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Register a new userQuantum cluster approach to the topological invariants in correlated Chern insulators
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We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the interacting bulk Chern number within the natural unit cell by means of the so-called topological Hamiltonian. With close investigations on a prototype model, the half-filled Haldane Hubbard model, which is subject to both periodic and open boundary conditions, we uncover the unexpected failure of this scheme due to the explicit breaking of the translation symmetry. Instead, we assert that the faithful interacting bulk Chern number in the framework of quantum cluster approaches can be computed in the enlarged unit cell, which is free of the fault caused by the explicit translation symmetry breaking and consistent with the interacting bulk-edge correspondence.
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Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.
We explore the non-equilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and non-topological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally-observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample.
We construct a lattice model for a cubic Kondo insulator consisting of one spin-degenerate $d$ and $f$ orbital at each lattice site. The odd-parity hybridization between the two orbitals permits us to obtain various trivial and topological insulating phases, which we classify in the presence of cubic symmetry. In particular, depending on the choice of our model parameters, we find a strong topological insulator phase with a band inversion at the $mathrm{X}$ point, modeling the situation potentially realized in SmB$_6$, and a topological crystalline insulator phase with trivial $mathbb{Z}_2$ indices but nonvanishing mirror Chern numbers. Using the Kotliar-Ruckenstein slave-boson scheme, we further demonstrate how increasing interactions among $f$ electrons can lead to topological phase transitions. Remarkably, for fixed band parameters, the $f$-orbital occupation number at the topological transitions is essentially independent of the interaction strength, thus yielding a robust criterion to discriminate between different phases.
The adiabatic insertion of a pi flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that pi fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z_2 topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a pi flux gives rise to a Kramers doublet of spinon states with a Curie law signature in the magnetic susceptibility. Electronic correlations also provide a bosonic mode of magnetic excitons with tunable energy that act as exchange particles and mediate a dynamical interaction of adjustable range and strength between spinons. pi fluxes can therefore be used to build models of interacting spins. This idea is applied to a three-spin ring and to one-dimensional spin chains. Due to the freedom to create almost arbitrary spin lattices, correlated topological insulators with pi fluxes represent a novel kind of quantum simulator potentially useful for numerical simulations and experiments.
Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when $ pm 1, pm 2, pm 3$ electrons occupy each moir e unit cell and lead to the formation of correlated insulating, superconducting and ferromagnetic phases. While some phases have been shown to carry a non-zero Chern number, the local microscopic properties and topological character of many other phases remain elusive. Here we introduce a set of novel techniques hinging on scanning tunneling microscopy (STM) to map out topological phases in MATBG that emerge in finite magnetic field. By following the evolution of the local density of states (LDOS) at the Fermi level with electrostatic doping and magnetic field, we visualize a local Landau fan diagram that enables us to directly assign Chern numbers to all observed phases. We uncover the existence of six topological phases emanating from integer fillings in finite fields and whose origin relates to a cascade of symmetry-breaking transitions driven by correlations. The spatially resolved and electron-density-tuned LDOS maps further reveal that these topological phases can form only in a small range of twist angles around the magic-angle value. Both the microscopic origin and extreme sensitivity to twist angle differentiate these topological phases from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions and exhibits an unexpected splitting between zero Landau levels that can be as large as ${sim },3-5$ meV. Our results show how strong electronic interactions affect the band structure of MATBG and lead to the formation of correlation-enabled topological phases.
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