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Luna Liu

Yale University

Supervisors: Cong Su (Yale University) – Diana Qiu (Yale University)

Short Bio: I am currently a PhD student in the Department of Applied Physics at Yale University. Before that, I completed my undergraduate studies in Honours Physics at the University of British Columbia in Vancouver, BC. During my undergraduate, I conducted research in both experimental and theoretical physics, shaping my goal of bridging the gap between modern experimental and theoretical condensed matter physics. At Yale, my research focuses on linearly dispersive excitons in hexagonal boron nitride (hBN), which provide a real physical system hosting interesting quantum many body phenomena. My team and I were the first to observe these linearly dispersive massless excitons experimentally. In my experimental work, I use momentum-resolved electron energy loss spectroscopy (Q-EELS) to probe the exciton band structure. On the theoretical side, I perform density functional theory (DFT) and many-body perturbation theory calculations within the GW plus Bethe-Salpeter equation (GW-BSE) formalism to compute the exciton band structure and gain deeper insights into the material system. During the period of Enrico Fermi Fellowship, I hope to build upon my previous findings and work toward realizing exciton condensation in two-dimensions.

Realizing exciton condensate in two dimensions

Project summary: One of the most fascinating discoveries in modern physics is Bose-Einstein condensation (BEC), a phenomenon in which a group of particles called bosons behaves as a single macroscopic quantum state when cooled to extremely low temperatures. This unique state of matter enables the study of quantum mechanics on a large scale and has led to breakthroughs in areas such as superconductivity and quantum computing. While BEC is often associated with ultracold atomic gases, scientists are now exploring how similar quantum phenomena could emerge in solid-state materials.

In solid-state materials, a key factor that determines a material’s properties—such as how it conducts electricity or interacts with light—is its electronic band structure. This structure describes the relationship between an electron’s energy and momentum. In most materials, electrons have an effective mass due to the curvature of these energy bands. However, in rare cases, electrons can exhibit “linear dispersion,” meaning they behave as if they are massless, enabling extremely fast transport of energy and information. A well-known example is graphene, where electrons behave as massless Dirac fermion, leading to exceptional electronic mobility and exotic quantum phenomena like the anomalous quantum Hall effect.

Excitons, which are pairs of negatively charged electrons and positively charged “holes” bound together by Coulomb interaction, govern light-matter interactions and coupling to other electromagnetic fields. Unlike electrons, excitons are composite particles that can, in principle, form collective quantum states such as BEC. However, in most materials, excitons behave as if they have mass, limiting their potential for quantum coherence. My research focuses on an exciting prediction: in certain two-dimensional (2D) materials, excitons can exhibit linear dispersion, much like massless electrons. This discovery could lead to higher-temperature BECs, stable coherent quantum phases, and ultrafast energy transport—advancing fields like photonics and quantum information science. Interestingly, this behavior mirrors concepts in particle physics, where composite particles formed by massive quarks and antiquarks appear nearly massless under certain conditions.

In our recent work, my team and I provided the first experimental proof of these massless excitons in the 2D material hexagonal boron nitride (hBN). By using momentum-resolved electron energy loss spectroscopy, we mapped out the exciton’s energy-momentum relationship, confirming the predicted linear dispersion. Figure 1a shows the experimentally measured exciton band structure, while Figure 1b presents the exciton band structure predicted using many-body perturbation theory, with the linear dispersion highlighted by a white dashed line. This discovery challenges conventional assumptions about excitons and has profound implications for BEC. In standard 2D systems, exciton condensation is thought to be impossible in the absence of interactions. However, if excitons exhibit linear dispersion, as we demonstrated, BEC in 2D becomes theoretically viable—paving the way for new quantum states of matter.

Looking ahead, I aim to explore the implications of these massless excitons in the context of Bose-Einstein condensation. By developing new theoretical models based on first-principles calculations, we hope to predict and identify clear experimental signatures of exciton BEC in 2D. We also plan to design innovative experimental techniques to directly observe and manipulate these exotic quantum states. Demonstrating exciton condensation in 2D systems would significantly advance our fundamental understanding of Bose-Einstein condensation and quantum mechanics.