Topological Phenomena in Non-equilibrium Systems
The efforts to realize new topological phases have focused mostly on equilibrium systems at zero temperature. The exciting possibility of realizing topological phenomena in out-of-equilibrium systems has been recently proposed in the context systems subjected to periodic external driving forces. A major advantage of this setup is the wider range of experimental controls it allows, and new types of accessible topological states. An intriguing example is the proposal that a non-topological material subject to electromagnetic radiation can have properties that mimic those of a topological insulator; this may open a completely new route to exploring topological phases, which are not accessible in equilibrium setups. Combined with the highly developed technology for controlling low-frequency electromagnetic modes, potential applications such as devices which utilize fast switching of edge state transport might become possible. Following this route, many important questions remain to be explored: What is the nature of topological phenomena in periodically driven systems? What kinds of phases can be realized following this route, and how different are they from the equilibrium ones? How does topology interplay with many-body interactions and the coupling to the environment to determine their properties? In which experimentally accessible systems can they be realized?
Universal Chiral Quasisteady States in Periodically Driven Many-Body SystemsMany novel experimental systems, such as cold atom and trapped ion systems, allow us to study the non-equilibrium many-body states of closed, interacting quantum systems subjected to a periodic drive. Generically, such systems are expected to absorb energy and heat up rapidly washing away any interesting quantum, and in particular, topological effects. In this work, we show that the tendency of driven quantum systems to heat up can in fact yield a new universal quantum phenomenon, which persists over a long intermediate time window. In the one dimensional prototype system we study, the universality is manifested in a persistent current, whose magnitude depends only on topological properties of the driving protocol and the density of particles. Quick heating of the low-energy degrees of freedom erases the initial details of the system. The high-energy degrees of freedom, meanwhile, remain cold for a long time, during which the system exhibits its topological properties. Our analysis serves as a prototype for a new class of phenomena that can arise in a variety of driven quantum systems.
Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge PumpTopological phases typically exhibit protected edge or surface modes, which necessarily coexist with propagating bulk modes that are spread throughout the system. The presence of such propagating bulk modes is required in order to avoid a quantum anomaly. This situation remains true even when disorder is present. A periodically driven system, however, is not bound by the same rules. In this paper, we show that the special character of periodically driven systems drastically changes the relationships among topology, disorder, and localization. We introduce a topological phase that has chiral edge modes, despite all of the bulk states of the system being localized by disorder. This topological phase is only achievable in a periodically driven system. We refer to this unique non-equilibrium phase of matter as an anomalous Floquet-Anderson insulator (AFAI). The AFAI phase possesses remarkable properties and is robust over a wide swath of parameter space. Most strikingly, it exhibits non-adiabatic yet precisely quantized charge pumping at a finite driving frequency. This quantized transport is observed when all of the states near one edge of the system are filled with fermions. The quantization of the charge pump is protected by disorder and the two-dimensional nature of the system. This situation is in contrast to adiabatic quantum pumps, proposed by Thouless three decades ago, in which quantization can only be stabilized by going to the zero-frequency (adiabatic) limit. The finite frequency quantized pumping phenomenon of the AFAI may find applications in the development of precision current standards.
Disorder-induced Floquet Topological InsulatorsWe investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically-driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topological state is confirmed by exact numerical time-evolution of wavepackets on the edge of the system. We consider the optimal driving regime for experimentally observing the Floquet-Anderson topological insulator, and discuss its possible realization in photonic lattices.
Lighting up topological insulators: large surface photocurrents from magnetic superlatticesThe gapless surface states of topological insulators (TI) can potentially be used to detect and harvest low-frequency infrared light. Nonetheless, it was shown that significant surface photocurrents due to light with frequency below the bulk gap are rather hard to produce. Here we demonstrate that a periodic magnetic pattern added to the surface dramatically enhances surface photocurrents in TI’s . The ability to produce substantial photocurrents on TI surfaces from mid-range and far-infrared light could be used in photovoltaic applications, as well as for detection of micrometer wavelength radiation.
- Netanel H. Lindner, Aaron Farrell, Eran Lustig, Gil Refael, Felix von Oppen, Lighting up topological insulators: large surface photocurrents from magnetic superlattices, arXiv:1403.0010