Date of Award
Spring 2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Engineering and Applied Science
First Advisor
Xia, Fengnian
Abstract
Geometry, an old yet vibrant field in mathematics whose name originates from Ancient Greek, signifying “land measurement,” holds profound and expansive applications across a spectrum of disciplines including art, architecture, science, and engineering. Fundamental concepts within geometry, such as vector bundles and connections, curvature and metric, symmetry and topology, serve as indispensable tools for comprehending the physical universe: from the standard model of elementary particles to Einstein’s general theory of relativity, and electromagnetic waves and matter at various scales. Quantum geometry emerges as a set of geometrical principles crucial for understanding the natural world when quantum mechanics dominates the underlying physics. In solids, Berry curvature and the quantum metric are representative quantum geometric properties embedded within electron Bloch wave functions. Such properties vary with the momentum of the electron for a specific electronic band, thereby describing local characteristics of Bloch electrons. By integrating such local geometric properties, such as Berry curvature, over momentum space for a specific electronic band, a global description of a band known as the topology emerges. Quantum geometry and topology have significant influence over the behavior of electrons in both ground and excited states, responsible for various phenomena such as the electric polarization of materials, orbital magnetization, quantum and anomalous Hall effects and nonlinear electromagnetic responses. Recently, graphene moiré superlattices have emerged as compelling platforms for investigating strongly correlated electron systems. These systems have unveiled remarkable phenomena, such as the emergence of Mott-like insulating states, superconductivity, and ferromagnetism, all primarily attributed to the formation of flat electronic bands. Beyond the band flatness, quantum geometry and topology are two other critical elements in these emerging systems yet receive comparatively less attention. In this thesis, we first study the band topology of the simplest graphene moiré superlattices, known as the twisted bilayer graphene (TBG), and its impact on the electron transport, i.e., the ground-state behavior of electrons. We conduct a systematic study through nonlocal transport measurements, where we observe pronounced nonlocal resistant maxima in the superlattice-induced insulating states of TBGs. We further reveal that the nonlocal responses are robust to the twist angle and edge termination, exhibiting a universal scaling law. By supplementing our experimental findings with a thorough theoretical analysis, we provide a detailed elucidation of the two nontrivial Z2 topological invariants characterizing the moiré Dirac bands of TBG. This topological feature implies the presence of counter-propagating edge states which play a pivotal role in driving the observed nonlocal responses. These findings provide a new perspective for understanding the strong electron correlation in graphene moiré superlattices, and suggest a potential strategy to achieve topologically nontrivial metamaterials from trivial materials. Subsequently, we discuss the influence of quantum geometry in the excited-state behaviors of electrons through light-matter interactions. Stemming from the formation of moiré superlattices in real space, the folding of the Brillouin zone in reciprocal space results in a notable enhancement of the electron density of states and the emergence of superlattice-induced bandgaps, typically ranging from tens to hundreds of meV. These properties of graphene moiré superlattices are favorable for strong interactions with infrared light, making them ideal platforms for investigating exotic infrared photoresponses. Our study starts by demonstrating that in graphene moiré superlattices, the first-order photoresponse is strikingly large although the active channel only comprises a few layers of carbon atoms. This robust response arises from the strong optical absorption and a bolometric effect. Furthermore, we uncover the presence of a strong bulk photovoltaic effect (BPVE) in twisted double bilayer graphene (TDBG), a second-order nonlinear photoresponse resulting in a static photovoltage or photocurrent. This effect emerges from the pronounced symmetry breaking and quantum geometric contributions induced by the moiré superlattice. Intriguingly, we find that BPVE in TDBG exhibits substantial dependence on the power, polarization, and wavelength of the incident light, with remarkable tunability by external electric fields. Leveraging the distinctive properties of BPVE in TDBG, we generate photovoltage mappings of which each captures light power, polarizations and wavelengths in a unique way. Employing a convolutional neural network, we demonstrate an intelligent TDBG sensor with a remarkably compact footprint of 3 × 3 µm2. This intelligent sensor possesses the capability to simultaneously extract the power, polarization and wavelength of the incident light from the photovoltage mapping. This work not only reveals the unique role of moiré engineered quantum geometry in tunable nonlinear light–matter interactions but also identifies a pathway for future intelligent sensing technologies in an extremely compact, on-chip manner. Finally, building upon our research in quantum geometry-enabled intelligent sensing, alongside recent advancements in optical sensing and imaging, we introduce an innovative concept dubbed as "geometric deep optical sensing." In this novel framework, a compact sensor (or an array thereof), initially collectively captures a comprehensive set of information which may encompass spectral data, power characteristics, polarization details, and the spatial distribution of the incoming light, using multiple elements or a single element under different operational states and generates a high-dimensional photoresponse vector. Subsequently, an advanced algorithm is employed to interpret this vector and efficiently reconstruct the complete set of light information. This approach transfers the physical complexity of conventional optical sensors to computation. We further discuss the new opportunities that this emerging scheme can enable, along with the associated challenges and prospects for future advancements in the field.
Recommended Citation
Ma, Chao, "Quantum Geometry and Topology in Graphene Moiré Superlattices" (2024). Yale Graduate School of Arts and Sciences Dissertations. 1412.
https://elischolar.library.yale.edu/gsas_dissertations/1412
