arXiv subjects

Jacob Cook

Publications and source records attributed to Jacob Cook.

17 recordsLinked to original sources

arXiv2025

Observation of Anomalous Hall Effect in Bulk Single Crystals of n-type Cr-doped Sb$_{2}$Te$_{3}$ Magnetic Topological Insulator

The exploration of topological Dirac surface states is significant in the realms of condensed matter physics and future technological innovations. Among the materials garnering attention is Sb$_{2}$Te$_{3}$, a compound that theoretically exhibits topological insulating properties. However, its inherent p-type nature prevents the direct experimental verification of its Dirac surface state due to the Fermi level alignment with the valence band. In this study, by doping Cr atoms into Sb$_{2}$Te$_{3}$, n-type behavior is observed in the Hall resistance measurements. Remarkably, the Cr-doped Sb$_{2}$Te$_{3}$ not only shows ferromagnetism with a high transition temperature of approximately 170 K but also exhibits an anomalous Hall effect (AHE). The Cr doping also allows for a controlled method for Fermi level tuning into the band gap. These properties spotlight its potential as an n-type magnetic topological insulator (MTI) as well as a material candidate for the quantum anomalous Hall effect (QAHE), opening new avenues for applications in spintronics and quantum devices.

cond-mat.mtrl-sci↗

arXiv2025

Programmable phase selection between altermagnetic and non-centrosymmetric polymorphs of MnTe on InP via molecular beam epitaxy

Phase selecting nearly degenerate crystalline polymorphs during epitaxial growth can be challenging yet is critical to targeting physical properties for specific applications. Here, we establish how phase selectivity of altermagnetic and non-centrosymmetric polymorphs of MnTe with high structural quality and phase purity can be programmed by subtle changes to the surface of lattice-matched InP substrates in molecular beam epitaxial (MBE) growth. Bulk altermagnetic MnTe is thermodynamically stable in the hexagonal NiAs-structure and is synthesized here on the (111)A surface (In-terminated) of InP, while the non-centrosymmetric, cubic ZnS-structure with wide band gap (> 3eV) is stabilized on the (111)B surface (P-terminated). Here we use electron microscopy, photoemission spectroscopy, and reflection high-energy electron diffraction, which together indicate that the phase selection is triggered at the interface and proceeds along the growing surface. First principles calculations suggest that interfacial termination and strain have a significant effect on the interfacial energy; stabilizing the NiAs polymorph on the In-terminated surface and the ZnS structure on the P-terminated surface. Selectively grown, high-quality films of MnTe polymorphs are key platforms that will enable our understanding of the novel properties of these materials, thereby facilitating their use in new applications ranging from spintronics to microelectronic devices.

cond-mat.mtrl-sci↗

arXiv2024

Emergent Spin Fluctuation and Structural Metastability in Self-Intercalated Cr$_{1+x}$Te$_2$ Compounds

Intercalated van der Waals (vdW) magnetic materials host unique magnetic properties due to the interplay of competing interlayer and intralayer exchange couplings, which depend on the intercalant concentration within the van der Waals gaps. Magnetic vdW compound chromium telluride, Cr$_{1+x}$Te$_2$, has demonstrated rich magnetic phases at various Cr concentrations, such as the coexistence of ferromagnetic and antiferromagnetic phases in Cr$_{1.25}$Te$_2$ (equivalently, Cr$_{5}$Te$_8$). The compound is induced by intercalating 0.25 Cr atom per unit cell within the van der Waals gaps of CrTe$_2$. In this work, we report a notably increased Curie Temperature and an emergent in-plane spin fluctuation by slightly reducing the concentration of Cr intercalants in Cr$_{1.25}$Te$_2$. Moreover, the intercalated Cr atoms form a metastable 2$\times$2 supercell structure that can be manipulated by electron beam irradiation. This work offers a promising approach to tuning magnetic and structural properties by adjusting the concentration of intercalated magnetic atoms.

cond-mat.mtrl-sci↗

arXiv2023

Tunable High Spin Chern-Number Insulator Phases in Strained Sb Monolayer

High spin Chern-number insulators (HSCI) have emerged as a novel 2D topological phase of condensed matter that is beyond the classification of topological quantum chemistry. In this work, we report the observation of a semimetallic Sb monolayer carrying the same band topology as HSCI with a spin Chern number equal to 2. Our calculations further indicate a moderate lattice strain can make Sb monolayer an insulator or a semimetal with a tunable spin Chern number from 0 to 3. The results suggest strained Sb monolayers as a promising platform for exploring exotic properties of the HSCI topological matter.

cond-mat.mtrl-sci↗

arXiv2023

Observation of 2D Weyl Fermion States in Epitaxial Bismuthene

A two-dimensional (2D) Weyl semimetal featuring a spin-polarized linear band dispersion and a nodal Fermi surface is a new topological phase of matter. It is a solid-state realization of Weyl fermions in an intrinsic 2D system. The nontrivial topology of 2D Weyl cones guarantees the existence of a new form of topologically protected boundary states, Fermi string edge states. In this work, we report the realization of a 2D Weyl semimetal in monolayer-thick epitaxial bismuthene grown on SnS(Se) substrate. The intrinsic band gap of bismuthene is eliminated by the space-inversion-symmetry-breaking substrate perturbations, resulting in a gapless spin-polarized Weyl band dispersion. The linear dispersion and spin polarization of the Weyl fermion states are observed in our spin and angle-resolved photoemission measurements. In addition, the scanning tunneling microscopy/spectroscopy reveals a pronounced local density of states at the edge, suggesting the existence of Fermi string edge states. These results open the door for the experimental exploration of the exotic properties of Weyl fermion states in reduced dimensions.

cond-mat.mtrl-sci↗

arXiv2022

Observation of Gapped Topological Surface States and Isolated Surface Resonances in PdTe$_2$ Ultrathin Films

The superconductor PdTe$_2$ is known to host bulk Dirac bands and topological surface states. The coexistence of superconductivity and topological surface states makes PdTe$_2$ a promising platform for exploring topological superconductivity and Majorana bound states. In this work, we report the layer-by-layer molecular beam epitaxy growth and spectroscopic characterization of high quality PdTe$_2$ films with thickness down to 3 monolayers (ML). In the 3 ML PdTe$_2$ film, we observed spin-polarized surface resonance states, which are isolated from the bulk bands due to the quantum size effects. In addition, the hybridization of surface states on opposite faces leads to a thickness-dependent gap in the topological surface Dirac bands. Our photoemission results show clearly that the size of the hybridization gap increases as the film thickness is reduced. The success in growing high quality PdTe$_2$ films by state-of-art molecular beam epitaxy technique and the observation of surface resonances and gaped topological surface states sheds light on the applications of PdTe$_2$ quantum films in spintronics and topological computation.

cond-mat.mes-hall↗

arXiv2022

Moir\'e Modulated Lattice Strain and Thickness-Dependent Lattice Expansion in Epitaxial Ultrathin Films of PdTe$_2$

We report the epitaxial growth of PdTe$_2$ ultrathin films on topological insulator Bi$_2$Se$_3$. A prominent Moir\'e pattern was observed in STM measurements. The Moir\'e periodicity increases as film thickness decreases, indicating a lattice expansion of epitaxial PdTe$_2$ thin films with lower thicknesses. In addition, our simulations based on Moir\'e Metrology reveal uniaxial lattice strains at the edge of PdTe$_2$ domains, and anisotropic strain distributions throughout the Moir\'e supercell with a net change in lattice strain up to ~2.9%. Our DFT calculations show that this strain effect leads to a narrowing of the band gap at $\Gamma$ point near the Fermi level. Under a strain of ~2.8%, the band gap at $\Gamma$ closes completely. Further increasing the lattice strain makes the band gap reopen and the order of conduction band and valence bands inverted in energy. The results offer a proof of concept for constructing quantum grids of topological materials under the modulation of Moir\'e potentials.

cond-mat.mes-hall↗

arXiv2022

Multi-layered atomic relaxation in van der Waals heterostructures

When two-dimensional van der Waals materials are stacked to build heterostructures, moir\'e patterns emerge from twisted interfaces or from mismatch in lattice constant of individual layers. Relaxation of the atomic positions is a direct, generic consequence of the moir\'e pattern, with many implications for the physical properties. Moir\'e driven atomic relaxation may be naively thought to be restricted to the interfacial layers and thus irrelevant for multi-layered heterostructures. However, we provide experimental evidence for the importance of the three dimensional nature of the relaxation in two types of van der Waals heterostructures: First, in multi-layer graphene twisted on graphite at small twist angles ($\theta\approx0.14^\circ$) we observe propagation of relaxation domains even beyond 18 graphene layers. Second, we show how for multi-layer PdTe$_2$ on Bi$_2$Se$_3$ the moir\'e lattice constant depends on the number of PdTe$_2$ layers. Motivated by the experimental findings, we developed a continuum approach to model multi-layered relaxation processes based on the generalized stacking fault energy functional given by ab-initio simulations. Leveraging the continuum property of the approach enables us to access large scale regimes and achieve agreement with our experimental data for both systems. Furthermore it is well known that the electronic structure of graphene sensitively depends on local lattice deformations. Therefore we study the impact of multi-layered relaxation on the local density of states of the twisted graphitic system. We identify measurable implications for the system, experimentally accessible by scanning tunneling microscopy. Our multi-layered relaxation approach is not restricted to the discussed systems, and can be used to uncover the impact of an interfacial defect on various layered systems of interest.

cond-mat.mes-hall↗

arXiv2021

Thermodynamic constraints on the assembly and diversity of microbial ecosystems are different near to and far from equilibrium

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. Microbial communities are a natural system to decipher this mechanistic basis because their interactions in the form of substrate consumption, metabolite production, and cross-feeding can be described explicitly in thermodynamic terms. Previous work has considered how thermodynamic constraints impact competition between pairs of species, but restrained from analysing how this manifests in complex dynamical systems. To address this gap, we develop a thermodynamic microbial community model with fully reversible reaction kinetics, which allows direct consideration of free-energy dissipation. This also allows species to interact via products rather than just substrates, increasing the dynamical complexity, and allowing a more nuanced classification of interaction types to emerge. Using this model, we find that community diversity increases with substrate lability, because greater free-energy availability allows for faster generation of niches. Thus, more niches are generated in the time frame of community establishment, leading to higher final species diversity. We also find that allowing species to make use of near-to-equilibrium reactions increases diversity in a low free-energy regime. In such a regime, two new thermodynamic interaction types that we identify here reach comparable strengths to the conventional (competition and facilitation) types, emphasising the key role that thermodynamics plays in community dynamics. Our results suggest that accounting for realistic thermodynamic constraints is vital for understanding the dynamics of real-world microbial communities.

q-bio.PE↗

arXiv2021

Observation of Unpinned Two-Dimensional Dirac States in Antimony Single Layers with Phosphorene Structure

The discovery of graphene has stimulated enormous interest in two-dimensional (2D) electron gas with linear band structure. 2D Dirac materials possess many intriguing physical properties such as high carrier mobility and zero-energy Landau level thanks to the relativistic dispersion and chiral spin/pseudospin texture. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at $\overline{\Gamma}$ in topological insulators Bi$_2$Se(Te)$_3$ and Dirac cones at $K$ and $K'$ in graphene. In this work, we report the realization of 2D Dirac states at generic $k$-points in antimony atomic layers with phosphorene structure ($i.e.$ $\alpha$-antimonene). The unpinned nature enables versatile ways to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points exhibit intrinsically anisotropic behaviors due to the reduced symmetry of generic momentum points. These properties make the $\alpha$-antimonene films a promising platform for exploring interesting physics in unpinned 2D Dirac fermions that are distinct from the conventional Dirac states in graphene.

cond-mat.mes-hall↗

arXiv2021

Giant Topological Hall Effect in van der Waals Heterostructures of CrTe2/Bi2Te3

Discoveries of interfacial topological Hall effect (THE) provide an ideal platform for exploring physics arising from the interplay between topology and magnetism. The interfacial topological Hall effect is closely related to the Dzyaloshinskii-Moriya interaction (DMI) at interface and topological spin textures. However, it is difficult to achieve a sizable THE in heterostructures due to the stringent constraints on the constituents of THE heterostructures such as strong spin-orbit coupling (SOC). Here we report the observation of a giant THE signal of 1.39 $\mu\Omega\cdot$cm in the van der Waals heterostructures of CrTe2/Bi2Te3 fabricated by molecular beam epitaxy, a prototype of two-dimensional (2D) ferromagnet (FM)/topological insulator (TI). This large magnitude of THE is attributed to an optimized combination of 2D ferromagnetism in CrTe2, strong SOC in Bi2Te3, and an atomically sharp interface. Our work reveals CrTe2/Bi2Te3 as a convenient platform for achieving large interfacial THE in hybrid systems, which could be utilized to develop quantum science and high-density information storage.

cond-mat.mes-hall↗

arXiv2021

Dirac Fermion Cloning, Moir$\bf{\'e}$ Flat Bands and Magic Lattice Constants in Epitaxial Monolayer Graphene

Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two-dimensional material, enhance electron correlations, and give rise to novel condensed-matter phases such as superconductors, Mott insulators, Wigner crystals and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different graphene layers. In this work, we propose a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates. We take gaphene/SiC heterostructure as a role model and demonstrate experimentally the substrate modulation leads to Dirac fermion cloning and consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Our theoretical modeling captures the cloning mechanism of Dirac states and indicates that flat bands can emerge at certain magic lattice constants of substrate when the period of modulation becomes nearly commensurate with the $(\sqrt{3}\times\sqrt{3})R30^{\circ}$ supercell of graphene. The results show that the epitaxial monolayer graphene is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.

cond-mat.mes-hall↗

arXiv2021

Observation of Symmetry-Protected Dirac States in Nonsymmorphic $\alpha$-Antimonene

Two-dimensional (2D) Dirac states with linear band dispersion have attracted enormous interest since the discovery of graphene. However, to date, 2D Dirac semimetals are still very rare due to the fact that 2D Dirac states are generally fragile against perturbations such as spin-orbit couplings. Nonsymmorphic crystal symmetries can enforce the formation of Dirac nodes, providing a new route to establishing symmetry-protected Dirac states in 2D materials. Here we report the symmetry-protected Dirac states in nonsymmorphic alpha-antimonene. The antimonene was synthesized by the method of molecular beam epitaxy. Two Dirac cones with large anisotropy were observed by angle-resolved photoemission spectroscopy. The Dirac state in alpha-antimonene is of spin-orbit type in contrast to the spinless Dirac states in graphene. The result extends the 'graphene' physics into a new family of 2D materials where spin-orbit coupling is present.

cond-mat.mes-hall↗

arXiv2019

Thermodynamics of switching in multistable non-equilibrium systems

Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and entropy production. Here, we will link fluctuation theorems for the entropy production along trajectories with the action obtainable from the Freidlin--Wentzell theorem to elucidate the thermodynamics of switching between states in the large volume limit of multistable systems. We find that the entropy production at steady state plays no role, but the entropy production during switching is key. Steady-state entropy and diffusive noise strength can be neglected in this limit. The relevance to biology, ecological, and climate models is apparent.

physics.bio-ph↗

arXiv2019

Unconventional Josephson junctions with topological Kondo insulator weak links

Proximity-induced superconductivity in three dimensional (3D) topological insulators forms a new quantum phase of matter and accommodates exotic quasiparticles such as Majorana bound states. One of the biggest drawbacks of the commonly studied 3D topological insulators is the presence of conducting bulk that obscures both surface states and low energy bound states. Introducing superconductivity in topological Kondo insulators such as SmB$_6$, however, is promising due to their true insulating bulk at low temperatures. In this work, we develop an unconventional Josephson junction by coupling superconducting Nb leads to the surface states of a SmB$_6$ crystal. We observe a robust critical current at low temperatures that responds to the application of an out-of-plane magnetic field with significant deviations from usual Fraunhofer patterns. The appearance of Shaphiro steps under microwave radiation gives further evidence of a Josephson effect. Moreover, we explore the effects of Kondo breakdown in our devices, such as ferromagnetism at the surface and anomalous temperature dependence of supercurrent. Particularly, the magnetic diffraction patterns show an anomalous hysteresis with the field sweep direction suggesting the coexistence of magnetism with superconductivity at the SmB$_6$ surface. The experimental work will advance the current understanding of topologically nontrivial superconductors and emergent states associated with such unconventional superconducting phases.

cond-mat.supr-con↗

arXiv2016

Classifying the provably total set functions of KP and KP(P)

This article is concerned with classifying the provably total set-functions of Kripke-Platek set theory, KP, and Power Kripke-Platek set theory, KP(P), as well as proving several (partial) conservativity results. The main technical tool used in this paper is a relativisation technique where ordinal analysis is carried out relative to an arbitrary but fixed set x. A classic result from ordinal analysis is the characterisation of the provably recursive functions of Peano Arithmetic, PA, by means of the fast growing hierarchy [10]. Whilst it is possible to formulate the natural numbers within KP, the theory speaks primarily about sets. For this reason it is desirable to obtain a characterisation of its provably total set functions. We will show that KP proves the totality of a set function precisely when it falls within a hierarchy of set functions based upon a relativised constructible hierarchy stretching up in length to any ordinal below the Bachmann-Howard ordinal. As a consequence of this result we obtain that IKP + forall x,y (x in y or x not in y) is conservative over KP for forall-exists-formulae, where IKP stands for intuitionistic Kripke-Platek set theory. In a similar vein, utilising [56], it is shown that KP(P) proves the totality of a set function precisely when it falls within a hierarchy of set functions based upon a relativised von Neumann hierarchy of the same length. The relativisation technique applied to KP(P) with the global axiom of choice, AC-global, also yields a parameterised extension of a result in [58], showing that KP(P) + AC-global is conservative over KP(P) + AC and CZF + AC for Pi_2 in powerset statements. Here AC stands for the ordinary axiom of choice and CZF refers to constructive Zermelo-Fraenkel set theory.

math.LO↗

arXiv2016

Ordinal analysis of intuitionistic power and exponentiation Kripke Platek set theory

Until the 1970s, proof theoretic investigations were mainly concerned with theories of inductive definitions, subsystems of analysis and finite type systems. With the pioneering work of Gerhard Jaeger in the late 1970s and early 1980s, the focus switched to set theories, furnishing ordinal-theoretic proof theory with a uniform and elegant framework. More recently it was shown that these tools can even sometimes be adapted to the context of strong axioms such as the powerset axiom, where one does not attain complete cut elimination but can nevertheless extract witnessing information and characterize the strength of the theory in terms of provable heights of the cumulative hierarchy. Here this technology is applied to intuitionistic Kripke-Platek set theories IKP(P) and IKP(E), where the operation of powerset and exponentiation, respectively, is allowed as a primitive in the separation and collection schemata. In particular, IKP(P) proves the powerset axiom whereas IKP(E) proves the exponentiation axiom. The latter expresses that given any sets A and B, the collection of all functions from A to B is a set, too. While IKP(P) can be dealt with in a similar vein as its classical cousin, the treatment of IKP(E) posed considerable obstacles. One of them was that in the infinitary system the levels of terms become a moving target as they cannot be assigned a fixed level in the formal cumulative hierarchy solely based on their syntactic structure. As adumbrated in an earlier paper, the results of this paper are an important tool in showing that several intuitionistic set theories with the collection axiom possess the existence property, i.e., if they prove an existential theorem then a witness can be provably described in the theory, one example being intuitionistic Zermelo-Fraenkel set theory with bounded separation.

math.LO↗