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We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well-defined and nontrivial in the $D to infty$ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semi-metal states, which are unconventional already in the non-interacting case. Topological phases are characterized by a non-quantized Chern density replacing the Chern number as $Dto infty$.
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Detailed understanding of the role of single dopant atoms in host materials has been crucial for the continuing miniaturization in the semiconductor industry as local charging and trapping of electrons can completely change the behaviour of a device. Similarly, as dopants can turn a Mott insulator into a high temperature superconductor, their electronic behaviour at the atomic scale is of much interest. Due to limited time resolution of conventional scanning tunnelling microscopes, most atomic scale studies in these systems focussed on the time averaged effect of dopants on the electronic structure. Here, by using atomic scale shot-noise measurements in the doped Mott insulator Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$, we visualize sub-nanometer sized objects where remarkable dynamics leads to an enhancement of the tunnelling current noise by at least an order of magnitude. From the position, current and energy dependence we argue that these defects are oxygen dopant atoms that were unaccounted for in previous scanning probe studies, whose local environment leads to charge dynamics that strongly affect the tunnelling mechanism. The unconventional behaviour of these dopants opens up the possibility to dynamically control doping at the atomic scale, enabling the direct visualization of the effect of local charging on e.g. high T$_{text{c}}$ superconductivity.
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.
We develop a theory for manipulating the effective band structure of interacting helical edge states realized on the boundary of two-dimensional time-reversal symmetric topological insulators. For sufficiently strong interaction, an interacting edge band gap develops, spontaneously breaking time-reversal symmetry on the edge. The resulting spin texture, as well as the energy of the the time-reversal breaking gaps, can be tuned by an external moire potential (i.e., a superlattice potential). Remarkably, we establish that by tuning the strength and period of the potential, the interacting gaps can be fully suppressed and interacting Dirac points re-emerge. In addition, nearly flat bands can be created by the moire potential with a sufficiently long period. Our theory provides a novel way to enhance the coherence length of interacting helical edges by suppressing the interacting gap. The implications of this finding for ongoing experiments on helical edge states is discussed.
We study the transport properties of the Kondo insulator SmB$_6$ with a specialized configuration designed to distinguish bulk-dominated conduction from surface-dominated conduction. We find that as the material is cooled below 4 K, it exhibits a crossover from bulk to surface conduction with a fully insulating bulk. We take the robustness and magnitude of the surface conductivity, as is manifest in the literature of SmB$_6$, to be strong evidence for the topological insulator metallic surface states recently predicted for this material.
Bulk and surface state contributions to the electrical resistance of single-crystal samples of the topological Kondo insulator compound SmB6 are investigated as a function of crystal thickness and surface charge density, the latter tuned by ionic liquid gating with electrodes patterned in a Corbino disk geometry on a single surface. By separately tuning bulk and surface conduction channels, we show conclusive evidence for a model with an insulating bulk and metallic surface states, with a crossover temperature that depends solely on the relative contributions of each conduction channel. The surface conductance, on the order of 100 e^2/h and electron-like, exhibits a field-effect mobility of 133 cm^2/V/s and a large carrier density of ~2x10^{14}/cm^2, in good agreement with recent photoemission results. With the ability to gate-modulate surface conduction by more than 25%, this approach provides promise for both fundamental and applied studies of gate-tuned devices structured on bulk crystal samples.
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