Floquet Chiral Magnetic Effect

Abstract

A single Weyl fermion, which is prohibited in static lattice systems by the Nielsen-Ninomiya theorem, is shown to be realized in a periodically driven three-dimensional lattice system with a topologically nontrivial Floquet unitary operator, manifesting the chiral magnetic effect. We give a topological classification of Floquet unitary operators in the Altland-Zirnbauer symmetry classes for all dimensions, and use it to predict that all gapless surface states of topological insulators and superconductors can emerge in bulk quasienergy spectra in Floquet systems.In 1981, Nielsen and Ninomiya proved that a single Weyl fermion cannot be realized in lattice systems [1,2]. This theorem places a fundamental constraint on band structures due to the topology of the Brillouin zone. Weyl fermions have recently played a key role in crossfertilizing ideas from high-energy physics and condensedmatter physics. A prime example is the prediction of Weyl semimetals [3,4], where the low-energy effective field theory of Weyl fermions predicts novel electromagnetic responses originating from the chiral anomaly [5][6][7][8]. In particular, the observations of the surface Fermi arc [9][10][11][12][13][14][15] and anomalous transport [16][17][18][19] have aroused considerable interest. However, if a system is defined on a lattice and thus anomaly-free, the Nielsen-Ninomiya theorem dictates that a Weyl fermion be accompanied by its partner with opposite chirality. By the same token, an anomaly-induced response known as the chiral magnetic effect (CME) [20] does not occur in equilibrium [21], and numerous attempts to circumvent this difficulty have been made [22][23][24][25][26][27][28][29].In this Letter, we demonstrate that a single Weyl fermion can be realized on a periodically driven lattice, thereby overcoming the above limitations. In periodically driven (Floquet) systems, the unitary time-evolution operator over one period defines an effective Hamiltonian and the associated quasienergies [30]. Despite the apparent similarity to static systems, Floquet systems enable the realization of exotic phases that cannot be achieved in equilibrium, such as anomalous topological insulators [31,32] and time crystals [33,34]. The key idea of our proposal is an emerging topological structure in unitary operators associated with the periodicity of quasienergies [31]. We here show that a driving protocol for a three-dimensional (3D) Thouless pump [31,35] given by a topological Floquet unitary operation realizes a single Weyl fermion in a 3D lattice system, thereby providing a platform to observe the CME. We demonstrate that chiral transport emerges under a topological 3D Floquet drive with an applied synthetic magnetic field, leading to a Floquet realization of the CME. Our proposal can be implemented by using ultracold atomic gases, where the Thouless pump has been realized experimentally [36,37]. Furthermore, by exploiting the correspondence between anomalous gapless spectra and topological unitary operators, we provide a topological classificat...

Reversible to irreversible transitions in periodically driven skyrmion systems

“…Another potential avenue for future research is in the area of Floquet engineering [56]. In particular, it may be possible to use the Floquet-Magnus expansion to obtain an approximate description of the relaxation to steady state, as recently demonstrated for the Kapitza pendulum with friction [57].…”

Wannier representation of Floquet topological states

“…A topological classification of Floquet operators was performed in Ref. 32. It was shown that the classification of Floquet operators in d spatial dimensions coincides with that of gapless surface states of static topological insulators/superconductors in d dimensions.…”

“…So far we have assumed that U (k, T ) = 1 N ×N . When U (k, T ) = 1 N ×N , we use the deformed evolution operator (32). Note that…”

Topological quantum walk with discrete time-glide symmetry

“…Recently, topological phases in periodically driven systems (Floquet systems) have attracted much attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A large number of approaches to realize Floquet topological phases have been theoretically proposed [2,4,5,11,13,14,17] and experiments have been carried out [6,8] to engineer Floquet systems with nontrivial topological phases.…”