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We reveal a topological burning glass effect, where the local response of a system exhibits a topological quantization that is enhanced by an integer due to its environmental coupling. As a paradigmatic platform for this intriguing phenomenon, we study a central spin that is quasiperiodically driven by two incommensurate frequencies, and statically coupled to $N-1$ surrounding spins. In the strong coupling regime, the adiabatic dynamics of the total system is readily understood to imprint on the central spin an $N$-fold enhanced topological frequency conversion between the two driving frequencies. We argue that the topological burning glass effect is induced by the non-unitary dynamics of the central spin, which locally involves the collective motion of the surrounding spins. Our results are derived in the framework of adiabatic perturbation theory and fully corroborated by exact numerical simulations., 17 pages, 8 figures

The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is only visible if processes that do not conserve the single particle energy are included. Paradigmatic examples of such processes are electron-electron interactions and time dependent external drivings. We analyze the effects of a periodically driven Rashba impurity at the helical edge, in the presence of electron-electron interactions. Interactions are treated by means of bosonization and the backscattering current is computed perturbatively up to second order in the impurity strength. We show that the backscattering current is non-monotonic in the driving frequency. This property is a fingerprint of the Rashba impurity, being absent in the case of a magnetic impurity in the helical liquid. Moreover, the non-monotonic behaviour allows us to directly link the backscattering current to the Luttinger parameter $K$, encoding the strength of electron-electron interactions., 5+4 pages, 2 figures

We show that an interacting two-spin model subjected to two circularly polarized drives enables a feasible realization of a correlated topological phase in synthetic dimensions. The topological observable is given by a quantized frequency conversion between the dynamical drives, which is why we coin it the interacting topological frequency converter (ITFC). The ITFC is characterized by the interplay of interaction and synthetic dimension. This gives rise to striking topological phenomena that have no counterpart in the noninteracting regime. By calculating the topological phase diagrams as a function of interaction strength, we predict an enhancement of frequency conversion as a direct manifestation of the correlated topological response of the ITFC., 9 pages, 6 figures

The manipulation of the helical edge states of two-dimensional topological insulators is crucial for the development of technological applications. Recently, an important step forward, namely, the experimental realization of a quantum point contact between helical edges, has been accomplished. We theoretically predict that such a quantum point contact, in the presence of a time periodic applied electric field, is characterized by a topological quantum phase transition in the Floquet spectrum. Moreover, we show that it is possible to detect this dynamical topological quantum phase transition by a bare conductance measurements., 5 pages, 3 figures

We study a periodically driven central site coupled to a disordered environment. In comparison to the static model, transport features are either enhanced or reduced, depending on the frequency of the drive. We demonstrate this by analyzing the statistics of quasienergies and the logarithmic growth of bipartite entanglement entropy, which show similar features: For frequencies larger than disorder strength, localization is enhanced due to a reduced effective coupling to the central site. Remarkably, localization can even be increased up to almost perfect freezing at particular frequencies, at which the central site decouples due to the emergence of ``dark Floquet states.'' This high-frequency domain of our model is bounded from below by a critical frequency ${\ensuremath{\omega}}_{c}$, at which transport increases abruptly. We demonstrate that ${\ensuremath{\omega}}_{c}$ is determined by one-photon resonances, which connect states across the mobility edge and generically delocalize the system. This sensitive frequency dependence allows us to fine-tune transport properties of the driven central-site model with unprecedented precision.

Recently, it has been proposed that a mechanism for the appearance of non-equilibrium superconductivity in a resonantly driven semiconductor with repulsive interband interactions exists.~\cite{Goldstein_PRB15} The underlying microscopic model relies on the appearance of a specific fermionic dissipation mechanism and the careful simultaneous tailoring of the electronic dispersion relation and electron-electron interactions. We, instead, show that the phenomenon is rather general and does not need a special fine tuning of parameters. By considering a pair of bands with locally the same sign of concavity, we demonstrate that interband pairing arises under the natural assumption of the presence of phononic baths and radiative recombination. In light of these findings, we demonstrate how the emergence of superconductivity can be understood in terms of standard equilibrium interband BCS theory., Comment: 11 pages, 7 figures

Simulated quantum annealing (SQA) is a classical computational strategy that emulates a quantum annealing (QA) dynamics through a path-integral Monte Carlo whose parameters are changed during the simulation. Here we apply SQA to the one-dimensional transverse field Ising chain, where previous works have shown that, in the presence of disorder, a coherent QA provides a quadratic speedup with respect to classical simulated annealing, with a density of Kibble-Zurek defects decaying as ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{QA}}\ensuremath{\sim}{({log}_{10}\ensuremath{\tau})}^{\ensuremath{-}2}$ as opposed to ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{SA}}\ensuremath{\sim}{({log}_{10}\ensuremath{\tau})}^{\ensuremath{-}1}, \ensuremath{\tau}$ being the total annealing time, while for the ordered case both give the same power law ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{QA}}\ensuremath{\approx}{\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{SA}}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$. We show that the dynamics of SQA, while correctly capturing the Kibble-Zurek scaling ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for the ordered case, is unable to reproduce the QA dynamics in the disordered case at intermediate $\ensuremath{\tau}$. We analyze and discuss several issues related to the choice of the Monte Carlo moves (local or global in space), the time-continuum limit needed to eliminate the Trotter-discretization error, and the long autocorrelation times shown by a local-in-space Monte Carlo dynamics for large disordered samples.

We study Thouless pumping out of the adiabatic limit. Our findings show that despite its topological nature, this phenomenon is not generically robust to nonadiabatic effects. Indeed, we find that the Floquet diagonal ensemble value of the pumped charge shows a deviation from the topologically quantized limit which is quadratic in the driving frequency for a sudden switch on of the driving. This is reflected also in the charge pumped in a single period, which shows a nonanalytic behavior on top of an overall quadratic decrease. Exponentially small corrections are recovered only with a careful tailoring of the driving protocol. We also discuss thermal effects and the experimental feasibility of observing such a deviation. © 2018 American Physical Society.

We study quantum spin Hall insulators with local Coulomb interactions in the presence of boundaries using dynamical mean field theory. We investigate the different influence of the Coulomb interaction on the bulk and the edge states. Interestingly, we discover an edge reconstruction driven by electronic correlations. The reason is that the helical edge states experience Mott localization for an interaction strength smaller than the bulk one. We argue that the significance of this edge reconstruction can be understood by topological properties of the system characterized by a local Chern marker., Comment: 5 pages, 4 figures

Inducing topological transitions by a time-periodic perturbation offers a route to controlling the properties of materials. Here we show that the adiabatic preparation of a non-trivial state involves a selective population of edge-states, due to exponentially-small gaps preventing adiabaticity. We illustrate this by studying graphene-like ribbons with hopping's phases of slowly increasing amplitude, as for, e.g., a circularly polarized laser slowly turned-on. The induced currents have large periodic oscillations, but flow solely at the edges upon time-averaging, and can be controlled by focusing the laser on either edge. The bulk undergoes a non-equilibrium topological transition, as signaled by the local Chern marker introduced by Bianco & Resta in equilibrium. The failure of the adiabatic picture in presence of intraband resonances is discussed., Revised version, improved discussion of resonant case, new clearer figures, improved presentation; 5 pages, 4 figures, plus supplementary material