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The rich order parameter of Spin Density Waves allows for unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of a staggered magnetization. It becomes energetically preferable to ordinary dislocation due to enhanced Coulomb interactions in the semiconducting regime. Generation of these objects changes e.g. the narrow band noise frequency.
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The rich order parameter of Spin Density Waves allows for an unusual object of a complex topological nature: a half-integer dislocation combined with a semi-vortex of the staggered magnetization. It becomes energetically preferable to ordinary dislocation due to enhanced Coulomb interactions in the semiconducting regime. Generation of these objects changes the narrow band noise frequency.
The discovery that spin-orbit coupling can generate a new state of matter in the form of quantum spin-Hall (QSH) insulators has brought topology to the forefront of condensed matter physics. While QSH states from spin-orbit coupling can be fully understood in terms of band theory, fascinating many-body effects are expected if the state instead results from interaction-generated symmetry breaking. In particular, topological defects of the corresponding order parameter provide a route to exotic quantum phase transitions. Here, we introduce a model in which the condensation of skyrmion defects in an interaction-generated QSH insulator produces a superconducting (SC) phase. Because vortex excitations of the latter carry a spin-$1/2$ degree of freedom numbers, the SC order may be understood as emerging from a gapless spin liquid normal state. The QSH-SC transition is an example of a deconfined quantum critical point (DQCP), for which we provide an improved model with only a single length scale that is accessible to large-scale quantum Monte Carlo simulations.
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and Hofstadter bands; in both cases, a large magnetic field is required to engineer the underlying flat band. The recent observation of quantum anomalous Hall effects (QAH) in narrow band moire systems has led to the theoretical prediction that such phases may be realized even at zero magnetic field. Here we report the experimental observation of insulators with Chern number $C=1$ in the zero magnetic field limit at $ u=3/2$ and $7/2$ filling of the moire superlattice unit cell in twisted monolayer-bilayer graphene (tMBG). Our observation of Chern insulators at half-integer values of $ u$ suggests spontaneous doubling of the superlattice unit cell, in addition to spin- and valley-ferromagnetism. This is confirmed by Hartree-Fock calculations, which find a topological charge density wave ground state at half filling of the underlying $C=2$ band, in which the Berry curvature is evenly partitioned between occupied and unoccupied states. We find the translation symmetry breaking order parameter is evenly distributed across the entire folded superlattice Brillouin zone, suggesting that the system is in the flat band, strongly correlated limit. Our findings show that the interplay of quantum geometry and Coulomb interactions in moire bands allows for topological phases at fractional superlattice filling that spontaneously break time-reversal symmetry, a prerequisite in pursuit of zero magnetic field phases harboring fractional statistics as elementary excitations or bound to lattice dislocations.
Linear Heisenberg antiferromagnets (HAFs) are chains of spin-$S$ sites with isotropic exchange $J$ between neighbors. Open and periodic boundary conditions return the same ground state energy in the thermodynamic limit, but not the same spin $S_G$ when $S ge 1$. The ground state of open chains of N spins has $S_G = 0$ or $S$, respectively, for even or odd N. Density matrix renormalization group (DMRG) calculations with different algorithms for even and odd N are presented up to N = 500 for the energy and spin densities $rho(r,N)$ of edge states in HAFs with $S = 1$, 3/2 and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with $rho(r,N)propto(-1)^{r-1}$ for $r=1,2,ldots N$. The SDWs are in phase when N is odd, out of phase when N is even, and have finite excitation energy $Gamma(N)$ that decreases exponentially with N for integer $S$ and faster than 1/N for half integer $S$. The spin densities and excitation energy are quantitatively modeled for integer $S$ chains longer than $5 xi$ spins by two parameters, the correlation length $xi$ and the SDW amplitude, with $xi = 6.048$ for $S = 1$ and 49.0 for $S = 2$. The BI-SDWs of $S = 3/2$ chains are not localized and are qualitatively different for even and odd N. Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases $|Gamma(N)|$ and weakens the size dependence. The nonlinear sigma model (NL$sigma$M) has been applied the HAFs, primarily to $S = 1$ with even N, to discuss spin densities and exchange between localized states at the ends as $Gamma(N) propto (-1)^N exp(-N/xi)$...
We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, we find that the defect density first increases and then decreases. Furthermore, we find switching phenomena, due to the formation of channels of dislocations. These results are in qualitative accord with recent dynamical x-ray scattering experiments by Ringlandet al. and transport experiments by Lemay et al.
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