Papers

The experimental observation of the fractional quantum anomalous Hall effect in rhombohedral graphene multilayers has raised questions about the nature of the fractional Chern insulator (FCI) states and the role of the moiré potential. In this Letter we develop a composite fermion (CF) description and discuss how moiré modulation and Coulomb interactions stabilize the FCI ground states. Under a flux-attachment transformation and mean-field approximation, the CF spectrum forms Landau levels that are further split by the moiré potential. At moiré filling fractions in the Jain sequence, an integer number of CF bands are occupied, resulting in an incompressible ground state with fractionally quantized Hall response. Remarkably, when the attached flux opposes the Berry curvature of the conduction band of rhombohedral graphene, the CF Landau levels are widely spaced in energy and delocalized across layers, leading to a reduced density of states that helps protect the CF mean-field state and amplifying effects of the moiré potential acting on the layer away from the doped electrons. Interactions between CFs further enlarge the moiré-induced band gap and stabilize the FCI ground state. Our work sheds light on the nature of the FCI states in rhombohedral graphene and provides a new theoretical framework for further studies.

One-dimensional SM-SC hybrid nanowires with Rashba spin-orbit coupling and applied Zeeman field can support Majorana zero modes (MZMs) at the ends of the wire. In finite-length systems, residual wave-function overlap between the end modes produces an energy splitting. In a two-sided tetron qubit, composed of a pair of parallel Majorana wires coupled by a trivial SC backbone in the middle, this splitting limits the parity lifetime associated with Majorana pairs involving both wires and the coherence of the qubit, adversely affecting measurement-based braiding and readout operations. Here, we propose a one-sided tetron made of four parallel Majorana wires connected at a common end by an SC backbone. In the topological phase, the free wire ends host four MZMs that define the topological qubit, while the Majoranas localized near the opposite ends hybridize through the backbone and acquire finite energy. To study the basic hybridization mechanism, we consider a simpler two-wire subsystem, i.e., half of a one-sided tetron, which we call a doublon. In a doublon, the backbone, or bridge, strongly hybridizes the two Majorana modes at the connected end and shifts them away from zero energy, while the modes at the free ends form a near-zero energy fermion. We show that the splitting of the surviving MZM pair can fall by about two orders of magnitude compared to the splitting energies in a two-sided tetron, thereby dramatically increasing the parity lifetimes. Thus, the one-sided tetron ensures a suppression of the Majorana overlap comparable to doubling the length of the corresponding two-sided tetron.

In this paper, we theoretically study the electron and hole $g$-factors in inorganic lead-halide perovskites for the reference cubic phase. We employ an 18-band $k \cdot p$ model and determine its parameters using target band structures obtained from DFT calculations. We use the linear response theory to calculate the $g$-factors and investigate their dependence on external strain. We then perform real-space calculations of the electron and hole $g$-factors in perovskite nanocrystals. We show that the bulk $g$-factors can be tuned over a wide range by external strain. In some cases, strain can be used to tune the $g$-factor through zero. By contrast, the carrier $g$-factors in CsPb$X_3$ nanocrystals are considerably less sensitive to strain due to quantum confinement.

Does any integer survive in the shift current, and does the Chern number control its sign? We show that the shift vector is a singular field on the Brillouin torus. Its curl has two sources: the interband Berry curvature and quantised point charges at the zeros of the transition dipole. Inverting this relation gives an exact decomposition of the shift conductivity, valid at every frequency, into one sector linear in the integer charges and three continuous sectors. As a testing ground, we take a graphene-Haldane bilayer: a model that lets us sweep the interband Chern number through five values at fixed gap to isolate its role. We also test the formalism against the time-reversal-symmetric biased AB bilayer. Whenever a charge sits at the band edge, and trigonal warping is present, the integer sector alone accounts for the band-edge peak. The relevant integer is not the Chern number but the winding of that single charge. Its sign, combined with a valley-dependent profile, sets the sign of the photocurrent. In these bilayers, sign reversals across topological transitions follow this winding; the invariant changes with it only when the same gap closing does both. A band-edge charge needs no invariant. It only requires that the two band-edge sublattices not be connected by the nearest-neighbour hopping, and trigonal warping makes it visible.

We derive a quantum master equation in Lindblad form for the open quantum Rabi model in the perturbative deep strong coupling regime, where the spectrum is close to degenerate and harmonic. The Lindblad form is obtained by combining secular and singular-coupling approximations, working in a Schrieffer-Wolff transformed frame. We benchmark our equation against a Bloch-Redfield one, analyzing the time-evolution and steady state properties of several observables and find excellent agreement. Analytical results are obtained in limiting cases.

We investigate the effects of quenched disorder on two-dimensional electron solids using Hartree-Fock theory and classical molecular dynamics. Increasing disorder weakens crystalline correlations, broadens the structure factor, and reduces the measured coherence length toward the pristine lattice spacing. This evolution is consistent with the Imry-Ma and Larkin picture: random pinning disrupts translational order on sufficiently long scales, and stronger disorder reduces the distance over which crystalline organization survives. Classical simulations further show that stronger pinning raises the temperature for particle rearrangement even after crystalline order has disappeared. Disorder thus suppresses structural coherence while stabilizing an amorphous solid against thermal rearrangement.

3D NAND flash has become the foundational non-volatile storage platform of the AI era, underpinning workloads from model training to large-scale inference and cold data archival. With roadmaps now targeting kilolayer stacks and tens of trillions of devices per die, scaling is no longer governed primarily by process integration or lithography. Instead, it is increasingly constrained by the physics of charge storage itself: lateral charge migration, electrostatic coupling, read disturb, and transport limitations are entering a margin-limited regime. In this regime, their collective interaction, not any single mechanism, compresses operating margins with each generation. In this Perspective, we examine these converging bottlenecks and argue that sustaining NAND scaling will require application-specific co-optimization rather than a monolithic device roadmap. In this framework, conventional charge-trap flash, ferroelectric storage, alternative channel materials, and system-level integration are best viewed as complementary solutions targeted to distinct tiers of data-centric computing.

Compact, reliable, and cost-effective gas sensors have become a highly demanding subject for safety management in the medical sector, chemical manufacturing, food quality monitoring, agriculture, and industrial safety. Hazardous gas emissions need to be controlled and monitored with fast-responsive and highly sensitive sensing devices. A first-principles study employing density functional theory (DFT) was used to investigate the adsorption behavior of Cl2, CO, CO2, NO, NO2, and HCN gas molecules with our proposed alloys, which consisted of hexagonal boron nitride (hBN) and graphene (Gr). The alloy consisting of 22% carbon (BNGr-2) was found to be most competent for sensing Cl2, CO, CO2, and HCN with sufficient adsorption energy, charge transfer, and bandgap alteration. However, NO and NO2 gas molecules showed more engagement with 33% carbon-proportioned alloy (BNGr-3) in terms of adequate gas sensing properties. NOx gases exhibited the most chemiresistive sensitivity towards the adsorbents. Other gases also showed significant chemiresistive sensitivity and distinct selectivity ratios, which would facilitate these alloys as chemiresistive sensors. Besides, noticeable work function variation (~20%) of these systems manifested potential as work function based sensors. Cl2 and NO2 showed strong physical adsorption, while the rest of the gases were weakly to moderately physisorbed, resulting in very short recovery times (10-1 ~ 10-6 seconds). Additionally, the distinctive absorption spectra observed for the gas analyte systems highlighted the potential of the proposed alloys as optical gas sensors. Temperature variation revealed that all gas molecules can be freed from the adsorbent BNGr-2 at 425 K. These findings imply hBN-Gr alloys as promising gas sensors for pollution auditing.

The manipulation of non-Abelian anyons is a foundational ingredient for topological quantum computing and underlies topologically protected quantum memories. Here we analyze a quantum-impurity-based protocol for braiding non-Abelian anyons. Exploiting mobile impurities with addressable internal spin states, we provide a concrete protocol to experimentally measure the matrix elements of the $R$ and $F$ matrices that characterize the non-Abelian statistics of anyons. In particular, focusing on the case of Ising and Fibonacci anyons, we illustrate how the anyonic nature of the excitations emerges directly in the Ramsey interferometer we propose. Building on this framework, we further introduce a conventional-to-topological qubit encoder to transfer quantum information from conventional flying qubits into a topologically protected quantum memory.

We construct two superconducting pairing models on doped Kitaev honeycomb, whose microscopic kernels are derived rather than assumed. Both are driven by a bond-local glue neutral between the even- and odd-parity pairing channels; the chirality–parity linkage is set by bond-star geometry, not by the microscopic glue. (i) Model~1(odd-parity sector): the kernel follows from the flux-sector selection rule of the pure model, fixing its component-diagonal, nearest-neighbor separable, rank-one-per-bond form, with $w_\alpha=J_K^2\chi_\alpha\propto r_\alpha m_\alpha$, where $m_\alpha$ follows from the Hellmann–Feynman theorem and $r_\alpha\simeq0.24$ is computed numerically. The spin-vertex state is a unitary triplet with a bond-locked anisotropic $\mathbf d$ vector; its gap is a Gram sum of bond sines, so nodal directions are fixed by geometry. (ii) Model~2(even): the kernel is fixed by the $C_3$ little-group selection rule of a zone-corner chiral phonon, up to a Cooper-channel extension whose momentum constraint we state explicitly. The charge-vertex pairing is a $d+id$ singlet: the parity decomposition $f_\pm=g_\pm+p_\pm$ projects onto $g_\pm$, so chirality is slaved to the phonon polarization, with $C=\pm4$ and $\kappa_{xy}/T=2\kappa_0$. Reversing the pump helicity reverses the Chern number, Kerr rotation, and thermal Hall sign. (iii) General theorem: on odd-fold bond stars, the angular-momentum ladder of a single-star chiral form factor alternates in parity. Every chiral state selected by such a bond-local form factor is a geometrically enforced singlet–triplet composite with universal amplitude ratios ($n=3$: $d\oplus p$; $n=5$: $g\oplus p$ or $d\oplus f$); coherent doubled-star combinations can restore parity purity. The Chern number of the mixed state follows the dominant on-shell component across a topological boundary. The spin glue drives $C=\pm2$; the charge kernel $C=\pm4$.

We formulate equations of motion for uniform magnetization dynamics in multisublattice magnets, with emphasis on a recently proposed inertial damping torque. We include intra- and intersublattice contributions to Gilbert damping, reactive inertia, and inertial damping. For a two-sublattice uniaxial antiferromagnet in an easy-axis static magnetic field, we derive the dynamical magnetic susceptibilities and approximate eigenfrequencies across all field-dependent equilibrium phases. In particular, we show how inertial damping affects the relaxation of the nutational modes and propose an experimental protocol to determine the dynamical coefficients.

In this contribution we provide a compact model for the description of inelastic x-ray scattering of spatially localized excitons. We combine our analytical theory with first principles calculations and apply it to the material lithium fluoride (LiF). A comparison of two different approaches for the underlying single-particle wave functions to calculate the spectrum yield a qualitatively good agreement with experimental data but also shows that a detailed description of the wave functions is essential to obtain qualitative results.

The realization of fractional Chern insulators has largely relied on isolated flat bands in complex bilayer or multilayer moiré systems with ideal quantum geometry. Whether such phases can emerge in genuinely dispersive bands, and by what mechanism, remains an open question. Here, we propose a mechanism for magnetic-field-induced strong correlations in the highly dispersive bands of monolayer graphene on hexagonal boron nitride. In the low-field classical-to-quantum crossover regime of the second moiré miniband, we show that the interplay of the moiré potential and weak magnetic fields (B < 1.5 T) profoundly alters electron dynamics. Saddle-point van Hove singularities produce extended open orbits that strongly suppress carrier propagation, potentially favoring a regime in which Coulomb interactions become comparatively more important, while weak magnetic fields lift valley degeneracy and trigonal warping redistributes Berry curvature. High-resolution magnetotransport and temperature-dependent measurements reveal fractional-slope transport features and signatures of interaction-driven incompressibility. Because the Hall conductivity is not fully quantized and the longitudinal resistance remains finite, we describe these observations as incipient FCI behavior: transport signatures consistent with a developing fractional Chern insulating state, without claiming a fully developed FCI phase established by complete Hall quantization and vanishing longitudinal resistance. Our results suggest a possible fermiology-driven route toward correlated topological states in dispersive bands in the classical-to-quantum crossover, distinct from the conventional flat-band scenario.

In this work, we study bimerons (in-plane skyrmions) and their clusters composed of states with mixed topological indices. These clusters provide flexibility in controlling the skyrmion Hall angle, which depends on the cluster's total topological charge. First, using the simplest such cluster, a bimeron-antibimeron pair, we examine its stability with the geodesic nudged elastic band method and identify three mechanisms – bimeron separation, interchange, and annihilation – with comparable energy barriers that determine the pair's overall stability. This provides an upper bound for the stability of more sophisticated clusters of bimerons and antibimerons. Then, we numerically study the clusters' dynamics for currents applied in-plane and perpendicular to the plane, corresponding to the Zhang-Li and Slonczewski mechanisms. Finally, we analyze the dynamics of a wide variety of bimeron clusters within the Thiele approach and show that their velocities always lie on a specific ellipse whose parameters are fully governed by the model Hamiltonian.

The effect of spin-orbit coupling (SOC) in monolayer graphene has been thoroughly studied in the past. Its impact is commonly disregarded since the electronic structure of graphene is almost unaffected. Consequently, SOC has also been ignored in other graphitic systems. In this work, we calculate the intrinsic SOC in stacks of graphene layers from a model that includes all the valence orbitals of carbon as well as the intra-atomic SOC.The leading spin-orbit term in a graphene multilayer combines a Rashba-like spin-flip process with interlayer hopping. We find that this intrinsic term modifies the phase diagram and Fermi surfaces of finite rhombohedral stacks, and it leads to a distinct density-dependence of the magnetization in weak magnetic fields. This Letter shows that, unlike in the single-layer case, SOC has important consequences in multilayer graphitic systems and it should not be neglected when studying their physical properties.

We show that an intense low-frequency laser field can qualitatively modify the local extremal structure of an interband energy gap in a crystal. Using an instantaneous laser-dressed basis obtained from the nonperturbative diagonalization of the multiband crystal Hamiltonian, we derive a quartic normal form for the dressed gap near a high-symmetry point. At a critical field, the quadratic part of this normal form changes sign, and the gap experiences a bifurcation: a single symmetric minimum splits into two symmetry-related minima separated by a local maximum. We identify the microscopic origin of this bifurcation by decomposing the quadratic part into a homogeneous Stark contribution and a field-modified band-curvature contribution. The latter originates from the multiband redistribution of interband polarizations and provides the mechanism for the field-induced change of the gap extrema. A realization for the Kronig–Penney model demonstrates the same bifurcation at multiple high-symmetry points and for different interband gaps. As an illustration of its spectral consequences, we show that the bifurcation gives rise to an additional van Hove feature in the instantaneous interband susceptibility above the absorption edge. Our results establish a general mechanism by which strong-field dressing modifies the local geometry of the electronic spectrum.

Graphene nanoscrolls form a unique radial superlattice whose geometry enables transport behaviors distinct from their flat counterparts. We theoretically demonstrate that rolling a graphene nanoribbon into a few-turn nanoscroll (1.0-1.2 turns) triggers a giant enhancement in longitudinal conductance by an order of magnitude (nearly twentyfold). We show that this effect stems from interlayer hopping between open boundaries, which not only transforms localized edge states into one-dimensional-like conducting channels and also induces a significant Fermi energy shift. Our results reveal an inverse scaling of conductance with turn number, establishing GNSs as a platform for geometry-driven quantum transport and offering a tunable approach to engineering nanoarchitectural electronic states.

We present a simple model of a Bloch line in a thin-film ferromagnet with strong easy-axis and intermediate in-plane anisotropies. The meron is represented as a charged, massless particle that slides along the linear domain wall in a background magnetic field- a gyroscopic bead on a string. Its gyroscopic behavior dynamically isolates the wall segments on either side of the meron, motivating the model for a Bloch line as two strings joined at a moving boundary. The meron clamps the wall at this junction, completely reflecting low-amplitude spin waves that propagate along it. Out-of-plane and in-plane magnetic fields and spin-transfer torques then act in two ways: by exerting a force on the Bloch line itself, or by driving the wall as a whole. Predictions of this model are in agreement with numerical simulations.

Transverse optical rectification has been reported in a one-dimensional asymmetric Au grating even though an ideal profile $h(x)$ retains the $xz$ mirror $\Me:y\to-y$. Because $J_y$ is odd under $\Me$, whereas the $p$-polarized bilinears $|E_x|^2$, $|E_z|^2$, and $\mathrm{Re}(E_xE_z^*)$ are even, the transverse dc current requires a distinct mirror-odd factor $\Lamy$. We formulate a symmetry-complete effective model combining the origin-independent cell invariant $\Astr=\mathrm{Im}(h_1^2h_2^*)$, Drude–Edelstein spin polarization, and spin–orbit conversion. We then propose a dynamical realization of $\Lamy$ for a finite-width device. A driven pump-like plasmonic mode at $k_y\simeq0$ generates a mirror pair of transverse surface-plasmon-polariton quasinormal modes $(K_x,\pm q_y)$ through the same third-order susceptibility that produces self- and cross-Kerr shifts. Four-wave mixing creates the pair and locks its phase sum but, by itself, cannot change the pair-population difference. Weak coherent backscattering makes the relative drive phase observable; a small phase difference from incident $k_y$, spot displacement, edges, or disorder then unfolds a Kerr directional instability and deterministically selects its sign. The resulting population imbalance supplies the dynamical mirror-odd factor $\Ldyn=\lambda_\eta\eta$ in the structure-dependent $\Astr\Lamy\langle j_xs_y\rangle_t$ side-jump-like channel, which vanishes for the centered symmetric grating because $\Astr=0$. We give the complete three-mode equations, the pump-only and saturated-state Bogoliubov problems, the imperfect-pitchfork reduction, and a validated normalized numerical realization. The normalized equations exhibit a robust supercritical pitchfork with an approximately one-half critical exponent and phase-reversed branch selection.

The emergence of spin-polarized electrons from nonmagnetic chiral molecules and crystals is called Chirality-induced spin selectivity (CISS). A chiral phonon of definite wavevector $q$ can strongly enhance it, but near equilibrium the two helicities $+q$ and $-q$ are equally populated: they are time-reversal partners and their contributions cancel. We show that in a biased chiral conductor the current causes the phonon of one helicity to damp less than the other. The damping asymmetry is odd in the current, odd under $q\rightarrow-q$, invariant under a mirror that reverses the structural handedness, and equal, mode for mode, to the current-induced nonconservative Berry force on the phonon coordinate. Closing the phonon kinetics with a rate equation turns the asymmetry into a net lattice helicity: at any finite bias one helicity is preferentially populated, with no threshold, growing linearly with the current as $V\rightarrow0$; above a threshold that helicity becomes a self-sustained coherent travelling wave. We demonstrate this effect in elemental tellurium, treated as an open quantum system (electronic Hamiltonian, phonon bath, and electron-phonon coupling) within a quasi-ab initio framework. The electronic Hamiltonian is supplied by a vertex-corrected quasiparticle self-consistent $GW$ (QSGW) potential with spin-orbit coupling; nuclear displacements are modeled with a machine-learned interatomic potential, which yields chiral phonon modes at finite $\pm q_z$ on the $\Gamma$-A line. The perturbation to the electronic Hamiltonian from a nuclear displacement is approximated by a frozen-phonon deformation potential. No optical pump is needed: a bias alone drives the current and selects the phonon helicity; reversing the current reverses the selection.

The nonlinear Hall effect (NLHE) holds significant promise for next-generation electronic device applications, and it is essential to explore and engineer a strong and highly tunable NLHE. In this work, we report large second-order and third-order NLHEs in dual-gated BiSbTeSe2 devices. Both the second-order and third-order NLHE are highly gate-tunable. The second-order NLHE exhibits a higher generation efficiency than those reported in previous topological insulator systems, and it can be stably observed up to room temperature. Meanwhile, the generation efficiency of the third-order NLHE is comparable to previously reported values. The scaling analysis indicates that the second-order NLHE is consistent with contributions from skew scattering and a term compatible with either the Berry curvature dipole or side jump, whereas the third-order NLHE is consistent with contributions from the Berry connection polarizability tensor and higher-order skew scattering. Our work establishes a promising experimental platform for the development of NLHE-based devices.

For two decades, the origin of Chirality-Induced Spin Selectivity (CISS), the spin polarization of electrons by nonmagnetic chiral systems without magnetic fields, has remained unsettled. Here, we establish a single exact rule defining the fundamental conditions for the effect: in nonmagnetic, time-reversal-invariant conductors, all measurable CISS signals are time-reversal odd and vanish near equilibrium, proving that structural chirality alone is insufficient. By evaluating leading theoretical mechanisms across four levels of nonequilibrium transport, from coherent classical driving to fully non-Markovian quantum baths, we verify this selection rule to machine precision. We show that coherent chiral vibrations generate substantial collinear polarization (up to 10 percent across 0.5-6 THz) that reverses with handedness, whereas incoherent vibrations yield under 1 percent, and non-Markovian bath memory further suppresses the signal. The chiral geometry first makes the electronic motion chiral by accumulating orbital angular momentum; spin-orbit coupling (SOC) then converts that into spin. CISS therefore acts as both a spin polarizer and a spin filter, the latter an order of magnitude weaker. The polarization grows with molecular length and then saturates, matching trends reported for DNA and peptides. Reversing the drive converts decaying spin into a handedness-locked charge-current pulse (inverse-CISS). We find that once the system is driven, the polarization magnitude scales with an effective spin-orbit coupling: making heavy atoms and curved light-atom backbones indistinguishable at equivalent effective SOC. This enables us to chart how geometry, driving field, and length separate those routes.

The bulk photovoltaic effect (BPVE) provides a direct link between quantum geometry and nonlinear light-matter interactions, yet conventional far-field measurements cannot disentangle BPVE from contact- and interface-induced photothermoelectric signals. Here we develop cryogenic, polarization-sensitive terahertz microscopy with deep-subwavelength resolution and apply it to dual-gated AB bilayer graphene. Near resonance between the band gap and terahertz photon energy, we observe enhanced optical conductivity and spatially resolved BPVE. Polarization-dependent measurements reveal a characteristic twofold angular symmetry and a distinct shift-vector direction, both governed by crystalline symmetries and quantum geometry. The evolution of BPVE with carrier density and temperature provides a sensitive probe of the fine electronic structure of bilayer graphene, revealing signatures of trigonal warping and electron-hole asymmetry. Agreement with theory demonstrates that the terahertz nanoscopy of BPVE established here offers an optical lens into the interplay between band and quantum geometry in quantum materials.

Non-reciprocal transport underpins key functionalities in signal processing and logic; however, conventional semiconductor diodes exhibit reduced performance at sub-Kelvin temperatures. As cryogenic electronics continue to scale, there is increasing demand for diode operation compatible with low-temperature and low-dissipation conditions. This need has driven the development of alternatives to p-n junctions that rely on non-reciprocal electron transport mechanisms efficient in the deep-cryogenic regime. Superconducting devices constitute a natural low-loss platform, yet most existing superconducting diodes are restricted to either Cooper-pair or quasiparticle transport, often requiring complex material stacks, asymmetric geometries, or external magnetic fields. No single, geometrically symmetric junction has yet integrated rectification across both transport channels to achieve vanishing resistance under forward bias and strongly suppressed conduction under reverse bias. Here, we demonstrate a dynamically reconfigurable dual-function superconducting diode based on a conventional Al/AlOx/Al tunnel junction. Via microwave biharmonic driving, we exploit multi-tone photon-assisted tunneling to independently control dissipationless and dissipative transport channels within the same device. Varying the microwave drive amplitude induces a transition from a supercurrent diode to an ideal quasiparticle diode, achieving rectification efficiencies exceeding those of conventional Schottky diodes and contemporary superconducting diodes. We further demonstrate AC signal rectification under both current-bias and voltage-bias configurations. Finally, we implement a proof-of-concept "absolute diode" that combines zero forward resistance with strongly suppressed reverse conduction. This tunable approach provides a versatile building block for low-power cryogenic electronic architectures.

We introduce a distinct route for extending classical atomistic spin dynamics into the quantum regime for arbitrary spin $s$, based on a variational product-state ansatz that includes both pure and mixed local states. By construction, intersite entanglement – expected to remain negligible even on very short time scales in many real materials – is excluded, while local quantum effects are retained through the nonclassical structure of $s\geq 1$ density operators, and nonlinear dynamics arise from both the mean-field interdependence of the local states and the state-dependent dissipative terms. This framework clarifies the variational and geometric origin of the inequivalence between quantum Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics, provides a criterion for their equivalence under a common time rescaling, establishes connections with the classical theory through two qualitatively distinct limits ($s\to\infty$ and a large number of quantum spins $N$), and allows realistic $\mathcal{O}(N)$ simulations of quantum spin dynamics in materials.

Accurate modelling of the band-edge electronic structure of transition metal dichalcogenides (TMDs), such as MoS$_2$, is essential for understanding their optical, electronic and spintronic properties and enabling future applications. Here, we supplement the standard PBE exchange-correlation functional with on-metal ($U$) and metal–chalcogen ($V$) Hubbard corrections, which can control the orbital composition of band-edge states and consequently improve the quantitative accuracy of various properties. For MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, we optimise the $U$ and $V$ parameters by comparison with experimentally measured spin–orbit splittings at the conduction and valence band edges, and show that these optimal choices also improve agreement of the computed band gap, and ferroelectric potential drop in rhombohedral bilayers, with experimentally measured values. This provides a highly efficient, scalable framework for quantitatively accurate, high-throughput calculations of monolayer and multilayer TMDs, suitable for implementation in 2D-materials databases, as well as large-scale electronic and spintronic device modelling.

We study $N$ bosons on a three-site ring with nearest-neighbour hopping, density-assisted hopping of the opposite sign, and an on-site interaction, written equivalently as three momentum modes $q=0,\pm1$ with a channel-dependent quartic vertex. As the density-assisted term grows it inverts the band, and exact diagonalisation up to $N=400$ shows a first-order ground-state transition from the $q=0$ condensate to a state with $\avg{n_{+1}}=\avg{n_{-1}}\simeq N/2$; the avoided-crossing gap closes faster than exponentially with $N$. In its symmetric eigenstates this state is fragmented in the Penrose-Onsager sense, and at leading order in $N$ it has the energy of a Gross-Pitaevskii (GP) standing wave, as expected for a few-mode mean-field system. We distinguish two cases by switching off umklapp scattering, which is available because $2\cdot(+1)\equiv-1$ on three sites, and by varying the on-site interaction. Without umklapp, $n_{+1}-n_{-1}$ is conserved, the eigenstates form a rotor tower whose lowest member is a fragmented Fock state, and the transition leads to fragmentation exactly when the $\pm1$ interaction is attractive, as predicted by Nozières' exchange argument with the sign of the interaction reversed; otherwise the system forms a single current-carrying condensate. With umklapp, the standing wave is pinned to three positions, the three momentum sectors become degenerate exponentially in $N$, and coherent admixture of the $q=0$ mode stabilises the standing wave over a wider range; the exact ground state is then a number-squeezed, momentum-projected standing-wave condensate rather than a robustly fragmented state.

The extension of nanoscale quantum materials to the third dimension brings new possibilities to geometrically tune emergent properties, emulating or indeed going beyond the physics of bulk materials, with exciting implications for high-density technological integration. Realising such three-dimensional architectures requires nanofabrication techniques that not only enable complex 3D geometries, but also deliver functional quantum materials with emergent phenomena. Recent advances in focused electron- and ion-beam induced deposition (FEBID and FIBID) have made 3D nanopatterning of functional materials in complex geometries increasingly feasible, paving the way for the experimental realisation of new phenomena and device prototyping. In this review, we discuss the use of FEBID and FIBID 3D nanopatterning of superconducting and magnetic materials. We address the underlying mechanisms, and capabilities of these techniques, focusing on the physical phenomena that become accessible. Considering the resolution of the techniques in the context of the fundamental lengthscales of the materials, we discuss the emergent effects that arise due to three dimensional geometries in magnetic and superconducting nanostructures, and highlight perspectives for future developments of the techniques.

Structure leads to function: Knowing all possible ways to stack and slide identical monolayers enables the design of functionalities such as nonlinear optical responses and ferroelectricity in layered materials. Besides, mounting experimental evidence points to differing stacking configurations in few-monolayer and bulk samples. To exemplify the core concepts for stacking arbitrary monolayers, ground-state and metastable non-moiré SnSe stacks were first identified using density functional theory and employed to validate a “divide and conquer” combinatoral approach for determining the most probable stacking configurations in materials with an arbitrary number of identical monolayers. A small number of point groups accounts for all possible stacks, which explains experimental second-harmonic optical responses. Finite-temperature effects are also studied despite the granularity of available data. This comprehensive framework readily generalizes to provide a predictive description of arbitrary metastable few-homomonolayer stacks.

Electron cotunneling in semiconductor quantum dots is a higher-order tunneling mechanism that connects initial and final charge states through energetically inaccessible virtual intermediate configurations. In quantum-dot arrays, such processes can produce simultaneous charge motion across multiple tunnel junctions and enable transitions that would otherwise be suppressed by Coulomb blockade. Here, building on an earlier proof-of-principle demonstration, we investigate radio-frequency (rf)-driven correlated cotunneling and its application to dispersive quantum-dot readout. Using both theoretical modeling and experimental measurements in two different foundry-fabricated silicon devices, we show that an external rf drive can induce correlated cyclic single-electron transitions, resulting in enhanced charge-polarization of the system. We develop a general theoretical framework for rf electron-cascade readout, which exploits cotunneling events in quantum-dot systems with three or more dots to produce a relative signal enhancement, and extend its experimental demonstration to a gate-sensed device architecture. Our results establish the operating principles of rf electron-cascade readout and provide a route to increased dispersive readout fidelity in semiconductor quantum computing architectures.