[Paper Review] Berry curvature dipole senses topological transition in a moir\'e superlattice

Subhajit Sinha, Pratap Chandra Adak+9 more|arXiv (Cornell University)|Apr 6, 2022

Topological Materials and PhenomenaPhysics and Astronomy65 references139 citations

TL;DR

This study demonstrates that the Berry curvature dipole (BCD) in twisted double bilayer graphene (TDBG) acts as a direct experimental probe of topological transitions, detected via nonlinear Hall (NLH) voltage. By tuning the perpendicular electric field, the authors observe a sign reversal of the BCD concurrent with a change in valley Chern number, while hysteresis in longitudinal and NLH responses reveals electrically switchable metastable states, pointing to applications in topological memory devices.

ABSTRACT

Topological aspects of electron wavefunction play a crucial role in determining the physical properties of materials. Berry curvature and Chern number are used to define the topological structure of electronic bands. While Berry curvature and its effects in materials have been studied, detecting changes in the topological invariant, Chern number, is challenging. In this regard, twisted double bilayer graphene (TDBG) has emerged as a promising platform to gain electrical control over the Berry curvature hotspots and the valley Chern numbers of its flat bands. In addition, strain induced breaking of the three-fold rotation (C3) symmetry in TDBG, leads to a non-zero first moment of Berry curvature called the Berry curvature dipole (BCD), which can be sensed using nonlinear Hall (NLH) effect. We reveal, using TDBG, that the BCD detects topological transitions in the bands and changes its sign. In TDBG, the perpendicular electric field tunes the valley Chern number and the BCD simultaneously allowing us a tunable system to probe the physics of topological transitions. Furthermore, we find hysteresis of longitudinal and NLH responses with electric field that can be attributed to switching of electric polarization in moir\'e systems. Such a hysteretic response holds promise for next-generation Berry curvature-based memory devices. Probing topological transitions, as we show, can be emulated in other 3D topological systems.

Motivation & Objective

• To detect topological transitions in moiré superlattices, which are otherwise difficult to probe due to the challenge of measuring changes in topological invariants like the Chern number.
• To establish the Berry curvature dipole (BCD) as a measurable signature of topological phase transitions in time-reversal-symmetric systems with broken inversion and C3 symmetry.
• To explore the role of strain and electric field in generating and tuning the BCD in TDBG, enabling electrical control over topological properties.
• To demonstrate that hysteresis in NLH and longitudinal responses arises from switching between metastable polarization states, suggesting applications in Berry curvature-based memory devices.

Proposed method

• The study uses twisted double bilayer graphene (TDBG) with a twist angle of ~1.1°, where strain breaks C3 symmetry and enables a nonzero BCD.
• The BCD is calculated using the formula Λα = Σn ∫(mBZ) dk/(2π)² Ωn_z ∂ϵn_k/ℏ∂kα ∂f(ϵn_k)/∂ϵn_k, linking Berry curvature and band dispersion.
• Nonlinear Hall (NLH) voltage is measured at frequency 2ω using ac current excitation, with V²ω_xy serving as a direct probe of the BCD.
• Electric field tuning of the displacement field (D/ε₀) is used to control the valley Chern number and modulate the BCD, enabling dynamic probing of topological transitions.
• Hysteresis in NLH and longitudinal resistance is analyzed to identify metastable polarization states in the moiré system.
• A rigid band model with position-dependent band energy shifts (Hi = ϵi + eE⟨Zi⟩) is used to explain the polarization switching and metastable states in h-BN-Gr-Gr and Gr-Gr-h-BN trilayers.

Experimental results

Research questions

• RQ1 Can the Berry curvature dipole (BCD) serve as a detectable signature of topological transitions in moiré systems?
• RQ2 How does electric field tuning of the displacement field affect the BCD and valley Chern number in TDBG?
• RQ3 What causes the observed hysteresis in longitudinal and nonlinear Hall responses in TDBG?
• RQ4 Can the observed hysteresis be attributed to switching between metastable polarization states in the moiré heterostructure?
• RQ5 To what extent does strain-induced C3 symmetry breaking generate a measurable BCD in TDBG?

Key findings

• The BCD in TDBG reverses sign abruptly with increasing electric field, signaling a topological transition associated with a change in valley Chern number.
• The nonlinear Hall voltage (V²ω_xy) shows a clear sign reversal at the same field where the BCD changes sign, confirming the BCD as a direct probe of topological transitions.
• Hysteresis is observed in both longitudinal resistance and NLH voltage as a function of electric field, indicating switching between metastable electronic states.
• The hysteresis is attributed to electric polarization switching in the trilayer heterostructure, with a calculated polarization of Pz ≈ -0.34 µC/cm² in Gr-Gr-h-BN.
• Two distinct metastable states exist for E < -0.0039 V/Å and E > 0.0039 V/Å, with band crossings at these thresholds explaining the switching behavior.
• The DC voltage component of the NLH effect, measured at 177 Hz, further confirms the nonlinear Hall response and supports the BCD origin of the signal.