Talks

Quantum Geometry of Moiré Flat Bands Beyond the Valley Paradigm

March 19, 2026

Contributing Talk, APS March Meeting, Denver, CO

Abstract: Moiré superlattices provide platforms for strongly correlated and topological phenomena governed by quantum geometry. The prevailing ``valley paradigm''---which relies on well-defined valley structures at high-symmetry Brillouin zone points---successfully describes systems like twisted bilayer graphene and transition metal dichalcogenides, but fails for materials lacking valley degrees of freedom. Here, we establish a general framework for engineering flat-band quantum geometry in twisted bipartite heterobilayers through sublattice-selective interlayer tunneling. Using twisted graphene-on-dice heterobilayers as a prototype, we demonstrate that preserving bipartiteness while hybridizing layers produces isolated, zero-energy flat bands with twist-angle-tunable multiplicity and Chern-insulator-scale Berry curvature. Crucially, these bands exhibit finite quantum metric arising from controlled interlayer hybridization rather than valley physics. Our results provide a systematic route to quantum geometry engineering in moiré systems beyond existing paradigms, with realizations in oxide heterostructures, molecular lattices, and synthetic quantum matter.

Twist-Induced Quantum Geometry Reconfiguration in Moiré Flat Bands

March 16, 2026

Contributing Talk, APS March Meeting, Denver, CO

Abstract: Moiré superlattices have emerged as a powerful platform for engineering flat bands with nontrivial topology and quantum geometry. While much progress has been made in understanding systems where moiré bands inherit the characteristics of the associated monolayers, significant open questions remain when more intricate microscopic orderings or symmetry breakings are involved. Here we explore how moiré stacking and interlayer coupling can lead to restructured quantum geometry, especially in the presence of symmetry-breaking orders in the parent layers. We discuss scenarios in which the interplay between interlayer hybridization, symmetry breaking, and twist angle significantly modifies the quantum-geometric properties of the resulting flat bands. Our study establishes a broader design space for moiré materials toward engineering their unconventional responses. We conclude by commenting on potential materials platforms for the experimental realization of these novel effects.

More is different at the edge: helical Luttinger liquid in double quantum spin Hall insulators

February 10, 2026

Invited Talk (online), Institute of Physics, Academia Sinica, Taipei, Taiwan

Quantum spin Hall insulators (QSHIs) are a cornerstone of time-reversal-symmetric topological phases and play a central role in modern topological band theory. Their hallmark is the presence of helical edge states, where counterpropagating modes are locked to opposite spin orientations and are protected against elastic backscattering by time-reversal symmetry. These edge states provide an excellent platform for exploring frontier phenomena such as topological superconductivity and spintronic responses. While these helical edge states are often introduced within a noninteracting picture, electron–electron interactions are indispensable for the low-energy physics of one-dimensional systems, leading to the helical Luttinger liquid phase. Such a non-Fermi-liquid behavior further enriches the low-energy physics, supporting exotic states such as Majorana-Kramers pairs. In this talk, I will introduce our recent work on helical Luttinger liquid in double quantum spin Hall insulators (DQSHIs). In sharp contrast to QSHIs, DQSHIs support two pairs of helical edge states, enabling gap opening without breaking time-reversal symmetry. This leads to a richer low-energy phase diagram, such as a higher-order topological insulator phase [1] and a novel\ \pi-spin density wave phase. I will show that DQSHIs provides a versatile platform to engineer Majorana-Kramers pairs without relying on the superconducting proximity effect [2], as well as to study the competition between \pi-superconductivity and \pi-spin density wave phases [3].

Quantum Geometry Driven Fluctuation Phenomena in Flat-Band Systems

November 07, 2025

Contributing Talk, The New England Section of the American Physical Society, Providence, RI

Quantum geometry plays a fundamental role in shaping emergent phases in flat-band systems. Here, we discuss collective excitonic phenomena in quantum-geometry-induced flat bands, highlighting how the quantum metric influences both the condensation and fluctuation dynamics. We identify a novel state involving finite-momentum fluctuations linked to the underlying quantum geometry, which should be experimentally accessible via its magnetic responses. Our study points to a broader framework in which quantum geometry governs many-body behavior in engineered quantum materials.

Generation of Isolated Flat Bands with Tunable Numbers through Moiré Engineering

November 07, 2025

Poster Presentation, The New England Section of the American Physical Society, Providence, RI

In contrast to the Dirac-cone materials in which the low-energy spectrum features a pseudospin-1/2 structure, Lieb and Dice lattices both host triply degenerate low-energy excitations. Here, we discuss moiré structures involving twisted bilayers of these lattices, which are shown to exhibit a tunable number of isolated flat bands near the Fermi level due to the bipartite nature of their structures. These flat bands remain isolated from the high-energy bands even in the presence of small higher-order terms and chiral-symmetry-breaking interlayer tunneling. At small twist angles, many isolated flat bands can be generated with a notable Berry curvature, which could provide a geometric contribution to the superfluid weight under a BCS-type pairing potential. Remarkably, the emergence of isolated flat bands is insensitive to the twist angle, so that fine-tuning of the twist angle in an experimental setup would not be required. Our study suggests a promising new and efficient avenue for exploring and engineering flat bands based on the twisted bilayer Lieb and Dice lattices.

Quantum Materials and Topology: Toward Robust Platforms for Quantum Computation

July 14, 2025

Invited Talk (online), Annual Meeting of NSF-ExpandQISE 2: Exotic Physics and Applications of Solid-State Qubits, Arlington, VA

Emergent Majorana Kramers pairs in interacting spin/mirror Chern insulators

March 21, 2025

Contributing Talk, APS March Meeting, Anaheim, CA

Abstract: Recent studies of topological phases characterized by a high-spin (or mirror) Chern number suggest the potential for realizing multiple helical edge states in low-dimensional quantum systems. In this connection, we demonstrate that electron interactions at the edges can drive correlated phases and that the system can be adiabatically connected to a time-reversal-symmetric topological superconductor, suggesting the emergence of Majorana Kramers pairs in the strongly interacting regime. We propose an experimental setup using cold atom systems, which could offer a new pathway for realizing fault-tolerant topological quantum computation.

Moiré Engineering for Tunable Numbers of Flat Bands and Its Quantum Geometry

February 19, 2025

Invited Talk, Department of Physics, National Cheng Kung University, Tainan, Taiwan

Abstract: Moiré engineering, especially using twisted bilayers, has provided novel control on the creation of flat bands that are isolated from other high-energy bands through the emerging moiré potential. This advances studies like the quantum geometric effects of physical observables and novel interacting phases. On the other hand, flat bands can also be generated from the geometric structures of an untwisted lattice, such as the kagome lattice. Such a lattice-geometry-induced flat band lies robustly at zero energy with exactly flat dispersion in certain lattices, such as Lieb and dice lattices. Yet, combining these flat band-generating mechanisms remains unexplored. In this talk, I will briefly introduce moiré and flat band physics and present our recent findings on twisted bilayer dice and Lieb lattices [1]. We demonstrate that the number of flat bands within can be tuned by the twist angle, generating thousands of flat bands near the Fermi level at small twist angles. The interlayer tunneling further isolates those flat bands from other high-energy bands. We further proposed possible material realizations of our model. These discoveries offer new insights into flat band physics through moiré engineering.

Moiré Engineering for Tunable Numbers of Flat Bands and Its Quantum Geometry

February 13, 2025

Invited Talk, Institute of Physics, Academia Sinica, Taipei, Taiwan

Abstract: Moiré engineering, especially using twisted bilayers, has provided novel control on the creation of flat bands that are isolated from other high-energy bands through the emerging moiré potential. This advances studies like the quantum geometric effects of physical observables and novel interacting phases. On the other hand, flat bands can also be generated from the geometric structures of an untwisted lattice, such as the kagome lattice. Such a lattice-geometry-induced flat band lies robustly at zero energy with exactly flat dispersion in certain lattices, such as Lieb and dice lattices. Yet, combining these flat band-generating mechanisms remains unexplored. In this talk, I will briefly introduce moiré and flat band physics and present our recent findings on twisted bilayer dice and Lieb lattices [1]. We demonstrate that the number of flat bands within can be tuned by the twist angle, generating thousands of flat bands near the Fermi level at small twist angles. The interlayer tunneling further isolates those flat bands from other high-energy bands. We further proposed possible material realizations of our model. These discoveries offer new insights into flat band physics through moiré engineering.

Novel Moiré Pattern of a New Two-Dimensional Lattice

March 08, 2024

Contributing Talk, APS March Meeting, Minneapolis, MN

Abstract: We propose a new type of two-dimensional lattice structure, which hosts quadratic band touching in its bilayer form, resulting in intriguing strongly correlated physics such as superconductivity with high critical temperature. Further, multiple isolated flat bands near the Fermi level are induced by the Moiré pattern of its twisted bilayer structure. These isolated flat bands are topological and host high-spin Chern numbers: we demonstrate this formally and confirm our findings via numerical calculations. Non-trivial topology of flat bands indicates the presence of a significant quantum weight, implying a substantial superfluid weight when a BCS-type pairing potential is added. The number of flat bands and their superfluid weight here are greater than in the case of twisted bilayer graphene. Our study suggest a new platform for exploring flat-band physics via Moiré engineering. Work supported by the NSF.

Time-Reversal Soliton Pair in Two-Dimensional Topological Insulating Systems

March 08, 2023

Contributing Talk, APS March Meeting, Las Vegas, NV

Abstract: Solitons on the edges of two-dimensional systems with non-trivial topology, formed through the one-dimensional mass-kink mechanism, play an important role in driving the emergence of higher-order topological phases. In this connection, the existing work has focused on gaping a single edge Dirac cone by time-reversal symmetry breaking perturbations, which are not suitable for the edge solitons in time-reversal symmetric systems with multiple edge Dirac cones. Here, we discuss the mass-kink mechanism in systems where time-reversal symmetric perturbations open the gaps of time-reversal related Dirac cones. We thus explain the appearance of pairwise corner modes and predict the value of the corner charges. Furthermore, we have developed an efficient-numerical method based on real-space renormalization group using Green's functions to calculate the phase difference of the mass terms between the adjacent edges without using nano-disks and k.p modeling. Using this technique, we demonstrate that the in-gap corner modes and the corner charges in monolayer α-Sb are generated by the mass-kink mechanism that originates from gapping two pairs of edge Dirac cones with Sz-mixing spin-orbit coupling.

Edge Mass-Kink and Fractional Corner Charge in Higher-Order Topological Insulators

April 29, 2022

Invited Talk, 1-day workshop on Wannier-functions based Hamiltonians 2022, National Center for Theoretical Sciences, Physics Division, Taipei, Taiwan

Abstract: Higher-order topological insulators are d-dimensional topological insulators with the absence of (d-1)-dimensional gapless states, of which the bulk-boundary correspondence is manifested as (d-2)-dimensional in-gap states instead. There are various mechanisms that generate such topological phases, still, a unified theory is lacking. A recent theory shows that the 0-dimensional in-gap states emerge at corners where two edges have phase difference between their mass of edge Dirac cones, which explains the origin of the in-gap states in higher-order topological insulators. Yet, the analyses retain in the pen-and-paper level or need the energy spectrum of a nano-disk/nano-ribbons with considerable size, which are both impractical to apply on real materials. I will briefly introduce the concept of mass-kink and demonstrate how to use it to predict the numbers and the distributions of the in-gap states. Then, I will present my recent works on using material specific tight-binding hamiltonians and real-space renormalization group through Green’s function to calculate the phases of mass for edge Dirac cones, which is not only computational cheap but also gives accurate values for fractional corner charges.

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