arXiv subjects

Zhen Zhan

Publications and source records attributed to Zhen Zhan.

At least 19 recordsLinked to original sources

arXiv2026

Twist and strain identification in moir\'e heterostructures

The geometrical and electronic properties of moir\'e materials are highly sensitive to the twist and strain in the samples due to the moir\'e magnifying effect. Accurate identification of twist and strain in moir\'e materials is therefore essential. In this work, we establish a general framework to extract the twist and strain configurations from moir\'e images with either atomic or moir\'e scale resolution. With only moir\'e-wavelength information, we show that there is a continuous family of possible twist and strain configurations, each one accounting for different orientations of the moir\'e pattern. To estimate the most likely twist-strain configuration, we discuss additional constraints and methods involving the minimum elastic energy and the electronic spectra. The minimum elastic energy, in particular, reflects that shear configurations become much more favorable as the strain increases. As an example of the developed methodology, we discuss the formation and identification of strained triangular moir\'e patterns. Our framework provides a comprehensive approach to identify the twist and strain configurations in systems with moir\'e-scale resolution.

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arXiv2026

Tunable topological narrow bands in twisted bilayer-trilayer graphene

We investigate the low-energy band structure and topology of twisted bilayer--trilayer graphene with four stacking configurations: AB--ABC, BA--ABC, AB--ABA, and BA--ABA. Using both tight-binding and continuum models, we first establish that the two approaches show good agreement in the band structure in low-energy regime. We then study the evolution of the flat bands and their valley Chern numbers as functions of twist angle, perpendicular electric field, and the self-consistent Hartree potential. At relatively large twist angles and under electric field, we find a topological transition between the narrow bands, with the total Chern number of the flat bands following the Chern number sum rules derived from the chiral-limit description. We also observe another type of topological transition when the flat bands hybridize with adjacent remote bands, where gap closing and reopening processes lead to Chern number and charge density transfer. By constructing topological phase diagrams in the space of twist angle and electric field, we show that the perpendicular electric field provides an efficient tuning knob for controlling the stability and transitions of the Chern bands. Finally, we find that the Hartree potential mainly induce weak band shifts and reshaping in the narrow bands. However, with a combination of Hartree potential and the electric fields, the narrow bands show rich topological phase diagram. Our results clarify the interplay between the stacking, twist angle and electric field in manipulating the narrow bands and their topology in twisted bilayer--trilayer graphene, and provide guidance for engineering topological narrow bands with tunable Chern numbers in realistic twisted multilayer graphene systems.

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arXiv2026

Structural and electronic signatures of strain-tunable marginally twisted bilayer graphene

Marginally twisted bilayer graphene having small twist angles is predicted to exhibit unique structural and electronic properties, though experimental characterization remains limited. Using scanning tunneling microscopy, we investigate such systems with twist angles of 0.06^{\circ}-0.35^{\circ}. AA-stacked regions reveal a pronounced tunneling spectral peak signifying highly localized electronic states. Conversely, AB domains display uniform multiple spectral peaks, indicative of strong lattice reconstruction and enhanced electronic homogeneity. We identify two distinct strain-induced domain walls: one exhibits a sharp -120 meV spectral peak (shear type), while the other shows distinct spectral characteristics (mixed shear-tensile type). Tight-binding calculations verify strain-driven transformations of both domain wall types and confirm direct observation of strain-mediated domain wall transitions. These results elucidate the electronic structure of marginally twisted bilayer graphene and establish strain as a control parameter for domain wall states.

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arXiv2026

Straintronics and twistronics in bilayer graphene

The interplay of twist and strain in bilayer graphene enables the formation of moir\'e patterns and narrow bands that host correlated and topological phases. While magic-angle twisted bilayer graphene has been widely studied, strain provides an additional and realistic control knob for band engineering. In this work, we first generate a global method to construct commensurate supercells for arbitrary twist and heterostrain. Then, using atomistic tight-binding and strain-extended continuum models to study the commensurate structures, we identify configurations that minimize the bandwidth beyond the magic angle. The results reveal a strong dependence of band narrowing and topology on strain type, magnitude, direction and lattice relaxation. Particularly, shear strain produces a stronger distortion than uniaxial strain. Including electron-electron interactions through a self-consistent Hartree potential shows that strain broadens the bare bands while reducing electrostatic renormalization. Strain also drives topological transitions as the narrow and remote bands hybridize, establishing twisted and strained bilayer graphene as a tunable platform for flat-band and topological phenomena.

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arXiv2026

Moir\'e-driven equilibrium of perturbations in moir\'e systems

Perturbations in moir\'e materials, such as due to substrates or strain, are common in many experiments and can significantly modify the electronic properties of the system. Here, we show that perturbations in twisted bilayer graphene tend to be transferred between the coupled Dirac cones, eventually reaching an equilibrium near the magic angle. We connect our results to experiments and show that this equilibrium behavior remains robust even when the moir\'e potential itself is perturbed. Our findings extend the notion of the magic angle to a more general regime governed by moir\'e-driven equilibrium.

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arXiv2025

Geometrical properties of strained and twisted moir\'e heterostructures

The experimental observations of many interaction-driven electronic phases in moir\'e superlattices have stimulated intense theoretical and experimental efforts to understand and engineer these correlated physics. Strain is a powerful tool for manipulating and controlling the geometrical and electronic structures of moir\'e superlattices. This review provides a comprehensive introduction to the geometry of strained moir\'e superlattices. First, starting from the linear elasticity theory, we briefly introduce the general formalism of small deformations in two-dimensional materials, and discuss the particular cases of uniaxial, shear and biaxial strain. Then, we apply the theory to twisted and strained moir\'e materials, mainly focusing on the hexagonal homobilayers, hexagonal heterobilayers and monoclinic lattices. Special moir\'e geometries, like the quasi-unidimensional patterns, square patterns and hexagonal, are theoretically predicted by manipulating the strain and twist. Finally, we review recently developed strain techniques and the special moir\'e geometries realized via these approaches. This review aims at equipping the reader with a robust understanding on the description and implementation of strain in moir\'e materials, as well as highlight some major breakthroughs in this active field.

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arXiv2025

Review of the tight-binding method applicable to the properties of moir\'e superlattices

Moir\'e superlattices have emerged as a versatile platform for exploring a wide range of ex- otic quantum phenomena. Unlike angstrom-scale materials, the moir\'e length-scale system contains a large number of atoms, and its electronic structure is significantly modulated by the lattice relaxation. These features pose a huge theoretical challenge. Among the available theoretical approaches, tight-binding (TB) methods are widely employed to predict the electronic, transport, and optical properties of systems such as twisted graphene, twisted transition-metal dichalcogenides (TMDs), and related moir\'e materials. In this review, we pro- vide a comprehensive overview of atomistic TB Hamiltonians and the numerical techniques commonly used to model graphene-based, TMD-based and hBN-based moir\'e superlattices. We also discuss the connection between atomistic TB descriptions and effective low-energy continuum models. Two examples of different moir\'e materials and geometries are provided to emphasize the advantages of the TB methods. This review is intended to serve as a theoretical and practical guide for those seeking to apply TB methods to the study of various properties of moir\'e superlattices.

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arXiv2025

Twistraintronics in Square Moire Superlattices of Stacked Graphene Layers

We report the first observation of controlled, strain-induced square moire patterns in stacked graphene. By selectively displacing native wrinkles, we drive a reversible transition from the usual trigonal to square moire order. Scanning tunneling microscopy reveals elliptically shaped AA domains, while spectroscopy shows strong electronic correlation in the form of narrow bands with split Van Hove singularities near the Fermi level. A continuum model with electrostatic interactions reproduces these features under the specific twist-strain combination that minimizes elastic energy. This work demonstrates that the combination of twist and strain, or twistraintronics, enables the realization of highly correlated electronic states in moire heterostructures with geometries that were previously inaccessible.

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arXiv2025

Heavy fermion phase diagram in magic-angle twisted trilayer graphene

The interplay between localized magnetic moments and itinerant electrons gives rise to exotic quantum states in condensed matter systems. Here, we demonstrate an electrically tunable heavy fermion phase diagram in magic-angle twisted trilayer graphene, achieved by controlling the Kondo hybridization between localized flat-band electrons and itinerant Dirac electrons via a displacement field. Our results reveal a continuous quantum phase transition from an antiferromagnetic semimetal to a paramagnetic heavy fermion metal. At quantum critical point, we observe effective mass divergence and Fermi surface reconstruction. This highly tunable platform offers unprecedented control over heavy fermion physics, establishing moire heterostructures as a versatile arena for exploring correlated quantum phases-including potential unconventional superconductivity-in two-dimensional limit.

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arXiv2024

Designing Flat Bands and Pseudo-Landau Levels in GaAs with Patterned Gates

We investigate the electronic properties of two-dimensional electron gases (2DEGs) subjected to a periodic patterned gate. By incorporating the superlattice (SL) potential induced by patterning into the Schrodinger equation, we develop a methodology for obtaining exact analytical solutions. These solutions enable us to construct a comprehensive phase diagram illustrating the emergence of narrow bands and pseudo-Landau levels driven by the SL potential. To complement the analytical approach, we employ a standard plane-wave formalism to track the evolution of the band structure as the SL strength increases. By breaking the inversion symmetry of the SL potential, we found a nontrivial Berry curvature. Furthermore, we introduce a self-consistent Hartree screening to account for the interplay between the SL potential and electronic interactions. Our findings not only reveal the emergence of a non-trivial quantum geometry and a competition between SL strength and electron-electron interactions, but also highlight the value of exact analytical solutions for understanding and engineering electronic phases in patterned 2DEG systems.

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arXiv2024

Designing Band Structures by Patterned Dielectric Superlattices

We investigate the electronic structure of graphene monolayers subjected to patterned dielectric superlattices. Through a quantum capacitance model approach, we simulate realistic devices capable of imposing periodic potentials on graphene. By means of both tight-binding and continuum models, we analyze the electronic structure across varied patterning geometries, including triangular, kagome, and square configurations. We explicitly explore the influence of device parameters such as the superlattice potential strength, geometry, and periodicity on the electronic properties of graphene. By introducing a long-range Coulomb interaction, we found an emergent periodic potential strong enough to open a mass gap, thereby generating a Chern band. Our study highlights the robustness and versatility of patterned dielectric superlattices for band engineering in graphene systems.

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arXiv2024

Strain and twist angle driven electronic structure evolution in twisted bilayer graphene

In twisted bilayer graphene (TBG) devices, local strains frequently coexist and intertwine with the twist-angle-dependent moir\'e superlattice, significantly influencing the electronic properties of TBG, yet their combined effects remain incompletely understood. Here, using low-temperature scanning tunneling microscopy, we study a TBG device exhibiting both a continuous twist-angle gradient from 0.35{\deg} to 1.30{\deg} and spatially varying strain fields, spanning the first (1.1{\deg}), second (0.5{\deg}) and third (0.3{\deg}) magic angles. We visualize the evolution of flat and remote bands in energy and real space with atomic resolution. Near the first magic angle, we discover an anomalous spectral weight transfer between the two flat band peaks, signifying the role of strain and electronic correlations, as further evidenced by an unusual spatial dispersion of these peaks within a moir\'e unit cell. In contrast, remote band peak energy offers a strain-insensitive indicator of the local twist angle. Structural analysis further reveals non-negligible shear strain across the sample. All observations are quantitatively reproduced by a continuum model that incorporates heterostrain and a self-consistent Hartree potential, revealing the critical but unexplored role of shear strain in shaping the low-energy electronic landscape of TBG.

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arXiv2024

Terahertz photocurrent probe of quantum geometry and interactions in magic-angle twisted bilayer graphene

Moir\'e materials represent strongly interacting electron systems bridging topological and correlated physics. Despite significant advances, decoding wavefunction properties underlying the quantum geometry remains challenging. Here, we utilize polarization-resolved photocurrent measurements to probe magic-angle twisted bilayer graphene, leveraging its sensitivity to the Berry connection that encompasses quantum "textures" of electron wavefunctions. Using terahertz light resonant with optical transitions of its flat bands, we observe bulk photocurrents driven by broken symmetries and reveal the interplay between electron interactions and quantum geometry. We observe inversion-breaking gapped states undetectable through quantum transport, sharp changes in the polarization axes caused by interaction-induced band renormalization, and recurring photocurrent patterns at integer fillings of the moir\'e unit cell that track the evolution of quantum geometry through the cascade of phase transitions. The large and tunable terahertz response intrinsic to flat-band systems offers direct insights into the quantum geometry of interacting electrons and paves the way for innovative terahertz quantum technologies.

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arXiv2024

Infrared Spectroscopy for Diagnosing Superlattice Minibands in Magic-angle Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system owed to its unique flat electronic bands. However, understanding the single-particle band structure alone has been challenging due to complex lattice reconstruction effects and a lack of spectroscopic measurements over a broad energy range. Here, we probe the band structure of TBG around the magic angle using infrared spectroscopy. Our measurements reveal spectral features originating from interband transitions whose energies are uniquely defined by the twist angle. By combining with quantum transport, we connect spectral features over a broad energy range (10 to 700 meV) spanning several superlattice minibands and track their evolution with twist angle. We compare our data with calculations of the band structures obtained via the continuum model and find good agreement only when considering a variation of interlayer/intralayer tunnelling parameters with the twist angle. Our analysis suggests that the magic angle also shifts due to lattice relaxation, and is better defined for a wide angular range from 0.9° to 1.1°. Our work provides spectroscopic insights into TBG's band structure and offers an optical fingerprint of the magic angle for screening heterostructures before nanofabrication.

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arXiv2024

Designing Moiré Patterns by Strain

Experiments conducted on two-dimensional twisted materials have revealed a plethora of moiré patterns with different forms and shapes. The formation of these patterns is usually attributed to the presence of small strains in the samples, which typically arise during their fabrication. In this work we find that the superlattice structure of such systems actually depends crucially on the interplay between twist and strain. For systems composed of honeycomb lattices, we show that this can lead to the formation of practically any moiré geometry, even if each lattice is only slightly distorted. As a result, we show that under strain the moiré Brillouin zone is not a stretched irregular hexagon, but rather a primitive cell that changes according to the geometry of the strained moiré vectors. We identify the conditions for the formation of hexagonal moiré patterns arising solely due to shear or biaxial strain, thus opening the possibility of engineering moiré patterns solely by strain. Moreover, we study the electronic properties in such moiré patterns and find that the strain tends to suppress the formation of the flat moiré bands, even in the strain-induced hexagonal patterns analogous to those obtained by the twist only. Our work explains the plethora of moiré patterns observed in experiments, and provides a solid theoretical foundation from which one can design moiré patterns by strain.

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arXiv2024

Tuning flat bands by interlayer interaction, spin-orbital coupling, and external fields in twisted homotrilayer MoS$_2$

Ultraflat bands have already been detected in twisted bilayer graphene and twisted bilayer transition-metal dichalcogenides, which provide a platform to investigate strong correlations. In this paper, the electronic properties of twisted trilayer molybdenum disulfide (TTM) are investigated via an accurate tight-binding Hamiltonian. We find that the highest valence bands are derived from the $Γ$-point of the constituent monolayer, and they exhibit a graphenelike dispersion or become isolated flat bands that are dependent on the starting stacking arrangements. The lattice relaxation, local deformation, and external fields can significantly tune the electronic structures of TTM. After introducing the spin-orbital coupling effect, we find a spin-valley-layer locking effect at the minimum of the conduction band at the $K$- and $K^\prime$-point of the Brillouin zone, which may provide a platform to study optical properties and magnetoelectric effects.

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arXiv2024

Charge fluctuations, phonons and superconductivity in multilayer graphene

Motivated by the recent experimental detection of superconductivity in Bernal bilayer (AB) and rhombohedral trilayer (ABC) graphene, we study the emergence of superconductivity in multilayer graphene based on a Kohn-Luttinger (KL)-like mechanism in which the pairing glue is the screened Coulomb interaction. We find that electronic interactions alone can drive superconductivity in AB bilayer graphene and ABC trilayer graphene with the critical temperatures in good agreement with the experimentally observed ones, allowing us to further predict superconductivity from electronic interactions in Bernal ABA trilayer and ABAB tetralayer and rhombohedral ABCA tetralayer graphene. By comparing the critical temperatures ($T_c$) of these five non-twisted graphene stacks, we find that the ABC trilayer graphene possesses the highest $T_c\sim100$ mK. After considering the enhancement of superconductivity due to Ising spin-orbit coupling, we observe that the AB bilayer graphene has the largest enhancement in the critical temperature, increasing from 23 mK to 143 mK. The superconducting behaviors in these non-twisted graphene stacks could be explained by the order parameters (OPs). The OPs of Bernal stacks preserve intravalley $C_3$ symmetry, whereas rhombohedral stacks break it. In all stacks, the OPs have zeroes and change signs between valleys, which means that these multilayers of graphene are nodal spin-triplet superconductors. Moreover, dressing the purely electronic interaction with acoustic phonons, we observe minor changes of the critical temperatures in these five stacks. We adopt the KL-like mechanism to investigate the tendency of superconductivity in multilayer graphene without fitting parameters, which could provide guidance to future experiments exploring superconductivity in non-twisted graphene.

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arXiv2024

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides (TMDCs). Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

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