[Paper Review] Artificial gauge fields and topological insulators in Moire superlattices

Ce Shang, Adel Abbout+3 more|arXiv (Cornell University)|Dec 1, 2019

Topological Materials and Phenomena30 references4 citations

TL;DR

This paper proposes a tunable artificial gauge field in moiré superlattices via time-periodic modulation of onsite energies, inducing Peierls phases on hopping terms to realize a Haldane-like topological phase. Using a dynamical quench protocol, the Chern number—quantifying topological order—is directly measured from the linking number of Bloch vector trajectories, confirming robust topological invariants in a controllable quantum emulator platform.

ABSTRACT

We propose an innovative quantum emulator based on Moire superlattices showing that, by employing periodical modulation on each lattice site, one can create tunable, artificial gauge fields with imprinting Peierls phases on the hopping parameters and realize an analog of novel Haldane-like phase. As an application, we provide a methodology to directly quantify the topological invariant in such a system from a dynamical quench process. This design shows a robustly integrated platform which opens a new door to investigate topological physics.

Motivation & Objective

• To design a controllable quantum emulator based on moiré superlattices for realizing artificial gauge fields and topological insulators.
• To demonstrate how time-periodic modulation of onsite energies can imprint Peierls phases on tunneling terms, emulating a Haldane-like model with tunable topological order.
• To develop a dynamical quench protocol that directly quantifies the topological invariant (Chern number) through the linking number of Bloch vector trajectories in momentum-time space.
• To establish a robust, integrated platform for simulating and probing topological phases of matter with high tunability and experimental feasibility.

Proposed method

• Employing Floquet theory to derive an effective tight-binding Hamiltonian on the moiré superlattice, incorporating time-periodic modulation of onsite energies.
• Imprinting phase factors (Peierls phases) on inter-site hopping terms via spatially modulated external fields, enabling artificial gauge potential engineering.
• Using a quench protocol where the system is suddenly driven from a topologically trivial to a non-trivial Hamiltonian, with the initial state prepared as the lower-band eigenstate.
• Mapping the time evolution of the Bloch vector on the Bloch sphere via the time-dependent wavefunction, defined by the post-quench Hamiltonian.
• Calculating the Hopf invariant (linking number) of pre-images of the Bloch vector trajectories in the three-torus (kx, ky, t̃), which topologically equals the Chern number of the final Hamiltonian.
• Validating the method by comparing the extracted Chern number from quench dynamics with theoretical predictions and band structure analysis.

Experimental results

Research questions

• RQ1 Can time-periodic modulation of onsite energies in moiré superlattices generate tunable artificial gauge fields with controllable Peierls phases?
• RQ2 Can a Haldane-like topological phase be realized in moiré superlattices through engineered hopping phases?
• RQ3 Can the topological invariant (Chern number) be directly measured from a dynamical quench process without requiring full band structure calculations?
• RQ4 How does the topological phase diagram evolve with detuning parameter δ, and where do topological phase transitions occur?

Key findings

• The dynamical quench protocol successfully extracts the Chern number from the linking number of Bloch vector trajectories, matching theoretical predictions.
• A topologically non-trivial phase with Chern number C = 1 is identified in a finite interval of detuning δ, flanked by trivial phases with C = 0.
• The phase diagram reveals clear topological phase transitions at critical δ values, confirmed by band structure analysis showing opening and closing of Dirac points.
• The method achieves quantitative agreement between the quench-based Hopf invariant and the Chern number derived from the post-quench Hamiltonian.
• The system supports a robust, fully controllable platform for simulating topological phases, with potential for integration and experimental realization in moiré heterostructures.
• The proposed scheme enables direct, dynamic probing of topological order, offering a new tool for quantum simulation and control of topological matter.