of the temperature dependence of the single particle spectral function and in particular the energy scales at which one observes the appearance of edge states within the bulk gap.

Competing topological phases in few-layer graphene

We investigate the effect of spin-orbit coupling on the band structure of graphene-based two-dimensional Dirac fermion gases in the quantum Hall regime. Taking monolayer graphene as our first candidate, we show that a quantum phase transition between two distinct topological states -- the quantum Hall and the quantum spin Hall phases -- can be driven by simply tuning the Fermi level with a gate voltage. This transition is characterized by the existence of a chiral spin-polarized edge state propagating along the interface separating the two topological phases. We then apply our analysis to the more difficult case of bilayer graphene. Unlike in monolayer graphene, spin-orbit coupling by itself has indeed been predicted to be unsuccessful in driving bilayer graphene into a topological phase, due to the existence of an even number of pairs of spin-polarized edge states. While we show that this remains the case in the quantum Hall regime, we point out that by additionally breaking the layer inversion symmetry, a non-trivial quantum spin Hall phase can re-emerge in bilayer graphene at low energy. We consider two different symmetry-breaking mechanisms: inducing spin-orbit coupling only in the upper layer, and applying a perpendicular electric field. In both cases, the presence at low energy of an odd number of pairs of edge states can be driven by an exchange field. The related situation in trilayer graphene is also discussed.

Topological states in two-dimensional optical lattices

We present a general analysis of two-dimensional optical lattice models that give rise to topologically nontrivial insulating states. We identify the main ingredients of the lattice models that are responsible for the nontrivial topological character and argue that such states can be realized within a large family of realistic optical lattice Hamiltonians with cold atoms. We focus our quantitative analysis on the properties of topological states with broken time-reversal symmetry specific to cold-atom settings. In particular, we analyze finite-size effects, multiorbital phenomena that give rise to a variety of distinct topological states and transitions between them, the dependence on the trap geometry, and, most importantly, the behavior of the edge states for different types of soft and hard boundaries. Furthermore, we demonstrate the possibility of experimentally detecting the topological states through light Bragg scattering of the edge and bulk states.