Geometric phases in solids

Despite their innocuously simple definitions in classical electromagnetism, electric polarization and orbital magnetization become tricky concepts to deal with in solids with crystalline symmetries due to subtleties arising from periodic boundary conditions. The line of efforts on resolving these issues eventually led to the elegant formalism known today as the modern theory of polarization and magnetization, which reveals a profound connection between the bulk polarization and orbital magnetization in solids with the geometric properties of the quantum Bloch wave functions. As exemplified by some of our works below, the quantum geometric phases in solids bear far-reaching consequences on the electronic properties of quantum materials.

Quantum-Geometric Origin of Out-of-Plane Stacking Ferroelectricity

News coverage: UBC Science, Phys.org, QMI News

Ferroelectric materials with switchable electric polarity have a wide spectrum of applications ranging from non-volatile memory to photo-voltaic devices. The recent discovery of a great variety of atomically thin ferroelectrics holds the promise of high-density and energy-efficient devices for future optoelectronics. Among them, stacking ferroelectrics(SFEs) found in van der Waals stacked bilayers, such as tungsten ditelluride(WTe2), hexagonal boron nitride(hBN), and 3R-transition-metal dichalcogenides(TMDs), have attracted tremendous interest thanks to their switchable polarity by inter-layer sliding, which allows fast writing operations for ferroelectric memories.

In this Letter selected as PRL Editor's suggestion, we unveil the quantum geometric origin of various kinds of SFEs - we show that the Hamiltonian describing generic SFEs can be mapped to the two-cell limit of the celebrated Su-Schrieffer-Heeger(SSH) model with staggered sublattice potentials (see figure on the left panel). This mapping allows one to connect the polarization in SFEs to the solid angle subtended by the d-vector characterizing the two-level SSH model, which makes the physics of SFE materials accessible through the classic Berry phase introduced in elementary quantum mechanics.

Polarization-induced photo-voltaic effect in 3R-MoS2

This collaborative work with Ziliang Ye's group at UBC published in Nature Photonics reported the first observation of polarization-induced photovoltaic effect, i.e., the generation of photo-currents withough applied voltage bias, in a rhombohedrally stacked (3R) bilayer MoS2. The finding establishes rhombohedral transition-metal dichalcogenides as an atomically thin photodetector with high efficiency.

On the theory side, we clarify the Berry phase origin of the ferroelectric polarization in 3R-bilayer MoS2 as a consequence of the asymmetric inter-layer coupling due to its rhombohedral stacking order. Our theory further establishes a self-consistent framework which quantifies the potential difference across the two atomic layers and underpins the working principles of the atomically thin photo-voltaic device. This collaboration inspired our general theory [Phys. Rev. Lett. 132, 196801 (2024)] presented above for stacking ferroelectrics with out-of-plane polarization.

Nonlinear Hall effects in TMDs & twisted bilayer graphene

In 2015, Sodemann and Fu predicted that charge Hall effect with second-order response to applied voltage bias can occur in a wide class of non-centrosymmetric materials where time-reversal symmetry is respected [Phys. Rev. Lett. 115, 216806 (2015)].  The response function of the non-linear Hall effect (NHE) is characterized by the dipole moment of Berry curvatures in momentum-space, which induces a non-vanishing Berry curvature flux in the current-carrying state.

In two of our recent works we explore the NHEs in two different materials: (i) a strained polar TMD MoSSe, and (ii) strained twisted bilayer graphene (tBG). We find the nonlinear Hall currents to be highly tunable in polar TMDs due to  peculiar band anti-crossing behaviors, and that the nonlinear signal is huge in tBG - two orders of magnitude larger than other nonlinear Hall materials known at the time. We explain the giant NHE in tBG as a combined result of the nontrivial topology in the moiré flat bands and their strong susceptibility to symmetry breaking induced by weak strains. These two-dimensional nonlinear Hall materials can serve as tunable energy harvesting rectifiers - the working unit for wireless charging.

Key features of our prediction on the giant NHE in tBG, such as the topological band inversions signified by the sign change in Berry curvature dipole, were verified by two recent experiments [Nature Physics 18, 765–770 (2022), Phys. Rev. Lett. 129, 186801 (2022).]

New valley Hall physics in TMDs

In monolayer transition-metal dichalcogenides(TMDs), Berry curvatures of opposite signs arise in the neighborhood of opposite K valleys due to the breaking of spatial inversion symmetry. Upon application of an applied electric field, electrons of opposite valleys experience opposite effective magnetic fields and are thus driven in opposite transverse directions - the phenomena known as the valley Hall effect (VHE) which serves as one of the basic schemes for valleytronics. 

In this collaborative work with Prof. Ning Wang's group at HKUST, we explain the observation of long-range non-local charge transport mediated by intrinsic VHEs in atomically thin MoS2 (left panel). The dependence of non-local signals on the number parity of atomic layers reveals unambiguously the Berry phase origin of the observed non-local transport signals. This work marks an important step toward long-range valley transport and provides the basis for room-temperature micron-scale electrical control of valleys in TMDs.

In a separate theory work in collaboration with Prof. Yukio Tanaka's group at Nagoya University, we predict a novel spin-type Berry curvature generated by spin-orbit-couplings in monolayer TMDs. Distinct from the conventional orbital-type VHEs in monolayer TMDs, the magnitude and sign of the spin-type valley Hall currents can be easily tuned by electrostatic gating, which provides a new scheme for all-electrical valleytronics.