arXiv subjects

Tian-Le Wu

Publications and source records attributed to Tian-Le Wu.

3 recordsLinked to original sources

arXiv2026

Spectral Function Method and Janus Quantum Numbers in Quasiperiodic Systems

The absence of translational symmetry in quasiperiodic systems invalidates conventional band theory, posing the central challenge in the field. Building upon the incommensurate energy band (IEB) concept, we establish a unified spectral theory for quasiperiodic systems by introducing two key advances. First, we develop an efficient spectral function method that calculates $A(k,ω)$ using a small truncated Hamiltonian matrix, bypassing full diagonalization. It converges via a distinctive successive locking of energy moments, yielding exact thermodynamic-limit results without finite-size scaling. Second, we introduce that quasiperiodic eigenstates possess Janus quantum numbers: a single eigenstate, continuously tracked across localization transitions, carries dual labels in momentum and real space, which naturally reduce to the familiar Bloch momentum and band index in the commensurate limit. Together with IEB, these advances constitute a ``band theory'' for quasiperiodic systems, enabling us to define, compute, and label states with the same facility as in periodic ones.

cond-mat.mes-hall↗

arXiv2025

Sliding-tuned Quantum Geometry in Moiré Systems: Nonlinear Hall Effect and Quantum Metric Control

Sliding is a ubiquitous phenomenon in moiré systems, but its direct influence on moiré bands, especially in multi-twist moiré systems, has been largely overlooked to date. Here, we theoretically show that sliding provides a unique pathway to engineer the quantum geometry (Berry curvature and quantum metric) of moiré bands, exhibiting distinct advantages over conventional strategies. Specifically, we first suggest alternating twisted trilayer $\mathrm{MoTe_2}$ (AT3L-$\mathrm{MoTe_2}$) and chirally twisted triple bilayer graphene (CT3BLG) as two ideal paradigmatic systems for probing sliding-engineered quantum geometric phenomena. Then, two sliding-induced exotic quantum geometry phenomena are predicted: (1) an intrinsic nonlinear Hall effect via sliding-produced non-zero Berry curvature dipole, with CT3BLG as an ideal platform; (2) significant quantum metric modulation in AT3L-$\mathrm{MoTe_2}$, enabling tests of quantum geometric criteria for fractional Chern insulating state (FCIS). Our work establishes sliding as a new degree of freedom for manipulating quantum geometry of moiré bands, which emerges as a signature phenomenon of multi-twist moiré systems.

cond-mat.mes-hall↗

arXiv2025

Theory of Localized States in Quasiperiodic Lattices

The physics of localized states in quasiperiodic lattices has been extensively studied for decades, but still lacks an comprehensive theoretical framework. Recently, we developed a incommensurate energy band (IEB) theory, which extends the concept of energy bands to quasiperiodic systems lacking translational symmetry, thereby achieving a breakthrough in elucidating extended states. Here, we demonstrate that, due to the inherent duality between momentum and real space, the IEB theory also offers a comprehensive framework for elucidating localized states. Specifically, via a so-called spiral (module) mapping, the energy spectrum of localized states can be represented as a function defined on a compact circular manifold-akin to the Brillouin zone-whose form resembles conventional energy bands. These localized state energy bands (LSEBs) fully characterize all the properties of the localized states. Moreover, we show that quasiperiodic systems with mobility edges exhibit a unique hybrid band structure: the IEB for extended states (momentum space) and LSEB for localized states (real space), separated by mobility edges. Our theory thus establishes a comprehensive framework for analyzing the localized states in quasiperiodic lattices.

cond-mat.dis-nn↗