We study networks of Coulomb-blockaded integer quantum Hall islands with even fillings $ν=2k$ ($k$ being an integer), including cases with $2k$ layers each of $ν=1$ fillings. Allowing only spin-current interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating $SU(2)_k$ topologically ordered phases. The case with $k=1$ is dual to the Kalmeyer-Laughlin phase, $k=2$ to Kitaev's chiral spin liquid and the Moore-Read state, and $k=3$ contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the $SU(2)_k$ topological phases may be obtained also in an array of islands with $ν=2k$ integer quantum Hall states and critical spin chains in a checkerboard pattern. The array and checkerboard constructions gap out the charge mode and additional "flavor" modes by virtue of their geometry. Furthermore, we find that a fine tuning of the system parameter is not needed in the checkerboard configuration and the $ν=2$ case. We also discuss their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge $c=3k/(k+2)$ of the chiral edge modes.
An array of superconducting islands with semiconducting nanowires in the right regime provides a macroscopic implementation of Kitaev's toy model for Majorana wires. We show that a capacitive coupling between adjacent islands leads to an effective interaction between the Majorana modes. We demonstrate that even though strong repulsive interaction eventually drive the system into a Mott insulating state the competition between the (trivial) band-insulator and the (trivial) Mott insulator leads to an interjacent topological insulating state for arbitrary strong interactions.
The predicted interplay between Kondo physics and non-trivial topology in SmB$_{6}$ has stimulated many experimental reports, some of which are in apparent contradiction. The origin of the dispute may lie on the fragility of the Kondo insulating phase in the presence of Sm vacancies (Kondo holes) and/or natural impurities, such as Gd$^{3+}$. In this work, we locally investigated this fragility for Al-flux grown Sm$_{1-x}$Gd$_{x}$B$_{6}$ single crystals (0 $\leq$ $x$ $\leq$ 0.02) by combining electron spin resonance (ESR) and complementary bulk measurements. The Gd$^{3+}$ ESR spectra in a highl…
In two-dimensional (2D) insulating magnets, the thermal Hall effect of magnons is believed to be a consequence of topological magnon insulator with separated magnon bands and a well-defined Chern number. Due to broken time-reversal symmetry the thermal Hall effect vanishes in Dirac magnons. In this paper, we show that periodically driven semi-Dirac magnon in 2D insulating honeycomb ferromagnet results in a photoinduced Dirac magnon at the topological phase transition between a photoinduced topological and trivial magnon insulator. Remarkably, the photoinduced Dirac magnon and the photoinduced …
We show that the inclusion of nonlocal correlation effects in a variational wave function for the ground state of a topological Anderson lattice Hamiltonian is capable of describing both topologically trivial insulating phases and nontrivial ones characterized by an indirect gap, as well as its closure at the transition into a metallic phase. The method, though applied to an oversimplified model, thus captures the metallic and insulating states that are indeed observed in a variety of Kondo semiconductors, while accounting for topologically nontrivial band structures.
We propose multi-particle interference protocols in the time-energy domain which are able to probe localized topological quasiparticles. Using a set of quantum dots tunnel-coupled to a topologically nontrivial system, the time dependence of the dot level energies defines a many-body interferometry platform which (to some extent) is similar to the Hong-Ou-Mandel (HOM) interferometer. We demonstrate that for a superconducting island harboring at least four Majorana bound states, the probability distribution of the final dot occupation numbers will exhibit a characteristic interferometric pattern…
Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically coupled spin-1/2 su(2)$_k$ chains at any level $k$, focusing on the most prominent examples; the case $k = 2$ describes Ising anyons (equivalent to Majorana fermions) and $k = 3$ corresponds to Fibonacci anyons. We prove that the braiding of these emergent anyons exhibits the same braiding behavior as the physical quasiparticles. These results suggest a `solid…
We consider extended Hubbard models with repulsive interactions on a Honeycomb lattice and the transitions from the semi-metal phase at half-filling to Mott insulating phases. In particular, due to the frustrating nature of the second-neighbor repulsive interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spinful fermion models, respectively. We present the mean-field phase diagram and consider the effects of fluctuations within the random phase approximation (RPA). Functional renormalization group analysis also show tha…
Chiral magnets with topologically nontrivial spin order such as Skyrmions have generated enormous interest in both fundamental and applied sciences. We report broadband microwave spectroscopy performed on the insulating chiral ferrimagnet Cu$_{2}$OSeO$_{3}$. For the damping of magnetization dynamics we find a remarkably small Gilbert damping parameter of about $1\times10^{-4}$ at 5 K. This value is only a factor of 4 larger than the one reported for the best insulating ferrimagnet yttrium iron garnet. We detect a series of sharp resonances and attribute them to confined spin waves in the mm-si…
We study the nu=1/3 quantum Hall state in presence of the random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to unambiguously distinguish between insulating and current carrying states in an interacting system. The mobility gap can be determined numerically this way, which is found to agree with experimental value semiquantitatively. As the disorder strength increases towards a critical value, both the mobility gap and plateau width narrow continuously and ultimately collapse leading to an insulating phase.
We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Ou…
Role of localized magnetic moments in metal-insulator transitions lies at the heart of modern condensed matter physics, for example, the mechanism of high T$_{c}$ superconductivity, the nature of non-Fermi liquid physics near heavy fermion quantum criticality, the problem of metal-insulator transitions in doped semiconductors, and etc. Dilute magnetic semiconductors have been studied for more than twenty years, achieving spin polarized electric currents in spite of low Curie temperatures. Replacing semiconductors with topological insulators, we propose the problem of dilute magnetic topologica…
Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically non-trivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes 9 are realized for various parameters in this model. Specifically, at half-filling undistorted pyrochlore lattice with SO term yields a 'pristine' strong topological insulator with Z2 index (1;000). At quarter filling various strong and weak topological phases are obtained provided that both SO coupling and uniaxial lattice distortion are present. Our analy…
The charging energy $U$ of a small superconducting island containing Majorana zero modes---a Majorana Cooper-pair box---induces interactions between the Majorana zero modes. Considering a chain of many such boxes, a topological superconductor-insulator transition occurs when $U$ is much larger than the transfer matrix element $t$ between the boxes. In this Letter, we focus on the insulting phases occurring in this regime. We show that there are several competing insulating phases, and that the transition between them is described by a supersymmetric field theory with a central charge $c=7/10$.…
Based on density functional theory (DFT) calculations, we predict that a monolayer of OsCl$_3$---a layered material whose interlayer coupling is weaker than in graphite---possesses a quantum anomalous Hall (QAH) insulating phase generated by the combination of honeycomb lattice of osmium atoms, their strong spin-orbit coupling (SOC) and ferromagnetic ground state with {\em in-plane} easy-axis. The band gap opened by SOC is \mbox{$E_g \simeq 67$ meV} (or \mbox{$\simeq 191$ meV} if the easy-axis can be tilted out of the plane by an external electric field), and the estimated Curie temperature of…
Motivated by the recent experimental observation of a Mott insulating state for the layered Iridate Na2IrO3, we discuss possible ordering states of the effective Iridium moments in the presence of strong spin-orbit coupling and a magnetic field. For a field pointing in the [111] direction - perpendicular to the hexagonal lattice formed by the Iridium moments - we find that a combination of Heisenberg and Kitaev exchange interactions gives rise to a rich phase diagram with both symmetry breaking magnetically ordered phases as well as a topologically ordered phase that is stable over a small ran…
We investigate the nature of the Mott-insulating phases of half-filled 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of conformal field theory techniques and large-scale DMRG calculations, we show that the phase diagram strongly depends on the parity of $N$. First, we single out charged, spin-singlet, degrees of freedom, that carry a pseudo-spin ${\cal S}=N/2$ allowing to formulate a Haldane conjecture: for attractive interactions, we establish the emergence of Haldane insulating phases when $N$ is even, whereas a metallic behavior is found when $N$ …
The critical theories for the topological phase transitions of integer quantum Hall states to a trivial insulating state with the same symmetry can be obtained by calculating the ground state entanglement spectrum under a symmetric checkerboard bipartition. In contrast to the gapless edge excitations under the left-right bipartition, a quantum network with bulk gapless excitations naturally emerges at the Brillouin zone center without fine tuning. On a large finite lattice, the resulting critical theory for the $ν=1$ state is the (2+1) dimensional relativistic quantum field theory characterize…
A topological insulator (TI) is an unusual quantum state in which the insulating bulk is topologically distinct from vacuum, resulting in a unique metallic surface that is robust against time-reversal invariant perturbations. These surface transport properties, however, remains difficult to be isolated from the bulk in existing TI crystals (Bi2Se3, Bi2Te3 and Sb2Te3) due to impurity caused bulk conduction. We report in large crystals of topological Kondo insulator (TKI) candidate material SmB6 the thickness-independent surface Hall effects and non- local transport, which are robust against per…
Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d$th-order topology of a $d$-dimension system. In this work, we propose to predict different configurations of corner states from winding numbers defined for one-dimensional edges of the system. We first demonstrate the winding number characterization with a generalized two-dimensional square lattice belonging to the BDI symmetry class. In addition to the second-order topological insulating phase, the system may also be a no…
We investigate the necessary conditions for the emergence of complex, noncoplanar magnetic configurations in a Kondo lattice model with classical local moments on the geometrically frustrated Shastry-Sutherland lattice and their evolution in an external magnetic field. We demonstrate that topologically nontrivial spin textures, including a new canted flux state, with nonzero scalar chirality arise dynamically from realistic short-range interactions. Our results establish that a finite Dzyaloshinskii-Moriya (DM) interaction is necessary for the emergence of these novel magnetic states when the …
SmB6 is a strongly correlated material that has been attributed as a topological insulator and a Kondo insulator. Recent studies have found the topological surface states and low temperature insulating character to be profoundly robust against magnetic and non-magnetic impurities. Here, we use angle resolved photoemission spectroscopy to chart the evolution of topologically-linked electronic structure features versus magnetic doping and temperature in Sm$_{1-x}$M$_x$B$_6$ (M=Eu, Ce). Topological coherence phenomena are observed out to unprecedented ~30% Eu and 50% Ce concentrations that repres…
Using density functional theory calculations with a Hubbard $U$, we explore topologically nontrivial phases in $X_2$O$_3$ honeycomb layers with $X=$ $4d$ and $5d$ cation inserted in the band insulator $α$-Al$_2$O$_3$ along the [0001]-direction. Several promising candidates for quantum anomalous Hall insulators (QAHI) are identified. In particular, for $X$=Tc and Pt spin-orbit coupling (SOC) opens a gap of 54 and 59 meV, respectively, leading to Chern insulators (CI) with $C$=--2 and --1. The nature of different Chern numbers is related to the corresponding spin textures. The Chern insulating p…
Weyl semimetals are three-dimensional, topologically protected, gapless phases which show exotic phenomena such as Fermi arc surface states or negative magnetoresistance. It is an open question whether interparticle interactions can turn the topological semimetal into a topologically nontrivial Mott insulating phase. We investigate an experimentally motivated model for Weyl physics of cold atoms in optical lattices, with the main focus on interaction effects and topological properties by means of dynamical mean-field theory (DMFT). We characterize topological phases by numerically evaluating t…
Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a $\mathcal{Z}_2$-classification formul…
The newly-discovered three-dimensional strong topological insulators (STIs) exhibit topologically-protected Dirac surface states. While the STI surface state has been studied spectroscopically by e.g. photoemission and scanned probes, transport experiments have failed to demonstrate the most fundamental signature of the STI: ambipolar metallic electronic transport in the topological surface of an insulating bulk. Here we show that the surfaces of thin (<10 nm), low-doped Bi2Se3 (\approx10^17/cm3) crystals are strongly electrostatically coupled, and a gate electrode can completely remove bulk c…
Here we investigate antiferromagnetic Eu$_{5}$In$_{2}$Sb$_{6}$, a nonsymmorphic Zintl phase. Our electrical transport data show that Eu$_{5}$In$_{2}$Sb$_{6}$ is remarkably insulating and exhibits an exceptionally large negative magnetoresistance, which is consistent with the presence of magnetic polarons. From {\it ab initio} calculations, the paramagnetic state of Eu$_{5}$In$_{2}$Sb$_{6}$ is a topologically nontrivial semimetal within the generalized gradient approximation (GGA), whereas an insulating state with trivial topological indices is obtained using a modified Becke-Johnson potential.…
In this article we extend the celebrated Berry-phase formulation of electric polarization in crystals to higher electric multipole moments. We determine the necessary conditions under which, and minimal models in which, the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they manifest topologically protected corner states carrying fractional charge, i.e., fractionalization at the boundary of the boundary. To characterize these new insulating pha…
Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ν=2$ (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling $ν=1$ were observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers. However, how the topologically nontrivial s…
We show how quasi-one-dimensional correlated insulating states arise at two-thirds filling in organometallic multinuclear coordination complexes described by layered decorated honeycomb lattices. The interplay of spin-orbit coupling and electronic correlations leads to pseudospin-1 moments arranged in weakly coupled chains with highly anisotropic exchange and a large trigonal splitting. This leads to a quantum phase transition from a Haldane phase to a topologically trivial phase as the relative strength of the spin-orbit coupling increases.
We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model and characterize their phases via a topological invariant constructed out of their Green's functions. We demonstrate that the existence of topologically protected, zero-energy states at the boundaries of these systems can be tied to the values of their topological invariant, just like when working with the conventional, noninteracting topological insulators. We use a combination of analytical methods and the numerical density matrix renormalization group method to calculate the va…
Magnetic materials with noncoplanar magnetic structures can show unusual physical properties driven by nontrivial topology. Topologically-active states are often multi-q structures, which are challenging to stabilize in models and to identify in materials. Here, we use inelastic neutron-scattering experiments to show that the insulating double perovskites Ba2YRuO6 and Ba2LuRuO6 host a noncoplanar 3-q structure on the face-centered cubic lattice. Quantitative analysis of our neutron-scattering data reveals that these 3-q states are stabilized by biquadratic interactions. Our study identifies do…
In this paper we study a novel superconductor-ferromagnet-superconductor (SC-FM-SC) Josephson junction array deposited on top of a two-dimensional quantum spin Hall (QSH) insulator. The existence of Majorana bound states at the interface between SC and FM gives rise to charge-e tunneling, in addition to the usual charge-2e Cooper pair tunneling, between neighboring superconductor islands. Moreover, because Majorana fermions encode the information of charge number parity, an exact Z_2 gauge structure naturally emerges and leads to many new insulating phases, including a deconfined phase where e…
We consider a one-dimensional Josephson junction array, in the regime where the junction charging energy is much greater than the charging energy of the superconducting islands. In this regime we critically reexamine the continuum limit description and establish the relationship between parameters of the array and the ones of the resulting sine-Gordon model. The later model is formulated in terms of quasi-charge. We argue that despite arguments to the contrary in the literature, such quasi-charge sine-Gordon description remains valid in the vicinity of the phase transition between the insulati…
We investigate the groundstate properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the $p$-wave Kondo-Heisenberg lattice model) by means of the Density Matrix Renormalization Group method. The non-standard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the "$p$-wave" spin density of conduction electrons, inducing a topologically non-trivial insulating groundstate. Based on the analysis of the charge- and spin-excitation gaps, the string order parameter, and the spin …
Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected, quantized circulation. When this topological protection is absent, as in the case of $^3$He-A, the coherent quantum state no longer supports persistent superflow. Here we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex vector order parameter. We ap…
