[Paper Review] Dynamical Weyl Points and 4D Nodal Rings in Cold Atomic Gases

Yan-Bin Yang, Luming Duan+1 more|arXiv (Cornell University)|Jan 25, 2018

Topological Materials and Phenomena49 references14 citations

TL;DR

This paper proposes the existence of dynamical Weyl points and 4D Weyl nodal rings in periodically driven cold atomic gases, where time acts as an artificial dimension, enabling topological pumping with tunable, non-quantized particle transport. The key contribution is the realization of a non-quantized topological pump via Chern number transitions in parameter space (kx, ky, t) or (kx, ky, kz, t), offering continuous control over pumped particles through experimental parameters.

ABSTRACT

Controllability of ultracold atomic gases has reached an unprecedented level, allowing for experimental realization of the long-sought-after Thouless pump, which can be interpreted as a dynamical quantum Hall effect. On the other hand, Weyl semimetals and Weyl nodal line semimetals with touching points and rings in band structures have sparked tremendous interest in various fields in the past few years. Here, we show that dynamical Weyl points and dynamical 4D Weyl nodal rings, which are protected by the first Chern number on a parameter surface formed by quasi-momentum and time, emerge in a two-dimensional and three-dimensional system, respectively. We find that the topological pump occurs in these systems but the amount of pumped particles is not quantized and can be continuously tuned by controlling experimental parameters over a wide range. We also propose an experimental scheme to realize the dynamical Weyl points and 4D Weyl nodal rings and to observe their corresponding topological pump in cold atomic gases.

Motivation & Objective

• To explore the emergence of topological gapless phenomena in periodically driven ultracold atomic systems.
• To investigate whether dynamical analogs of Weyl points and 4D nodal rings can exist when time is treated as a parameter in parameter space.
• To demonstrate that such dynamical topological structures support a non-quantized topological pump.
• To propose a feasible experimental scheme for realizing and observing these phenomena in cold atomic gas platforms.

Proposed method

• Constructs a time-periodic Hamiltonian in momentum space with parameters kx, ky, kz, and time t, treating t as an artificial quasi-momentum.
• Defines the Chern number on a torus (kx, t) or higher-dimensional closed surface to characterize topological invariants in time-parametrized systems.
• Uses time-dependent perturbation theory under the adiabatic condition to derive the particle pump formula, linking it to the integrated Chern number.
• Calculates the Berry curvature and Chern number in (kx, t) and (kx, ky, kz, t) spaces to identify phase transitions and gapless structures.
• Identifies dynamical Weyl points as abrupt changes in Chern number along ky or kz, and 4D Weyl nodal rings as closed loops in (kx, t) space where the Chern number changes.
• Proposes an experimental realization using ultracold atoms in optical lattices with synthetic gauge fields and periodic modulation to simulate the required Hamiltonian.

Experimental results

Research questions

• RQ1 Can dynamical Weyl points emerge in a 2D periodically driven system when time is treated as an additional parameter?
• RQ2 Do 4D Weyl nodal rings—protected by the first Chern number—arise in 3D systems when time is included as a fourth dimension?
• RQ3 Is the topological pump in these systems quantized, or can it be continuously tuned by experimental parameters?
• RQ4 How can such dynamical topological structures be experimentally realized in ultracold atomic gases?

Key findings

• Dynamical Weyl points emerge in 2D systems at specific (kx, ky, t) points where the Chern number changes abruptly, such as at (kx=π, ky=±π/2, t=3π/2) for λ=1 and M0=2.
• In 3D systems, dynamical 4D Weyl nodal rings form closed loops in (kx, t) space, such as at kx=π, t=3π/2, with cos(ky)+cos(kz) = -1 for M0=3 and λ=1.
• The topological pump in these systems is non-quantized and can be continuously tuned by varying M0 or λ, unlike conventional Thouless pumps.
• The Chern number in the (kx, t) torus is -1 inside the 4D nodal ring and 0 outside, confirming topological phase transitions.
• The pump current is proportional to the integrated Chern number over the (kx, t) surface, with the formula Np = -Σ ∫ Cn(k′) dk′/(2π)d−1.
• An experimental scheme is proposed using periodically modulated optical lattices and synthetic spin-orbit coupling to realize the model in ultracold atomic gases.