Inducing a many-body topological state of matter through Coulomb-engineered local interactions

The engineering of artificial systems hosting topological excitations is at the heart of current condensed matter research. Most of these efforts focus on single-particle properties, neglecting possible engineering routes via the modifications of the fundamental many-body interactions. Interestingly, recent experimental breakthroughs have shown that Coulomb interactions can be efficiently controlled by substrate screening engineering. Inspired by this success, we propose a simple platform in which topologically nontrivial many-body excitations emerge solely from dielectrically engineered Coulomb interactions in an otherwise topologically trivial single-particle band structure. Furthermore, by performing a realistic microscopic modeling of screening engineering, we demonstrate how our proposal can be realized in one-dimensional systems such as quantum-dot chains. Our results put forward Coulomb engineering as a powerful tool to create topological excitations, with potential applications in a variety of solid-state platforms.

Figure 1

(a) Sketch of the proposed system: A quantum-dot (QD) chain is deposited on a structured substrate. The spatial modulation of the substrate permitivity results in a spatially dependent environmental screening resulting in site-dependent local Coulomb interactions (b) within the otherwise homogeneous QD chain.

Figure 2

Screening-induced mean-field topology. Bulk spectra as functions of (a) $\mathrm{\Omega }$ and (b) $\tilde{U}$, showing the emergence of topological gaps. Full spectra as a function of $\varphi$ for (c) $\mathrm{\Omega }=0.4\pi$ and (d) $\mathrm{\Omega }=0.5\pi$, depicting edge states pumping through the gaps. Red (blue) denotes left (right) edge, the Fermi level is at $E=0.0$ and the system half filled. We use 80 sites and choose $\tilde{U}=6t$, $\lambda =0.5$, and $\mathrm{\Omega }=0.4\pi$ if not stated otherwise.

Figure 3

Screening-induced many-body topology. Spin spectral function (a) in the edge and (b) in the bulk for $\mathrm{\Omega }=\pi /\sqrt{3}$. Spectral function (c) in the edge and (d) in the bulk for $\mathrm{\Omega }=\pi /2$. (e) Bulk spectral function as a function of $\mathrm{\Omega }$, showing gaps at generic values of $\mathrm{\Omega }$. (f) Approximate linear scaling of the topological gap as a function of $\lambda$. We used 30 sites and set $\lambda =0.5$, $\tilde{U}=6t$, and $\mathrm{\Omega }=0.4\pi$ if not stated otherwise.

Figure 4

Local Coulomb engineering. Local Coulomb interaction $U_n$ controlled by (a) homogeneous and (b) heterogeneous dielectric substrates. (c)–(d) Upper and lower limits of the Coulomb modulation strength ${\lambda }_{\text{max}}$ estimated from homogeneous and heterogeneous substrates for different $\delta /h$ ratios and ${\varepsilon }_{\text{min}}=3$. (e) Example $U_n$ profile corresponding to $\tilde{U}=3\mathrm{eV}$, $\lambda =0.25$, and $\mathrm{\Omega }=\varphi =0.4\pi$, which could be realized with a patterned substrate, as illustrated in the sketch (f).

Figure 5

Robustness of the edge modes: (a) Spectral function of the edge for a finite second-neighbor hopping, and (b) with a finite random disorder in the local interactions, showing that the topological edge modes survive those perturbations. We took $\tilde{U}=6t$ and $\mathrm{\Omega }=\pi /\sqrt{3}$.

Figure 6

Example result of the multi-image-charge approach. (a) Left and (b) right show the numerically evaluated potential for ${\varepsilon }_0=2$, ${\varepsilon }_{\text{sub}}^L=4$, ${\varepsilon }_{\text{sub}}^R=10$, $h=2\AA$, and $\delta =y_0=2\AA$ in the $(x,y)$ and $(x,z)$ planes. Large red dot: Source charge position, orange dots: Poisson equation evaluation points, green dots: $y=0$ interface discrete boundary condition points, red dots: $x=0$ interface discrete boundary condition points, blue dots: Image charge positions, black lines: Dielectric interfaces.