Session S54: Quenches and Transport in Driven Topological Systems

Quantized energy pumping in quasi-periodically driven Nitrogen Vacancy Centres

A spin strongly driven by two incommensurate tones can exhibit a topological class of dynamics in which it (i) pumps energy from one drive to the other at a quantized average rate, in precise relationship with the quantum Hall effect, and (ii) exhibits an oscillatory response to a perturbation to the phases of the drives. We show these remarkable signatures to be realized in experiments in Nitrogen Vacancy centres. We further provide an experimental demonstration of half-integer quantization of various responses at the transition between the topological and trivial classes of dynamics.
  

Z2 topological quench dynamics

In this talk, we present a quench setup for a realization of a Z2 topological quench dynamics in 3+1 dimensions. We show the Z2 feature can be identified from the flow of Berry phase. In addition, the entanglement spectra in both real and frequency space reveal the topological features. Finally, we discuss some possible realizations of our model.   

Photoinduced interfacial chiral modes in threefold topological semimetal

We investigate the chiral electronic modes at the interface between two regions of a threefold
topological semimetal, which is illuminated by left and right handed elliptically polarized waves.
The radiation effects on the band structure of semimetal is analyzed by using Floquet theory. Two
distinct solutions of the interface modes are found with the chirality depending on the phase of
the irradiation. We also consider the anomalous Hall response which is attributed to the interband
contribution between dispersionless flat band and conic bands.   

Space-time group symmetry and response functions Congjun Wu University of California, San Diego

Recently, space-time group was proposed to describe the dynamic crystalline symmetries of a large class of dynamic systems beyond the Floquet system (Xu and Wu, Phys. Rev. Lett. 120, 096401 (2018)), including laser-driven solid crystals, dynamic photonic crystals, and optical lattices. We further study its consequences on physical observables on the response functions by applying the group theory representation analysis. This work will provide useful guidance for studying physical properties in time-dependent systems.   

Electrons in Narrow-Band Moire Graphene: Electric and Magnetic Two-Dimensional Bloch Oscillations

Bloch oscillating electrons, moving in a two-dimensional crystal under a DC electric field, are described, in a quasiclassical picture, by trajectories that wind quasiperiodically around the 2D Brillouin zone. The oscillations feature two or more discrete frequencies that depend on the field, but not on individual particle velocities, producing narrow lines in ensemble-averaged noise power spectrum. An externally applied magnetic field alters the dynamics, creating new types of Bloch oscillations that do not exist in one-dimensional solids. The conventional “electric” oscillations persist at weak B fields; above a critical B value a different dynamics sets in that combines Bloch oscillations and Larmor drift. In this “magnetic” regime particle trajectories are extended in position space and confined in momentum space, with a complex chaotic behavior arising at the transition.   

Energy filtered leads for quantized transport in Floquet systems

In equilibrium, robust electronic edge or surface modes play key roles in the fascinating quantized responses exhibited by topological materials. Topological bands and edges states can be induced dynamically even in trivial materials, using a time-periodic drive. In contrast to their equilibrium counterparts, the dynamically induced Floquet topological insulators do not exhibit quantized transport when probed using conventional measurements, such as the differential conductance. This lack of quantization arises due to photon assisted tunneling from the system to the leads and vice versa. We show that quantization of the differential conductance can be restored by connecting the system and the leads via an energy filter. We discuss the utility of this approach for achieving quantization of other responses in topological Floquet systems.   

Photoinduced Topological Phase Transition and Optical Conductivity of Black Phosphorene

We theoretically study the photoinduced topological phase transition of black phosphorene induced by laser light with moderate-intensity, which can satisfy the experimentally realistic requirement to preserve the quality of the sample. By deriving the effective Floquet Hamiltonian in terms of pseudo-spin S=1/2 degrees of freedom, we calculate the Chern number and the optical conductivity of the system with varying laser frequency. As one can expect from the photon-assisted transport, the longitudinal optical conductivity has a threshold frequency at Ω=△/h with △ being the band gap of black phosphorene. Unlike the longitudinal optical conductivity, the optical Hall conductivity sharply increases when hΩ goes beyond one half of the band gap △/2. We also show that the Chern number changes from trivial to non-trivial one upon increasing frequency beyond hΩ=△/2.   

Enhancement of High Harmonics Generation by Floquet Engineering

High hramonic generation (HHG) in gaseous systems and solids is well studied. Since periodically driven systems can produce harmonic response, it is important to study the influence of external driving on the HHG power spectrum. We formulate a theory of high-harmonic current using Floquet theory of periodically driven systems. As an application of our theory, we study HHG in the Su-Schrieffer-Heeger (SSH) model with and without periodic drive. We find that there is a significant enhancement in higher harmonincs when the system is driven. Moreover, this enhancement peaks for an optimal harmonic at a value that increases when the intensity of the laser is reduced. This means HHG can be generated even at lower pulse intensities in a Floquet system. We obtain analytical expressions for HHG power spectrum in the high-frequency approximation for driven SSH model. Further, we study the effects of laser polarization and occupation of Floquet bands on HHG in two dimensional systems. We also investigate the consequences of spatiotemporal symmetries and Floquet topology for HHG in Floquet systems.   

Correlation-Enhanced Quantized Charge Pumping

We investigate charge pumping in the vicinity of order-obstructed topological phases. To explore this, we study a prototypical Su-Schreiffer-Heefer model with non-local interaction that gives rise to orbital charge density wave order, and characterize the impact of this order on the model’s topological properties. In the ordered phase, where the many-body topological invariant loses quantization, we find that not only is quantized chage pumping possible, it is assisted by the collective nature of the orbital charge density wave order.   

Stability of dynamical quantum phase transitions in quenched topological insulators: From multi-band to disordered systems

Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multi-band to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder. (arXiv:1909.01402)   

Observation of long excitation lifetime in photoexcited Sb-doped Bi2Se3 nanoplatelets

Bi₂Se₃ is a three-dimensional topological insulator (TI), characterized by a bulk band gap of approximately 0.3 eV and a Dirac-like protected surface state. The material is usually n-type due to selenium vacancies, and chemical substitution, such as Sb-doping, is typically needed to bring the chemical potential into the bulk band gap. We will present ultrafast transient reflectivity measurements on Bi₂Se₃ and Bi_2-xSb_xSe₃ nanoplatelets which reveal starkly different carrier decay dynamics in n-type vs. insulating samples. This will be discussed in the context of optoelectronic applications of TIs, including as a material for exciton condensation.   

Time-domain anyon interferometry in Kitaev honeycomb spin liquids and beyond

Motivated by recent evidence of a non-Abelian spin liquid in α-RuCl₃, we introduce a new experimental method for probing the edge and quasiparticle content of such a phase. Our scheme exploits a pair of ancillary quantum spins that communicate via judicious time-dependent tunneling of energy into and out of the spin liquid’s gapless chiral Majorana edge state. We show that the ancillary-spin dynamics not only probes the Majorana edge modes, but in suitable geometries allows one to detect individual non-Abelian anyons and emergent fermions via a time-domain counterpart of anyon interferometry developed in the quantum-Hall context. The tools that we develop are expected to be widely applicable to topological phases both in solid-state and cold-atoms settings.   

Electron localization in two-dimensional topological and non-topological bands

Many-body localization (MBL) is a well-established phase present in disordered one-dimensional spin models with short-range interaction. However, the stability of MBL in higher dimensions, in the presence of long range interaction and under the effect of a topologically non-trivial single-particle band structure, is still an area of ongoing research. We demonstrate a method to construct nearly flat subbands with arbitrary Chern numbers, using a weak periodic potential in the lowest Landau level. This two-dimensional system is a novel platform for the detailed study of the interplay between disorder, interaction and topology in a continuum model. Using exact diagonalization, we investigate the localization properties of single-particle eigenstates, as well as the tendency to many-body localize in the presence of interaction, both in the quasi 1-D and 2-D limits. Our results are based on an analysis of both the many-body eigenvalue spacings and the time evolution of an initial charge imbalance [1], [2].

[1] A. Krishna, M. Ippoliti, and R. N. Bhatt, Phys. Rev. B 99, 041111(R) (2019)
[2] A. Krishna, M. Ippoliti, and R. N. Bhatt, Phys. Rev. B 100, 054202 (2019)