arXiv subjects

Ziyu Xiang

Publications and source records attributed to Ziyu Xiang.

8 recordsLinked to original sources

arXiv2026

Imaging Interacting Two-Dimensional Anisotropic Electrons

We directly visualize a two-dimensional anisotropic Wigner crystal and its quantum melting in monolayer 1T-ReSe2 using non-invasive scanning tunnelling microscopy. In crystals with anisotropic effective mass, an electron's quantum wavefunction becomes elongated along the light-mass direction to reduce kinetic energy. At low electron density, such anisotropic electrons are predicted to form an oblique Wigner crystal rather than the familiar triangular lattice of isotropic systems. Despite longstanding theoretical interest, this physics has been little explored experimentally. Here we first image the anisotropic shape of individual electrons in gated monolayer ReSe2, whose wavefunctions are strongly elongated along the light-mass direction. At low density, these electrons crystallize into an oblique Wigner lattice. As the density increases, quantum fluctuations grow more rapidly along the light-mass direction than along the heavy-mass direction, driving a one-dimensional melting of the crystal. The resulting state retains order along one direction but melts along the other, consistent with a smectic electron liquid crystal between the electron solid and Fermi liquid phases. Our work establishes monolayer ReSe2 as a platform for studying anisotropic correlated electrons, quantum melting, and coupled one-dimensional electron chains.

cond-mat.str-el↗

arXiv2025

Visualizing the Impact of Quenched Disorder on 2D Electron Wigner Solids

Electron Wigner solids (WSs)1-12 provide an ideal system for understanding the competing effects of electron-electron and electron-disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has been limited by a lack of single-defect-resolved experimental measurements as well as accurate theoretical tools to enable realistic experiment/theory comparison. Here we overcome these limitations by combining atomically-resolved scanning tunneling microscopy (STM) with neural-quantum-state quantum Monte Carlo (NQS-QMC) simulation of disordered 2D electron WSs to discover new disorder-induced physical regimes of correlated electron behavior. STM was used to image the electron density ($n_e$) dependent evolution of electron WSs in gate-tunable bilayer MoSe2 devices with varying long-range ($n_\mathrm{LR}$) and short-range ($n_\mathrm{SR}$) disorder densities. These images were compared to NQS-QMC simulations using realistic disorder maps extracted from experiment, thus allowing the roles of different disorder types to be disentangled. We identify two distinct physical regimes for disordered electron WSs that depend on $n_\mathrm{SR}$. For $n_\mathrm{SR} \lesssim n_e$ the WS behavior is dominated by long-range disorder and features extensive mixed solid-liquid phases, a new type of local re-entrant melting/crystallization, and prominent Friedel oscillations. In contrast, when $n_\mathrm{SR} \gg n_e$ these features are suppressed and a more robust amorphous WS phase emerges that persists to higher ne, highlighting the importance of short-range disorder in this regime. Our work establishes a powerful framework for studying disordered quantum solids via a combined experimental-theoretical approach.

cond-mat.str-el↗

arXiv2025

A Materials Foundation Model via Hybrid Invariant-Equivariant Architectures

Machine learning interatomic potentials (MLIPs) can predict energy, force, and stress of materials and enable a wide range of downstream discovery tasks. A key design choice in MLIPs involves the trade-off between invariant and equivariant architectures. Invariant models offer computational efficiency but may not perform as well, especially when predicting high-order outputs. In contrast, equivariant models can capture high-order symmetries, but are computationally expensive. In this work, we propose HIENet, a hybrid invariant-equivariant materials interatomic potential model that integrates both invariant and equivariant message passing layers, while provably satisfying key physical constraints. HIENet achieves state-of-the-art performance with considerable computational speedups over prior models. Experimental results on both common benchmarks and downstream materials discovery tasks demonstrate the efficiency and effectiveness of HIENet.

cs.LG↗

arXiv2024

Imaging Tunable Luttinger Liquid Systems in van der Waals Heterostructures

One-dimensional (1D) interacting electrons are often described as a Luttinger liquid1-4 having properties that are intrinsically different from Fermi liquids in higher dimensions5,6. 1D electrons in materials systems exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using a novel scanning tunneling microscopy (STM) technique. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, while at intermediate densities dimerized Wigner crystals form due to an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase where electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures offers new opportunities to explore Luttinger liquid physics.

cond-mat.str-el↗

arXiv2024

Quantum Melting of a Disordered Wigner Solid

The behavior of two-dimensional electron gas (2DEG) in extreme coupling limits are reasonably well-understood, but our understanding of intermediate region remains limited. Strongly interacting electrons crystalize into a solid phase known as the Wigner crystal at very low densities, and these evolve to a Fermi liquid at high densities. At intermediate densities, however, where the Wigner crystal melts into a strongly correlated electron fluid that is poorly understood partly due to a lack of microscopic probes for delicate quantum phases. Here we report the first imaging of a disordered Wigner solid and its quantum densification and quantum melting behavior in a bilayer MoSe2 using a non-invasive scanning tunneling microscopy (STM) technique. We observe a Wigner solid with nanocrystalline domains pinned by local disorder at low hole densities. With slightly increasing electrostatic gate voltages, the holes are added quantum mechanically during the densification of the disordered Wigner solid. As the hole density is increased above a threshold (p ~ 5.7 * 10e12 (cm-2)), the Wigner solid is observed to melt locally and create a mixed phase where solid and liquid regions coexist. With increasing density, the liquid regions gradually expand and form an apparent percolation network. Local solid domains appear to be pinned and stabilized by local disorder over a range of densities. Our observations are consistent with a microemulsion picture of Wigner solid quantum melting where solid and liquid domains emerge spontaneously and solid domains are pinned by local disorder.

cond-mat.str-el↗

arXiv2023

Wigner Molecular Crystals from Multi-electron Moiré Artificial Atoms

Semiconductor moiré superlattices provide a versatile platform to engineer new quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid - the Fermi-Hubbard model - where intra-atom interactions are simplified to a single onsite repulsion energy U. These studies have revealed novel quantum phases ranging from Mott insulators to quantum anomalous Hall insulators at a filling of one electron per moiré unit cell. New types of quantum solids should arise at even higher filling factors where the multi-electron configuration of moiré artificial atoms provides new degrees of freedom. Here we report the experimental observation of Wigner molecular crystals emerging from multi-electron artificial atoms in twisted bilayer WS2 moiré superlattices. Moiré artificial atoms, unlike natural atoms, can host qualitatively different electron states due to the interplay between quantized energy levels and Coulomb interactions. Using scanning tunneling microscopy (STM), we demonstrate that Wigner molecules appear in multi-electron artificial atoms when Coulomb interactions dominate. Three-electron Wigner molecules, for example, are seen to exhibit a characteristic trimer pattern. The array of Wigner molecules observed in a moiré superlattice comprises a new crystalline phase of electrons: the Wigner molecular crystal. We show that these Wigner molecular crystals are highly tunable through mechanical strain, moiré period, and carrier charge type. Our study presents new opportunities for exploring quantum phenomena in moiré quantum solids composed of multi-electron artificial atoms.

cond-mat.mes-hall↗

arXiv2023

Imaging Moiré Excited States with Photocurrent Tunneling Microscopy

Moiré superlattices provide a highly tunable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators1-17 to moiré excitons7-10,18. Scanning tunneling microscopy has played a key role in probing microscopic behaviors of the moiré correlated ground states at the atomic scale1,11-15,19. Atomic-resolution imaging of quantum excited state in moiré heterostructures, however, has been an outstanding experimental challenge. Here we develop a novel photocurrent tunneling microscopy by combining laser excitation and scanning tunneling spectroscopy (laser-STM) to directly visualize the electron and hole distribution within the photoexcited moiré exciton in a twisted bilayer WS2 (t-WS2). We observe that the tunneling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the exotic in-plane charge-transfer (ICT) moiré exciton in the t-WS2 that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our photocurrent maps are in excellent agreement with our GW-BSE calculations for excitonic states in t-WS2. The photocurrent tunneling microscopy creates new opportunities for exploring photoexcited non-equilibrium moiré phenomena at the atomic scale.

cond-mat.mes-hall↗

arXiv2022

Mapping Charge Excitations in Generalized Wigner Crystals

Transition metal dichalcogenide-based moire superlattices exhibit very strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. Here we describe a new scanning single-electron charging (SSEC) spectroscopy technique with nanometer spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS2 moire heterostructures. High-resolution SSEC spectroscopy was achieved by combining scanning tunneling microscopy (STM) with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of order 50meV exist for the 1/3 and 2/3 generalized Wigner crystal states.

cond-mat.mes-hall↗