arXiv subjects

Matthew S. Foster

Publications and source records attributed to Matthew S. Foster.

At least 19 recordsLinked to original sources

arXiv2026

Fractal Confinement and Magnetic Self-sabotage of Current Flow: Electrons Near the Metal-insulator Crossover in a 2D $\delta$-layer

We study low-$T$ transport and itinerant magnetism in 2D $\delta$-doped semiconductors. Large-scale Hartree-Fock calculations with random hoppings and repulsion $U_0$ reveal two transport regimes near a critical density. The conductivity $\sigma(T)$ initially increases as $T$ drops below $U_0 / 10$. However, at $T \sim U_0/100$, a tiny density of magnetic moments forms, driving an insulating downturn. Fractal wavefunctions locally amplify magnetic interactions, initially concentrating currents into branched filaments, but ultimately choking them off via dynamic SU(2) symmetry breaking.

cond-mat.dis-nn↗

arXiv2026

Disparate Quantum Corrections to Conduction in Carbon Nanotube Bundles

Quantum interference effects such as weak localization (WL) and universal conductance fluctuations (UCF) normally yield consistent electronic phase-coherence lengths in homogeneous conductors. Here we show that in individual carbon nanotube bundles exfoliated from highly conductive solution-spun fibers, different probes, including the field scales and magnitudes of WL and UCF and nonlocal magnetoconductance, lead to strikingly disparate estimates of coherence lengths. WL magnetoconductance measured in a perpendicular magnetic field yields a phase-coherence length of approximately 50 nm. In contrast, UCF amplitudes are comparable to e squared over h even for an 8 micrometer long segment, and nonlocal magnetoconductance persists across a 4 micrometer separation of electrodes, revealing phase-coherent transport over micrometer length scales within a single bundle. The coexistence of short- and long-range coherence implies that locally diffusive electrons remain partially phase-correlated among nanotubes within the same bundle. These findings challenge the conventional single-scale picture of mesoscopic coherence and establish carbon nanotube bundles as a model platform for emergent, network-level quantum transport.

cond-mat.mes-hall↗

arXiv2025

Twisted Trilayer Graphene, Quasiperiodic Superconductor

Twisted multilayer moir\'e materials are generically quasiperiodic on the moir\'e scale due to the interference of different misaligned moir\'e periodicities. Spatial inhomogeneities such as these can be detrimental to superconductivity; nonetheless, superconductivity has been observed in quasiperiodic twisted trilayer graphene (TTG). Here, we systematically study the superconducting properties of TTG. We reveal that an interplay between quasiperiodicity and topology drives TTG into a critical regime, enabling it to host superconductivity with rigid phase stiffness for a wide range of twist angles, rather than at a fine-tuned value. The criticality in the normal state is due to the Dirac fermions coupled by quasiperiodic tunneling simulating 3D topological superconductor surface states. This critical-metal regime is marked by multifractal wave functions across the spectrum and scale-invariant transport reminiscent of the integer quantum Hall plateau transition. We demonstrate this with large-scale wave function and Kubo conductivity calculations. These observations lead to a clear experimental implication: stronger interlayer coupling in TTG further stabilizes both the criticality and superconductivity, allowing superconductivity to be seen across a wider range of angles with experimentally accessible pressures.

cond-mat.mes-hall↗

arXiv2025

Topological surface-state destruction via trivializing proximity effect: Lattice localization despite continuum criticality

In a significant conceptual revision to the tenfold classification scheme for topological insulators and superconductors, it was recently demonstrated that most three-dimensional (3D) classes are simultaneously "localizable" in two distinct, but intricately connected ways: (1) There is no obstruction to Wannier localization of all bulk eigenstates, and (2) Almost all surface states can be Anderson localized by arbitrarily weak symmetry-preserving quenched disorder. Here we consider the localizable class CI in 3D, and numerically investigate the stability of surface states. We demonstrate that surface states of a bulk class-CI topological lattice model are fragile in that they can be Anderson localized by the combination of weak quenched randomness and hybridization with an additional trivial 2D band (a trivializing proximity effect, TPE). With the TPE, stronger disorder is more destructive to the surface states of the bulk lattice model. By contrast, without additional bands the surface states remain extended, exhibiting robust spectrum-wide quantum criticality. We also investigate the fragility of surface states in effective 2D class-CI continuum Dirac theories, including the chiral limit of the Bistritzer-MacDonald model for twisted bilayer graphene. Although the continuum models exhibit signs of Anderson localization near gap edges for weak disorder, stronger disorder instead appears to heal the surface, restoring criticality whilst filling in spectral energy gaps. Our results provide further evidence that effective continuum field theories fail to capture key aspects of surface-state physics in localizable topological phases.

cond-mat.mes-hall↗

arXiv2025

Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. This is the most general problem of interacting fermions with weak fermion parity measurements. Without interactions, it is known that a noninteracting MIPT separates the area-law phase from a log-enhanced "thermal metal" phase at sufficiently weak monitoring. We conjecture that the MIPT with interactions is the same as the noninteracting one in this case; the volume-law phase arises through the dangerously irrelevant mass. The physical picture is that the mass represents a local Fermi's golden rule interparticle scattering rate density that is tantamount to the entangling rate density. The latter must vanish continuously at a continuous MIPT. On the other hand, the field theory capturing the MIPT for monitored fermions with additional continuous symmetries is expected to be different, because the interactions introduce additional terms associated to conserved Noether currents. We propose numerical tests of our conjecture. In addition, we analytically identify a candidate noninteracting critical point representing the MIPT, using a controlled $\epsilon$-expansion.

cond-mat.stat-mech↗

arXiv2025

Magnon scattering and transduction in Coulomb-coupled quantum Hall ferromagnets

The magnetization field of a quantum Hall ferromagnet (QHFM) can host a variety of spin textures, including skyrmions and magnons. When projected into the lowest Landau level with $\nu = 1$ filling, the topological (Pontryagin) charge density of the magnetization field is proportional to the electric charge density, allowing for long-range spin-spin interactions. Inspired by recent experimental developments that enable all-electrical generation and detection of magnons, in this work we theoretically demonstrate two phenomena that can occur due to Coulomb interactions that are unique to QHFMs: magnons can scatter off of point charges at a distance, and skyrmions can act as transmitters and receivers for magnons to be transduced between separate layers of a bilayer QHFM. The latter Coulomb-mediated spin drag effect occurs at arbitrary distance and could facilitate long-range magnonics, such as detection of spin waves for future experiments in 2D materials.

cond-mat.mes-hall↗

arXiv2025

Quantum Transport in Ultrahigh-Conductivity Carbon Nanotube Fibers

We investigate quantum transport in aligned carbon nanotube (CNT) fibers fabricated via solution spinning, focusing on the roles of structural dimensionality and quantum interference effects. The fibers exhibit metallic behavior at high temperatures, with conductivity increasing monotonically as the temperature decreases from room temperature to approximately 36 K. Below this temperature, the conductivity gradually decreases with further cooling, signaling the onset of quantum conductance corrections associated with localization effects. Magnetoconductance measurements in both parallel and perpendicular magnetic fields exhibit pronounced positive corrections at low temperatures, consistent with weak localization (WL). To determine the effective dimensionality of electron transport, we analyzed the data using WL models in 1D, 2D, and 3D geometries. We found that while the 2D model can reproduce the field dependence, it lacks physical meaning in the context of our fiber architecture and requires an unphysical scaling factor to match the experimental magnitude. By contrast, we developed a hybrid 3D+1D WL framework that quantitatively captures both the field and temperature dependences using realistic coherence lengths and a temperature-dependent crossover parameter. Although this combined model also employs a scaling factor for magnitude correction, it yields a satisfactory fit, reflecting the hierarchical structure of CNT fibers in which transport occurs through quasi-1D bundles embedded in a 3D network. Our results establish a physically grounded model of phase-coherent transport in macroscopic CNT assemblies, providing insights into enhancing conductivity for flexible, lightweight power transmission applications.

cond-mat.mes-hall↗

arXiv2024

Field theory of monitored, interacting fermion dynamics with charge conservation

Measurement-induced phase transitions (MIPTs) in monitored quantum dynamics are non-equilibrium phase transitions between quantum-chaotic (volume-law entangled) and entanglement-suppressed, area-law phases. We reveal how monitored dynamics are situated within the framework of general far-from-equilibrium, quantum condensed-matter physics. Measurement-induced heating effects scramble the distribution function in generic (interacting) monitored fermion systems, which enables a simplified symmetry-based description of the dynamics. We demonstrate the equivalence of the Keldysh technique with the conventional Statistical-Mechanics Model for circuits, resulting from a doubled Hilbert-space (Choi-Jamio{\l}kowski) mapping. We illustrate this using the monitored dynamics of interacting fermions with a conserved charge, deriving a unified effective field theory that captures all phases and phase transitions. The non-interacting counterpart in 1D space only has an area-law phase, with no MIPT. This was explained via an effective non-linear sigma model replica field theory possessing a very large symmetry. We show that other phases and phase transitions emerge when the replica symmetry is reduced by interactions. The reduced symmetry combines a replica permutation symmetry and charge-conservation within each replica. The former and its spontaneous breaking govern the MIPT, which can be recognized via a separatrix in the renormalization group flow. The replica-resolved charge conservation dictates the ``charge-sharpening" transition between two kinds of dynamics, where the global charge information is either hidden or reconstructible from the measurements. The field theory explains why the charge-sharpening transition should occur only in the volume-law phase. Our framework provides a template for other classes of MIPTs and situates these within the arena of non-equilibrium condensed matter physics.

cond-mat.stat-mech↗

arXiv2024

Suppression of Shot Noise in a Dirty Marginal Fermi Liquid

We study shot noise in a two-dimensional, disordered marginal Fermi liquid (MFL) driven out of equilibrium. We consider electrons with Planckian dissipation on the Fermi surface coupled to quantum-critical bosons in the presence of disorder. In the non-interacting and strong electron-boson drag limits, MFL effects disappear and our theory reproduces known results. For the case where the bosons remain in equilibrium, inelastic scattering strongly suppresses the noise by dissipating the injected energy. Interestingly, we find that MFL effects do play a role in this regime, and give a weak enhancement on top of the otherwise strong suppression. Our results suggest that shot noise can be strongly suppressed in quantum-critical systems, and this scenario may be relevant to recent measurements in a heavy-fermion strange metal.

cond-mat.str-el↗

arXiv2024

Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene

Multilayer moir\'e materials can exhibit topological electronic features yet are inherently quasiperiodic -- leading to wave function interference whose Anderson-localizing tendency can be mitigated by topology. We consider a quasiperiodic variant of the chiral Bistritzer-MacDonald model for twisted bilayer graphene with two incommensurate moir\'e potentials that serves as a toy model for twisted trilayer. We observe "filaments" linking magic angles with enhanced density of states and fractal wave functions that evade localization; states away from the filaments mimic fractal surface states of dirty topological superconductors. We demonstrate that topological quasiperiodicity can broadly enhance superconductivity without magic-angle fine-tuning.

cond-mat.mes-hall↗

arXiv2024

Fragility of surface states in non-Wigner Dyson topological insulators

Topological insulators and superconductors support extended surface states protected against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes A, AI, and AII, a band of extended surface states is continuously connected to a likewise extended set of bulk states forming a ``bridge'' between different surfaces via the mechanism of spectral flow. In this work we show that this mechanism is absent in the majority of non-Wigner-Dyson topological superconductors and chiral topological insulators. In these systems, there is precisely one point with granted extended states, the center of the band, $E=0$. Away from it, states are spatially localized, or can be made so by the addition of spatially local potentials. Considering the three-dimensional insulator in class AIII and winding number $ν=1$ as a paradigmatic case study, we discuss the physical principles behind this phenomenon, and its methodological and applied consequences. In particular, we show that low-energy Dirac approximations in the description of surface states can be treacherous in that they tend to conceal the localizability phenomenon. We also identify markers defined in terms of Berry curvature as measures for the degree of state localization in lattice models, and back our analytical predictions by extensive numerical simulations. A main conclusion of this work is that the surface phenomenology of non-Wigner-Dyson topological insulators is a lot richer than that of their Wigner-Dyson siblings, extreme limits being spectrum-wide quantum critical delocalization of all states vs. full localization except at the $E=0$ critical point. As part of our study we identify possible experimental signatures distinguishing between these different alternatives in transport or tunnel spectroscopy.

cond-mat.mes-hall↗

arXiv2023

Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid

We study superconductivity in a two-dimensional, disordered marginal Fermi liquid. At the semiclassical level, the transition temperature $T_c$ is strongly suppressed because marginal Fermi liquid effects destroy well-defined quasiparticles. However, we show that interference between quantum-critical collective modes must be included, and these enhance $T_c$, violating Anderson's theorem. Our results suggest that phase coherence in a disordered, quantum-critical system can survive and manifest in the form of collective excitations, despite the absence of coherent quasiparticles.

cond-mat.supr-con↗

arXiv2023

Magnetic instability and spin-glass order beyond the Anderson-Mott transition in interacting power-law random banded matrix fermions

In the presence of quenched disorder, the interplay between local magnetic-moment formation and Anderson localization for electrons at a zero-temperature, metal-insulator transition (MIT) remains a long unresolved problem. Here, we study the emergence of these phenomena in a power-law random banded matrix model of spin-1/2 fermions with repulsive Hubbard interactions. Focusing on the regime of weak interactions, we perform both analytical field theory and numerical self-consistent Hartree-Fock calculations. We show that interference-mediated effects strongly enhance the density of states and magnetic fluctuations upon approaching the MIT from the metallic side. These are consistent with results due to Finkel'stein obtained four decades ago. Our numerics further show that local moments nucleate from typical states as we cross the MIT, with a density that grows continuously into the insulating phase. We identify spin-glass order in the insulator by computing the overlap distribution between converged Hartree-Fock mean-field moment profiles. Our results indicate that itinerant interference effects can morph smoothly into moment formation and magnetic frustration within a single model, revealing a common origin for these disparate phenomena.

cond-mat.dis-nn↗

arXiv2022

Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa$_4$

Magnetic topological semimetals (TSMs) allow for an effective control of the topological electronic states by tuning the spin configuration, and therefore are promising materials for next-generation electronic and spintronic applications. Of magnetic TSMs, Weyl nodal-line (NL) semimetals likely have the most tunability, and yet they are the least experimentally studied so far due to the scarcity of material candidates. Here, using a combination of angle-resolved photoemission spectroscopy and quantum oscillation measurements, together with density functional theory calculations, we identify the square-net compound EuGa4 as a new magnetic Weyl nodal ring (NR) semimetal, in which the line nodes form closed rings in the vicinity of the Fermi level. Remarkably, the Weyl NR states show distinct Landau quantization with clear spin splitting upon application of a magnetic field. At 2 K in a field of 14 T, the transverse magnetoresistance of EuGa4 exceeds 200,000%, which is more than two orders of magnitude larger than that of other known magnetic TSMs. High field magnetoresistance measurements indicate no saturation up to 40 T. Our theoretical model indicates that the nonsaturating MR naturally arises as a consequence of the Weyl NR state. Our work thus point to the realization of Weyl NR states in square-net magnetic materials, and opens new avenues for the design of magnetic TSMs with very large magnetoresistance.

cond-mat.mtrl-sci↗

arXiv2022

Quantum Interference of Hydrodynamic Modes in a Dirty Marginal Fermi Liquid

We study the electrical transport of a two-dimensional non-Fermi liquid with disorder, and we determine the first quantum correction to the semiclassical dc conductivity due to quantum interference. We consider a system with $N$ flavors of fermions coupled to SU($N$) critical matrix bosons. Motivated by the SYK model, we employ the bilocal field formalism and derive a set of finite-temperature saddle-point equations governing the fermionic and bosonic self-energies in the large-$N$ limit. Interestingly, disorder smearing induces a marginal Fermi liquid (MFL) self-energy for the fermions. We next consider fluctuations around the saddle points and derive a MFL-Finkel'stein nonlinear sigma model. We find that the Altshuler-Aronov quantum conductance correction gives linear-$T$ resistivity that can dominate over the Drude result at low temperature. The strong temperature dependence of the quantum correction arises due to rapid relaxation of the mediating quantum-critical bosons. We verify that our calculations explicitly satisfy the Ward identity at the semiclassical and quantum levels. Our results establish that quantum interference persists in two-particle hydrodynamic modes, even when quasiparticles are subject to strong (Planckian) dissipation.

cond-mat.str-el↗

arXiv2022

Enhanced Amplitude for Superconductivity due to Spectrum-wide Wave Function Criticality in Quasiperiodic and Power-law Random Hopping Models

We study the interplay of superconductivity and a wide spectrum of critical (multifractal) wave functions ("spectrum-wide quantum criticality," SWQC) in the one-dimensional Aubry-André and power-law random-banded matrix models with attractive interactions, using self-consistent BCS theory. We find that SWQC survives the incorporation of attractive interactions at the Anderson localization transition, while the pairing amplitude is maximized near this transition in both models. Our results suggest that SWQC, recently discovered in two-dimensional topological surface-state and nodal superconductor models, can robustly enhance superconductivity.

cond-mat.supr-con↗

arXiv2022

Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities

The spatial modulation of the Fermi velocity for gapless Dirac electrons in quantum materials is mathematically equivalent to the problem of massless fermions on a certain class of curved spacetime manifolds. We study null geodesic lensing through these manifolds, which are dominated by curvature singularities, such as nematic singularity walls (where the Dirac cone flattens along one direction). Null geodesics lens across these walls, but do so by perfectly collimating to a local transit angle. Nevertheless, nematic walls can trap null geodesics into stable or metastable orbits characterized by repeated transits. We speculate about the role of induced one-dimensionality for such bound orbits in 2D dirty d-wave superconductivity.

cond-mat.mes-hall↗

arXiv2022

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behaviour on the two sides of a certain dynamical critical point. Dynamical phase transitions are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions, $ϕ^4$ quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.

cond-mat.stat-mech↗