Dongzhe (Denzel) Zheng

Ph.D. Researcher, MAE, Princeton University
Master of Mathematics, University of Cambridge

⚛ Physics

Accepted · March 16, 2026

Toroidal Loop-Current Order in Kagome \(AV_3Sb_5\): Zero-Field Diode and Anomalous Hall

Journal of Physics: Condensed Matter (JPCM)

Resolving the phenomenological coexistence of charge density wave-driven anomalous Hall effect (AHE) and zero-field superconducting diode effect (SDE) in kagome metals. This work establishes a unified theoretical framework connecting microscopic orbital current patterns to macroscopic transport signatures.

Long-Term Vision

Emergent Gauge Structures in Correlated Quantum Matter

Theoretical Framework

Establishing systematic theoretical connections between microscopic electron correlations and macroscopic quantum responses. The central thesis posits that collective electronic ordering in strongly correlated systems can be faithfully encoded as emergent gauge field configurations.

Demonstrating that composite toroidal loop-current order induces emergent orbital gauge fields, providing a gauge-covariant Ginzburg-Landau framework independent of material-specific microscopic details. This formalism enables predictive modeling of topological transport phenomena across diverse quantum material platforms.

Current Focus

Momentum Translation Equivalence in the Low-Energy Long-Wavelength Limit

Active Research

Mapping the odd-in-\(k\) electron self-energy induced by symmetry-breaking ordered states to emergent gauge field-driven momentum space translation. This mapping reveals deep connections between broken-symmetry phases and effective gauge theories in the \(k \to 0\), \(\omega \to 0\) regime.

Formulating how superconducting condensates couple to electromagnetic and orbital gauge potentials to spontaneously generate finite pairing momentum \(\mathbf{q} \neq 0\) and intrinsic Josephson phase bias \(\varphi_0\). This mechanism provides microscopic justification for observed nonreciprocal superconducting transport.

∫ Mathematics

Preprint

Picard Groups of Completed Period Images and the Deng–Robles Problem

Badre Mounda, Dongzhe Zheng

arXiv:2603.09709

We reduce the Deng–Robles problem—namely, whether the completed image of a degenerate period map can be naturally characterized as an intrinsic Proj-type algebro-geometric object—to a structural problem concerning Picard group generation, and provide a complete proof in the case where the pure period image is one-dimensional.

Preprint

Pseudoconvexity and Algebraization of the Generalized Satake–Baily–Borel Completion

ResearchGate

We establish the local pseudoconvexity and holomorphic extension input needed for the \(\theta\)-bundle algebraization of generalized Satake–Baily–Borel completions, using a new anisotropic weighted \(L^2\)-\(\bar\partial\) method adapted to degenerate Hodge metrics; this upgrades the analytic completion to an algebraic one in the weight-2 Hermitian and Calabi–Yau 3 cases.