What happens when fermions hop on a lattice with crystalline defects? The answer depends on topological quantum numbers that specify the action of lattice rotations and translations in the low energy theory. One can understand the topological quantum numbers as a twist of continuum gauge fields in terms of crystalline gauge fields. We find that disclinations and dislocations—defects of crystalline symmetries—generally lead to a certain “emanant” quantized magnetic flux in the continuum. To demonstrate these facts, we study in detail tight-binding models whose low-energy descriptions are $(2+1)\mathrm{D}$ Dirac cones. Our map from lattice to continuum defects explains the crystalline topological response to disclinations and dislocations, and motivates the fermion crystalline equivalence principle used in the classification of crystalline topological phases. When the gap closes, the presence of emanant flux leads to pair creation from the vacuum with the particles and antiparticles swirling around the defect. We compute the associated currents and energy density using the tools of defect conformal field theory. There is a rich set of renormalization group fixed points, depending on how particles scatter from the defect. At half flux, there is a defect conformal manifold leading to a continuum of possible low-energy theories. We present extensive numerical evidence supporting the emanant magnetic flux at lattice defects, and we test our map between lattice and continuum defects in detail. We also point out a no-go result, which implies that a single $(2+1)\mathrm{D}$ Dirac cone in symmetry class AII is incompatible with a commuting $C_M$ rotational symmetry with $(C_M{)}^M=+1$.

Intertwined charge and spin correlations are ubiquitous in a wide range of transition metal oxides and are often perceived as intimately related to unconventional superconductivity. Theoretically envisioned as driven by strong electronic correlations, the intertwined order is usually found to be strongly coupled to the lattice as signaled by pronounced phonon softening. Recently, both charge and spin density waves (CDW and SDW) and superconductivity have been discovered in several Ruddlesden-Popper (RP) nickelates, in particular trilayer nickelates $R{E}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ ($RE=\mathrm{Pr}$, La). The nature of the intertwined order and the role of lattice-charge coupling are at the heart of the debate about these materials. Using inelastic x-ray scattering, we mapped the low-energy phonon dispersions in $R{E}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ and found no evidence of softening near the CDW wave vector over a wide temperature range, which contrasts with the pronounced anomalies frequently observed in cuprate superconductors. Calculations of the electronic susceptibility revealed a peak at the observed SDW ordering vector but not at the CDW wave vector. Our experimental and theoretical findings highlight the crucial role of the spin degree of freedom and establish a foundation for understanding the interplay between superconductivity and density-wave transitions in RP nickelate superconductors and beyond.

Microwave drives are essential for implementing control and readout operations in superconducting quantum circuits. However, increasing the drive strength eventually leads to unwanted state transitions which limit the speed and fidelity of such operations. In this work, we systematically investigate such transitions in a fixed-frequency qubit subjected to microwave drives spanning a 9-GHz frequency range. We identify the physical origins of these transitions and classify them into three categories: (1) resonant energy exchange with parasitic two-level systems (TLSs), activated by drive-induced ac-Stark shifts, (2) multiphoton transitions to noncomputational states, intrinsic to the circuit Hamiltonian, and (3) inelastic scattering processes in which the drive causes a state transition in the superconducting circuit, while transferring excess energy to a spurious electromagnetic mode or TLS material defect. We show that the Floquet steady-state simulation, complemented by an electromagnetic simulation of the physical device, accurately predicts the observed transitions that do not involve TLS. Our results provide a comprehensive classification of these transitions and offer mitigation strategies through informed choices of drive frequency as well as improved circuit design.

The statistics of particles and extended excitations, such as loops and membranes, are fundamental to modern condensed matter physics, high-energy physics, and quantum information science, yet a comprehensive lattice-level framework for computing them remains elusive. In this work, we develop a universal microscopic method to determine the generalized statistics of Abelian excitations on lattices of arbitrary dimension and demonstrate it by deriving the statistics of particles, loops, and membranes in up to three spatial dimensions. Our approach constructs a sequence of local unitary operators whose many-body Berry phase encodes the desired statistical invariant. The required sequence is generated automatically from the Smith normal form of locality constraints and therefore needs no extra physical input. We prove that the resulting invariants are quantized, provide an algorithm that computes them efficiently, and show how they unify familiar braiding and fusion data of particles while also uncovering new self- and mutual statistics of loop and membrane excitations. We further demonstrate that each statistical invariant corresponds to an ’t Hooft anomaly of a generalized symmetry; we show that a nontrivial invariant both (i) obstructs gauging that symmetry and (ii) forbids any short-range-entangled (symmetry-preserving) ground state. This establishes a precise connection between microscopic lattice anomalies and many-body dynamics, providing a generalization of the Lieb-Schultz-Mattis theorem that constrains a wide class of quantum lattice systems.

Coulomb interactions among charge carriers that occupy an electronic flat band (FB) can give rise to captivating phenomena such as quantum criticality, Mott-Hubbard states, and unconventional superconductivity at different FB filling fractions. Consequently, the search for new FB materials with tunable charge carrier filling and strong interactions is a central research theme to broaden our fundamental understanding of strongly interacting quantum systems and to realize materials with novel functionalities. In this work, we present experimental evidence obtained from temperature-dependent scanning tunneling microscopy measurements for various strongly correlated states that appear in partially occupied kagome FBs of ${\mathrm{Co}}_{1-x}{\mathrm{Fe}}_x\mathrm{Sn}$ whose filling can be controlled by the Fe-doping level $x$. At elevated temperatures ($T\ge 16\mathrm{K}$), we find evidence for rotation symmetry breaking across a broad doping range $0.05<x<0.25$. Comparison with model calculations reveals that strong Coulomb interactions ($U>100\mathrm{meV}$) blend the states of two $3d$-orbital-derived FBs and impart a nematic order parameter. Introducing phase-sensitive lock-in measurements as a local scanning tunneling microscopy probe of incompressible states, we also find direct evidence for Hubbard bands in the partially filled kagome flat bands of samples with ideal Fe doping ($x=0.17$). Results from Hubbard model calculations suggest the presence of an orbital-selective Mott state in a half-filled kagome flat band. Doping-dependent measurements show that the orbital-selective Mott state descends into a correlated metal phase upon electron and hole doping, marked by a sudden collapse of the spectral gap. Our observations demonstrate that the electronic ground state of the kagome FBs sensitively depends on the complex interplay between geometric frustration, strong Coulomb repulsion, orbital degeneracy, and filling fraction at different temperatures. More broadly, our research establishes kagome lattice materials as a unique platform for novel quantum states that arise from strong electronic correlations in a topologically nontrivial FB.

We present a self-consistent many-body framework for computing phonon-limited electronic transport from first principles, incorporating both beyond-quasiparticle effects and vertex corrections. Using the recently developed first-principles $\mathrm{sc}G{D}_0$ method, we calculate spectral functions with nonperturbative effects such as broadening, satellites, and energy-dependent renormalization. We show that the $\mathrm{sc}G{D}_0$ spectral functions outperform one-shot $G_0{D}_0$ and cumulant approximations in model Hamiltonians and real materials, eliminating unphysical spectral kinks and correctly predicting the phonon emission continuum. Building on this, we introduce the self-consistent ladder formalism for transport, which captures vertex corrections due to electron-phonon interactions. This approach unifies and improves upon the two state-of-the-art approaches for first-principles phonon-limited transport: the bubble approximation and the Boltzmann transport equation. Moreover, as a charge-conserving approximation, it enables consistent calculations of the optical conductivity and dielectric function. We validate the developed method against numerically exact results for model Hamiltonians in the dilute polaronic limit and apply it to real materials. Our results show quantitative agreement with the experimental dc conductivities in intrinsic semiconductors Si and ZnO and the ${\mathrm{SrVO}}_3$ metal, as well as excellent agreement with the experimental THz optical and dielectric properties of Si and ZnO. This work unifies first-principles and many-body approaches for studying transport, opening new directions for applying many-body theory to materials with strong electron-phonon interactions.

We report measurements of phase-matched nonlinear x-ray and optical mixing from single-crystal silicon using subresonant 0.95 eV laser pulses and 9.5 keV hard x-ray pulses from the Linear Coherent Light Source free-electron laser. The mixing signal appears as energy and momentum sidebands to the elastic Bragg peak. It is proportional to the magnitude squared of the relevant temporal and spatial Fourier components of the optically induced microscopic charges and currents. We measure the first- and second-order sideband to the 220 Bragg peak and find that the efficiency is maximized when the applied field is along the reciprocal lattice vector. For an optical intensity of approximately ${10}^{12}\mathrm{W}/{\mathrm{cm}}^2$, we measure peak efficiencies of $3\times {10}^{-7}$ and $3\times {10}^{-10}$ for the first- and second-order sideband, respectively (relative to the elastic Bragg peak). The first-order sideband is consistent with induced microscopic currents along the applied electric field and an isotropic response. The second-order sideband depends nontrivially on the optical field orientation and is consistent with an anisotropic response originating from induced charges along the bonds with ${\mathrm{C}}_{3v}$ site symmetry. The results agree well with first-principles Floquet-Bloch calculations.

Twisted transition metal dichalcogenides are a new platform for realizing strongly correlated physics with high tunability. Recent transport experiments [A. Ghiotto et al., Nature (London) 597, 345 (2021)] have reported the bandwidth-driven evolution of a Mott insulator to a strange metal behavior via the tuning of a displacement field in twisted $\mathrm{WS}{\mathrm{e}}_2$ ($\mathrm{tWS}{\mathrm{e}}_2$) fixed at half filling. However, the nature of the correlated states and the related Mott physics involved in the whole process remain to be determined. Here, we unveil theoretically the evolution of the ground state of the half-filled moiré Hubbard model as applied to $\mathrm{tWS}{\mathrm{e}}_2$, transiting from a pseudogap state with Fermi arcs to a 120° Néel ordered Mott insulator, then to another pseudogap state with Fermi pockets, and eventually to a Fermi liquid via a Lifshitz transition. The pseudogap phases are definitely identified by the vanishing of quasiparticle weights over parts of the Fermi surface, with the remaining parts forming disconnected Fermi arcs or pockets with well-defined quasiparticles. We demonstrate that the Fermi arc or pocket results from the electronic band structure reconstruction driven by electron correlations, marked by the coexistence of the poles and zeros of the single-particle Green’s function. We ascribe the ground state of the strange metal featured by the linear-$T$ resistivity observed experimentally in ${\mathrm{tWSe}}_2$ to the second pseudogap state by further calculating the temperature dependence of resistivity. This work reveals the fundamental aspects of the Mottness in moiré system and will stimulate the direct probes of the underlying physics beyond transports via the angle-resolved photoemission spectroscopy and scanning tunneling microscopy.

Nanoscale defects such as nitrogen-vacancy (NV) centers can serve as sensitive and noninvasive probes of electromagnetic fields and fluctuations from materials, which in turn can be used to characterize these systems. Here we specifically discuss how NV centers can probe time-reversal symmetry breaking (TRSB) phenomena in low-dimensional electronic systems. We argue that the difference in relaxation rates ${\mathrm{\Gamma }}_{\pm \widehat{z}}$ of NV centers starting from $m=\pm 1$ spin states to the ground state with $m=0$ directly probes TRSB. The effect arises from the difference in the fluctuation spectrum of left- and right-polarized electromagnetic fields emanating from such materials. In the quantum Hall setting, the NV center experiences (nearly zero) large additional contribution to its relaxation due to the presence of the material when its magnetic dipole (anti)aligns with the external field. More generally, the difference in the relaxation rates is sensitive to the imaginary part of the wave-vector-dependent Hall conductivity. We argue that this can be used to determine the Hall viscosity, which can potentially distinguish candidate fractional quantum Hall states and be used to infer the pairing angular momentum in TRSB superconductors. We compute the average relaxation rate $[{\mathrm{\Gamma }}_{+\widehat{z}}+{\mathrm{\Gamma }}_{-\widehat{z}}]$ near thin film superconductors and find that it exhibits a Hebel-Slichter-like enhancement below $T_c$. The difference ${\mathrm{\Gamma }}_{+\widehat{z}}-{\mathrm{\Gamma }}_{-\widehat{z}}$ also inherits this peak but is only nonzero for $T<T_c$ and only if the superconductivity is chiral. We provide concrete estimates for observing this effect in stacked twisted bismuth strontium calcium copper oxide flakes.

${\mathrm{CeRh}}_2{\mathrm{As}}_2$ is rare among superconductors, in that the magnetic field tunes it between two distinct superconducting phases. Combined with a lack of local inversion symmetry and an upper critical field exceeding the Pauli paramagnetic limit, this excitingly suggests triplet multicomponent superconductivity. Preceding the superconducting onset, $f$-electron correlations cause long-range order, attributed both to local antiferromagnetism and itinerant (quadrupole) density waves. A magnetic field provides a significant perturbation of the $f$ electrons and may reveal the nature of the many-body correlations. Therefore, we report comprehensive magnetization and magnetotransport studies on microstructured devices in fields of up to 73 T. Applied along the $c$ axis, the field causes a low-temperature change of majority (hole) carrier density at ${\mu }_{0}H\approx 24\mathrm{T}$. By contrast, in-plane fields produce a cascade of phase transitions; the field-induced in-plane conductivity anisotropy and lack of accompanying magnetic features, plus the closed-dome nature of the overall phase boundary is consistent with a hierarchy of field-induced density-wave states.

The recent observation of superconductivity in the vicinity of Fermi surface reconstructed insulating or metallic states has established twisted bilayers of ${\mathrm{WSe}}_2$ as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries, and topology. In this work, we use a first-principles, material-specific theoretical treatment that is unbiased with respect to electronic instabilities to study the emergence of electronic ordering in twisted ${\mathrm{WSe}}_2$ driven by gate-screened Coulomb interactions. We construct exponentially localized moiré Wannier orbitals that faithfully capture the band structure and topology of the system, project the gate-screened Coulomb interaction onto them, and use unbiased functional renormalization group techniques to resolve the momentum and orbital structure of the leading instabilities and the relevant energy scales. We find an interplay between intervalley-coherent antiferromagnetic (IVC-AFM) order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near a displacement field and twist-angle-tunable van Hove singularity. Our microscopic approach establishes incommensurate IVC-AFM spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $\theta =5.08°$ twisted ${\mathrm{WSe}}_2$ and explains key aspects of recent experiments including the asymmetric density dependence of the spin ordering with respect to the van Hove line, the single- and double-peak structure of the DOS in the ordered (hole-doped) IVC-AFM phase, the emergence of superconductivity as the density is varied across the van Hove line, and the evolution of the displacement field-density phase diagram with twist angles between $3.7°\dots 5°$. We show that the interplay of electronic correlations and nontrivial quantum geometry in ${\mathrm{tWSe}}_2$ manifests in orbital-selective order parameters associated to the IVC-AFM and SC states that are detectable by local spectroscopy measurements.

We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section can algebraically be represented by a spinor. Defects in uniaxial, biaxial nematics, and cholesterics are represented by elements belonging to different Clifford algebras, suggesting that there are fundamental distinctions between topological defects in each of these phases. Our theory allows nematic defects to be interpreted as Majorana-like spinors, as defects and antidefects are topologically equivalent, while some cholesteric defects, such as screw dislocations, are better viewed as Weyl-like spinors of well-defined chirality. Defects can be described by a “defect bivector,” an algebraic element that quantifies the rototranslation associated with them. In cholesterics, fermionic defects of different types can combine to yield composite quasiparticles with either fermionic or bosonic nature. Under cylindrical confinement, these quasiparticles provide the way to understand the structure of screw dislocations. In the bulk, they may condensate to form topological phases, such as blue phases or skyrmion lattices. Our results provide a surprising link between liquid crystals, particle physics, and topological quantum matter.

This work rigorously establishes a universal lower bound $z\ge 2$ for the dynamical exponent in frustration-free quantum many-body systems whose ground states exhibit power-law decaying correlations. The derivation relies on the Gosset-Huang inequality, providing a unified framework applicable across various lattice structures and spatial dimensions, independent of specific boundary conditions. Remarkably, our result can be applied to prove bounds for dynamics of classical stochastic processes. Specifically, we utilize a well-established mapping from the time evolution of local Markov processes with detailed balance to that of frustration-free quantum Hamiltonians, known as Rokhsar-Kivelson Hamiltonians. This proves $z\ge 2$ for such Markov processes, which is an improvement over existing bounds. Beyond these applications, the quantum analysis of the $z\ge 2$ bound is further broadened to include systems exhibiting hidden correlations, which may not be evident from purely local operators.

Because of the large-period superlattices emerging in moiré two-dimensional (2D) materials, electronic states in such systems exhibit low energy flat bands that can be used to simulate strongly correlated physics in a highly tunable setup. While many investigations have thus far focused on moiré flat bands and emergent correlated electron physics in triangular, honeycomb, and quasi-one-dimensional lattices, tunable moiré realizations of square lattices subject to strong correlations remain elusive. Here we propose a feasible scheme to construct moiré square lattice systems by twisting two or more layers of 2D materials in a rectangular lattice by 90°. We demonstrate the concept with twisted $\mathrm{GeX}/\mathrm{SnX}$ ($\mathrm{X}=\mathrm{S}$, Se) moiré superlattices and calculate their electronic structures from first principles. We show that the lowest conduction flat band in these systems can be described by a square lattice Hubbard model with parameters which can be controlled by varying the choice of host materials, number of layers, and external electric fields. In particular, twisted double bilayer GeSe realizes a square lattice Hubbard model with strong frustration due to the next-nearest-neighbor hopping that could host unconventional superconductivity, in close analogy to the Hubbard model for copper-oxygen planes of cuprate high-temperature superconductors. The presented scheme uses 90° twisted 2D materials with rectangular unit cells as a promising platform for realizing the physical phenomena of square lattice Hubbard models, establishing a new route for studying its rich phase diagram of magnetism, charge order, and unconventional superconductivity in a highly tunable setting.

Premelting plays a key role across physics, chemistry, materials, and biology sciences but remains poorly understood at the atomic level due to surface characterization limitations. We report the discovery of an amorphous ice layer (AIL) preceding the quasiliquid layer during ice premelting, enabled by a machine learning framework integrating atomic force microscopy (AFM) with molecular dynamics simulations. This approach overcomes AFM’s depth and signal limitations, allowing for three-dimensional surface structure reconstruction from AFM images. It further enables structural exploration of premelting interfaces across a wide temperature range that are experimentally inaccessible. We identify the AIL present between 121 and 180 K displaying a disordered two-dimensional hydrogen-bond network with solidlike dynamics. Our findings refine the ice premelting phase diagram and offer new insights into the surface growth dynamic, dissolution, and interfacial chemical reactivity. Methodologically, this work establishes a novel framework for AFM-based 3D structural discovery, marking a significant leap in our ability to probe complex disordered interfaces with unprecedented precision and paving the way for future disciplinary research, including surface reconstruction, crystallization, ion solvation, and biomolecular recognition.

Two-dimensional electron systems (2DESs) have represented an ever-expanding frontier in condensed matter physics. Over the past two decades, this growth has primarily been propelled by the emergence of novel 2DESs, exemplified by graphene and other two-dimensional (2D) crystals, each exhibiting distinctive properties. In this study, we synthesize high-quality $\beta$-phase bismuth thin films on exfoliated hexagonal boron nitride (hBN) and establish that bismuth surface states form a high-mobility 2DES with strong spin-orbit coupling (SOC). The extreme two dimensionality of the 2DES is characterized by an out-of-plane to in-plane effective-mass-anisotropy lower bound exceeding ${10}^3$. We further demonstrate that the spin degeneracy of the hole pockets is completely lifted, providing unambiguous transport evidence that they originate from Rashba states induced by strong SOC in the bismuth thin film. Under magnetic fields up to 40 Tesla, electrostatic gating drives the carriers into the lowest Landau levels, revealing signatures of rotational symmetry breaking and electronic nematicity. These findings position the bismuth 2DES as a compelling platform for exploring topological quantum phenomena in systems with strong SOC and high carrier mobility.

Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice (SSL), offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these systems leads to the emergence of novel phases. We present the characterization of ${\mathrm{Er}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$, an SSL compound with ${\mathrm{Er}}^{3+}$ ions forming orthogonal dimers separated by nonmagnetic layers whose structure is invariant under the $P\overline{4}{2}_{1}m$ space group. Neutron scattering reveals an antiferromagnetic dimer structure at zero field, typical of Ising spins on that lattice and consistent with the anisotropic magnetization observed. However, magnetization measurements exhibit fractional plateaus at $1/4$ and $1/2$ of saturation, in contrast to the expected $1/3$ plateau of the SSL Ising model. By comparing the energy of candidate states with ground-state lower bounds we show that this behavior requires spatially anisotropic interactions, leading to an anisotropic Shastry-Sutherland Ising model symmetric under the $Cmm2$ space group. This anisotropy is consistent with the small orthorhombic distortion observed with single-crystal neutron diffraction. The other properties, including thermodynamics, which have been investigated theoretically using tensor networks, point to small residual interactions, potentially due to further couplings and quantum fluctuations. This study highlights ${\mathrm{Er}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$ as a promising platform for investigating exotic magnetic phenomena.

Twisted bilayer ${\mathrm{MoTe}}_2$ (${\mathrm{tMoTe}}_2$) is an emergent platform for exploring exotic quantum phases driven by the interplay between nontrivial band topology and strong electron correlations. Direct experimental access to its momentum-resolved electronic structure is essential for uncovering the microscopic origins of the correlated topological phases therein. Here, we report angle-resolved photoemission spectroscopy measurements of ${\mathrm{tMoTe}}_2$, revealing pronounced twist-angle-dependent band reconstruction shaped by orbital character, interlayer coupling, and moiré potential modulation. Density functional theory captures the qualitative evolution, yet underestimates key energy scales across twist angles, highlighting the importance of electronic correlations. Notably, the hole effective mass at the $K$ point exhibits a nonmonotonic dependence on twist angle, peaking near 2°, consistent with band flattening at the magic angle predicted by continuum models. Via electrostatic gating and surface dosing, we further visualize the evolution of electronic structure versus doping, enabling direct observation of the conduction band minimum and confirm ${\mathrm{tMoTe}}_2$ as a direct band gap semiconductor. These results establish a spectroscopic foundation for modeling and engineering emergent quantum phases in this moiré platform.

By combining ab initio downfolding with cluster dynamical mean-field theory, we study the degree of correlations in monolayer, bilayer, and bulk breathing-mode kagome van der Waals materials ${\mathrm{Nb}}_3(\mathrm{F},\mathrm{Cl},\mathrm{Br},\mathrm{I}{)}_8$. Our new material-specific many-body model library shows that in low-temperature bulk structures the Coulomb correlation strength steadily increases from I to Br, Cl, and F, allowing us to identify ${\mathrm{Nb}}_3{\mathrm{I}}_8$ as a weakly correlated insulator whose gap is only mildly affected by the local Coulomb interaction. ${\mathrm{Nb}}_3{\mathrm{Br}}_8$ and ${\mathrm{Nb}}_3{\mathrm{Cl}}_8$ are strongly correlated insulators, whose gaps are significantly influenced by Coulomb-induced vertex corrections. ${\mathrm{Nb}}_3{\mathrm{F}}_8$ is a prototypical bulk Mott insulator whose gap is initially opened by strong correlation effects. Angle-resolved photoemission spectroscopy measurements comparing ${\mathrm{Nb}}_3{\mathrm{Br}}_8$ and ${\mathrm{Nb}}_3{\mathrm{I}}_8$ allow us to experimentally confirm these findings by revealing spectroscopic footprints of the degree of correlation. Our calculations further uncover how the thickness and the stacking affect the degree of correlations and predict that the entire material family can be tuned into correlated charge transfer or Mott-insulating phases upon electron or hole doping. Our magnetic property analysis based on our model parameter library additionally confirms that interlayer magnetic interactions likely drive the lattice phase transition to the low-temperature structures. The accompanying bilayer hybridization through interlayer dimerization yields magnetic singlet-like ground states in the Cl, Br, and I compounds. We further prove that all low-temperature compounds are dynamically stable and that electron-phonon coupling to the low-energy subspace is suppressed. Our findings establish ${\mathrm{Nb}}_3{\mathrm{X}}_8$ as a robust, versatile, and tunable class for van der Waals-based Coulomb and Mott engineering with a rich phase diagram and allow us to speculate on the symmetry-breaking effects necessary for the recently observed Josephson diode effect in ${\mathrm{NbSe}}_2/{\mathrm{Nb}}_3{\mathrm{Br}}_8/{\mathrm{NbSe}}_2$ heterostructures.

Understanding how the vibrational and thermal properties of solids are influenced by atomistic structural disorder is of fundamental scientific interest and paramount to designing materials for next-generation energy technologies. While several studies indicate that structural disorder strongly influences the thermal conductivity, the fundamental physics governing the disorder-conductivity relation remains elusive. Here we show that order-of-magnitude, disorder-induced variations of conductivity in network solids can be predicted from a “bond-network” entropy, an atomistic structural descriptor that quantifies heterogeneity in the topology of the atomic-bond network. We employ the Wigner formulation of thermal transport to demonstrate the existence of a relation between the bond-network entropy and observables such as smoothness of the vibrational density of states and macroscopic conductivity. We also show that the smoothing of the vibrational density of states encodes information about the thermal resistance induced by disorder and can be directly related to phenomenological models for phonon-disorder scattering based on the semiclassical Peierls-Boltzmann equation. Our findings rationalize the conductivity variations of disordered carbon polymorphs ranging from nanoporous electrodes to defective graphite used as a moderator in nuclear reactors.