Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

Abstract

Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual topological defects that are analogous to extended monopoles. In this work, we describe a scheme by which nodal rings and nodal spheres can be realized in synthetic quantum matter through well-defined periodic-driving protocols. As a central result of our work, we characterize these nodal defects through the quantum metric, which is a gauge-invariant quantity associated with the geometry of quantum states. In the case of nodal rings, where the Berry curvature and conventional topological responses are absent, we show that the quantum metric provides an observable signature for these extended topological defects. Besides, we demonstrate that quantum-metric measurements could be exploited to directly detect the topological charge associated with a nodal sphere. We discuss possible experimental implementations of Floquet nodal defects in few-level atomic systems, paving the way for the exploration of Floquet extended monopoles in quantum matter. arXiv:1912.00930v1 [cond-mat.mes-hall]

The Weyl side of ultracold matter

“…Weyl semimetals also exhibit anomalous Hall and circular photogalvanic effects (1) that could both be revealed in optical-lattice setups through circular shaking (11). The tunability of this setting could be exploited to engineer various types of semimetals displaying exotic nodal lines, rings, or spheres in the band structure (12,13). Synthetic 3D SOCs also constitute a central ingredient for the engineering of 3D topological insulators with cold gases (3).…”

Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

“…In condensed matter, the quantum metric generally defines a notion of distance over momentum space, and it was shown to provide essential geometric contributions to various phenomena, including exotic superconductivity [6][7][8] and superfluidity [9], orbital magnetism [10,11], the stability of fractional quantum Hall states [12][13][14][15][16][17], semiclassical wavepacket dynamics [18,19], topological phase transitions [20], and lightmatter coupling in flat-band systems [21]. Besides, the quantum metric plays a central role in the construction of maximally-localized Wannier functions in crystals [22,23], and it provides practical signatures for exotic momentum-space monopoles [24,25] and entanglement in topological superconductors [26,27].…”

Floquet-Weyl semimetals generated by an optically resonant interband-transition

“…6,18 An interaction of topological SMs with a continuouswave laser provides the studies of topological materials with another avenue from the perspective of the quantum control of underlying topological properties by means of built-in laser parameters -intensity, frequency ω, and polarization -and the exploration of topological phases that are in non-equilibrium. [43][44][45][46][47][48][49][50][51][52][53][54] Here, the to-tal Hamiltonian H(t) of concern at time t has temporal periodicity H(t) = H(t + T ) to ensure the Floquet theorem, with T = 2π/ω. 55 By the drive with a circularly polarized laser -in place of the application of a static intrinsic Zeeman field -, the T-symmetry in the DSMs and NLSMs is broken to form the WSMs, and these are termed as Floquet WSMs (FWSMs).…”