Interplay of Cooper Pairs and Zero-Energy Quasiparticles in a Gapless Superconductor

The interplay between Cooper pairs and Bogoliubov-de Gennes (BdG) quasiparticles is a topic of considerable interest in the quantum properties of solids, but its important ingredient, the sufficient amount of low-energy quasiparticles to interact with Cooper pairs remains elusive in conventional superconductors. Here a gapless superconductor with coupled paramagnetic atomic layers is used to generate a significant amount of zero-energy quasiparticles that Anderson-localize and bifurcate into regions of high and low zero-energy quasiparticle density of states. The enriched zero-energy quasiparticles induce puddled superconductivity and Josephson vortices. This discovery not only advances the understanding of the mutual interaction of Cooper pairs and BdG quasiparticles but also opens a new avenue for exploring and controlling exotic quantum phenomena where superconductivity, disorder, and spin degrees of freedom are entangled.

Charged Exciton Generation by Curvature-Induced Band Gap Fluctuations in Structurally Disordered Two-Dimensional Semiconductors

Curvature is a general factor for various two-dimensional (2D) materials due to their flexibility, which is not yet fully unveiled to control their physical properties. In particular, the effect of structural disorder with random curvature formation on excitons in 2D semiconductors is not fully understood. Here, the correlation between structural disorder and exciton formation in monolayer MoS2 on SiO2 was investigated by using photoluminescence (PL) and Raman spectroscopy. We found that the curvature-induced charge localization along with band gap fluctuations aid the formation of the localized charged excitons (such as trions). In the substrate-supported region, the trion population is enhanced by a localized charge due to the microscopic random bending strain, while the trion is suppressed in the suspended region which exhibits negligible bending strain, anomalously even though the dielectric screening effect is lower than that of the supported region. The redistribution of each exciton by the bending strain leads to a huge variation (∼100-fold) in PL intensity between the supported and suspended regions, which cannot be fully comprehended by external potential disorders such as a random distribution of charged impurities. The peak position of PL in MoS2/SiO2 is inversely proportional to the Raman peak position of E12g, indicating that the bending strain is correlated with PL. The supported regions exhibit an indirect portion that was not shown in the suspended regions or atomically flat substrates. The understanding of the structural disorder effect on excitons provides a fundamental path for optoelectronics and strain engineering of 2D semiconductors.

Quantum multifractality as a probe of phase space in the Dicke model

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.

Structural-disorder-driven critical quantum fluctuation and localization in two-dimensional semiconductors

Quantum fluctuations of wavefunctions in disorder-driven quantum phase transitions (QPT) exhibit criticality, as evidenced by their multifractality and power law behavior. However, understanding the metal-insulator transition (MIT) as a continuous QPT in a disordered system has been challenging due to fundamental issues such as the lack of an apparent order parameter and its dynamical nature. Here, we elucidate the universal mechanism underlying the structural-disorder-driven MIT in 2D semiconductors through autocorrelation and multifractality of quantum fluctuations. The structural disorder causes curvature-induced band gap fluctuations, leading to charge localization and formation of band tails near band edges. As doping level increases, the localization-delocalization transition occurs when states above a critical energy become uniform due to unusual band bending by localized charge. Furthermore, curvature induces local variations in spin-orbit interactions, resulting in non-uniform ferromagnetic domains. Our findings demonstrate that the structural disorder in 2D materials is essential to understanding the intricate phenomena associated with localization-delocalization transition, charge percolation, and spin glass with both topological and magnetic disorders.

Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition

An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a good agreement with existing analytical expressions in the metallic regime and with heuristic relations widely used in studies of the PBRM model in the presence of orthogonal and unitary symmetries. Moreover, our results confirm that the multifractal behavior of disordered systems at criticality can be probed by measuring scattering and transport properties, which is of paramount importance from the experimental point of view. Thus, a full picture of the scattering and transport properties of the PBRM model at criticality corresponding to the three classical Wigner-Dyson ensembles is provided.

Exploring the Metal-Insulator Transition in (Ga,Mn)As by Molecular Absorption

The metal-insulator transition (MIT) is normally assisted by certain external power input, such as temperature, pressure, strain, or doping. However, these may increase the disorder of the crystal or cause other effects, which makes device fabrication complicated and/or hinders large-scale application. Here, we adopt a new approach to obtain robust modulation of physical properties in magnetic semiconductor (Ga,Mn)As by surface molecular modification. We have probed both sides of the MIT with n- and p-type molecular doping. Density functional theory calculations are carried out to determine the stable absorption configuration and charge transfer mechanism of electron acceptor and donor molecules on the semiconductor surface. Both experimental and theoretical results confirm a remarkable modulation in carrier concentrations without introducing impurities or defects. This work points out the possibility of effectively tuning physical properties of solid-state materials by functional molecules, which is clean, flexible, nondestructive, and easily achieved.

Structure, Properties and Applications of Two-Dimensional Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) has emerged as a strong candidate for two-dimensional (2D) material owing to its exciting optoelectrical properties combined with mechanical robustness, thermal stability, and chemical inertness. Super-thin h-BN layers have gained significant attention from the scientific community for many applications, including nanoelectronics, photonics, biomedical, anti-corrosion, and catalysis, among others. This review provides a systematic elaboration of the structural, electrical, mechanical, optical, and thermal properties of h-BN followed by a comprehensive account of state-of-the-art synthesis strategies for 2D h-BN, including chemical exfoliation, chemical, and physical vapor deposition, and other methods that have been successfully developed in recent years. It further elaborates a wide variety of processing routes developed for doping, substitution, functionalization, and combination with other materials to form heterostructures. Based on the extraordinary properties and thermal-mechanical-chemical stability of 2D h-BN, various potential applications of these structures are described.

Multifractality in Quasienergy Space of Coherent States as a Signature of Quantum Chaos

We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate the Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking strength is able to capture the structural changes of the phase space. The onset of chaos is clearly identified by the phase-space-averaged multifractal dimensions, which are well described by random matrix theory in a strongly chaotic regime. We further investigate the probability distribution of expansion coefficients, and show that the deviation between the numerical results and the prediction of random matrix theory behaves as a reliable detector of quantum chaos.

Spin relaxation in diluted magnetic semiconductors: GaMnAs as example

The paper deals with a study of the magnetic impurities spin relaxation in the diluted magnetic semiconductors above the Curie temperature. Systems with a high concentration of magnetic impurities where magnetic correlations take place were studied. The proposed theory assumes the main channel of the spin relaxation being the mobile carriers, which provide the indirect interactions of the magnetic impurities. This theoretical model is supported by the experimental measurements of the manganese spin relaxation time in the GaMnAs by means of spin-flip Raman scattering. As has been found with a temperature increase the spin relaxation rate of the ferromagnetic samples grows, tending to that measured in a paramagnetic sample.

Chaos-Assisted Long-Range Tunneling for Quantum Simulation

We present an extension of the chaos-assisted tunneling mechanism to spatially periodic lattice systems. We demonstrate that driving such lattice systems in an intermediate regime of modulation maps them onto tight-binding Hamiltonians with chaos-induced long-range hoppings t_{n}∝1/n between sites at a distance n. We provide a numerical demonstration of the robustness of the results and derive an analytical prediction for the hopping term law. Such systems can thus be used to enlarge the scope of quantum simulations to experimentally realize long-range models of condensed matter.

Pseudogap and Weak Multifractality in 2D Disordered Mott Charge-Density-Wave Insulator

We investigate electronic states of Se-substituted 1T-TaS₂ by scanning tunneling microscopy/spectroscopy (STM/STS), where superconductivity emerges from the unique Mott-charge-density-wave (Mott-CDW) state. Spatially resolved STS measurements reveal that a pseudogap replaces the Mott gap with the CDW gaps intact. The pseudogap has little correlation with the unit-cell-to-unit-cell variation in the local Se concentration but appears globally. The correlation length of the local density of states (LDOS) is substantially enhanced at the Fermi energy and decays rapidly at high energies. Furthermore, the statistical analysis of LDOS indicates the weak multifractal behavior of the wave functions. These findings suggest a correlated metallic state induced by disorder and provide a new insight into the emerging superconductivity in two-dimensional materials.

Visualization of Multifractal Superconductivity in a Two-Dimensional Transition Metal Dichalcogenide in the Weak-Disorder Regime

Eigenstate multifractality is a distinctive feature of noninteracting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic, weakly disordered single-layer NbSe₂ by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth, and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. The strong spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f(α) shows anomalous scaling behavior typical from 2D weakly disordered systems.

Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI

Dual topological materials are unique topological phases that host coexisting surface states of different topological nature on the same or on different material facets. Here, we show that Bi₂TeI is a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band, which classify it as a weak topological insulator with metallic states on its 'side' surfaces. The mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. We investigated Bi₂TeI spectroscopically to show the existence of both two-dimensional Dirac surface states, which are susceptible to mirror symmetry breaking, and one-dimensional channels that reside along the step edges. Their mutual coexistence on the step edge, where both facets join, is facilitated by momentum and energy segregation. Our observation of a dual topological insulator should stimulate investigations of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

Dynamics of quasiperiodically driven spin systems

We study the stroboscopic dynamics of a spin-S object subjected to δ-function kicks in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed in the large spin limit, S→∞. On evolving such a map for large kicking strength and time period, the phase space appears to be chaotic; interestingly, however, the geodesic distance increases linearly with the stroboscopic time implying that the Lyapunov exponent is zero. We derive the Sutherland invariant for the underlying SO(3) matrix governing the dynamics of classical spin variables and study the orbits for weak kicking strength. For the quantum dynamics, we observe that although the phase coherence of a state is retained throughout the time evolution, the fluctuations in the mean values of the spin operators exhibit fractality which is also present in the Floquet eigenstates. Interestingly, the presence of an interaction with another spin results in an ergodic dynamics leading to infinite temperature thermalization.

Multifractality of open quantum systems

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and we quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but these states are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems.

Scale-invariant magnetic textures in the strongly correlated oxide NdNiO3

Strongly correlated quantum solids are characterized by an inherently granular electronic fabric, with spatial patterns that can span multiple length scales in proximity to a critical point. Here, we use a resonant magnetic X-ray scattering nanoprobe with sub-100 nm spatial resolution to directly visualize the texture of antiferromagnetic domains in NdNiO₃. Surprisingly, our measurements reveal a highly textured magnetic fabric, which we show to be robust and nonvolatile even after thermal erasure across its ordering temperature. The scale-free distribution of antiferromagnetic domains and its non-integral dimensionality point to a hitherto-unobserved magnetic fractal geometry in this system. These scale-invariant textures directly reflect the continuous nature of the magnetic transition and the proximity of this system to a critical point. The present study not only exposes the near-critical behavior in rare earth nickelates but also underscores the potential for X-ray scattering nanoprobes to image the multiscale signatures of criticality near a critical point.

Enhanced Ferromagnetism in Cylindrically Confined MnAs Nanocrystals Embedded in Wurtzite GaAs Nanowire Shells

Nearly a 30% increase in the ferromagnetic phase transition temperature has been achieved in strained MnAs nanocrystals embedded in a wurtzite GaAs matrix. Wurtzite GaAs exerts tensile stress on hexagonal MnAs nanocrystals, preventing a hexagonal to orthorhombic structural phase transition, which in bulk MnAs is combined with the magnetic one. This effect results in a remarkable shift of the magneto-structural phase transition temperature from 313 K in the bulk MnAs to above 400 K in the tensely strained MnAs nanocrystals. This finding is corroborated by the state of the art transmission electron microscopy, sensitive magnetometry, and the first-principles calculations. The effect relies on defining a nanotube geometry of molecular beam epitaxy grown core-multishell wurtzite (Ga,In)As/(Ga,Al)As/(Ga,Mn)As/GaAs nanowires, where the MnAs nanocrystals are formed during the thermal-treatment-induced phase separation of wurtzite (Ga,Mn)As into the GaAs-MnAs granular system. Such a unique combination of two types of hexagonal lattices provides a possibility of attaining quasi-hydrostatic tensile strain in MnAs (impossible otherwise), leading to the substantial ferromagnetic phase transition temperature increase in this compound.

Charge Disproportionation Triggers Bipolar Doping in FeSb2- xSn xSe4 Ferromagnetic Semiconductors, Enabling a Temperature-Induced Lifshitz Transition

Ferromagnetic semiconductors (FMSs) featuring a high Curie transition temperature ( T_c) and a strong correlation between itinerant carriers and localized magnetic moments are of tremendous importance for the development of practical spintronic devices. The realization of such materials hinges on the ability to generate and manipulate a high density of itinerant spin-polarized carriers and the understanding of their responses to external stimuli. In this study, we demonstrate the ability to tune magnetic ordering in the p-type FMS FeSb_{2- x}Sn _xSe₄ (0 ≤ x ≤ 0.20) through carrier density engineering. We found that the substitution of Sb by Sn FeSb_{2- x}Sn _xSe₄ increases the ordering of metal atoms within the selenium crystal lattice, leading to a large separation between magnetic centers. This results in a decrease in the T_c from 450 K for samples with x ≤ 0.05 to 325 K for samples with 0.05 < x ≤ 0.2. In addition, charge disproportionation arising from the substitution of Sb³⁺ by Sn²⁺ triggers the partial oxidation of Sb³⁺ to Sb⁵⁺, which is accompanied by the generation of both electrons and holes. This leads to a drastic decrease in the electrical resistivity and thermopower simultaneously with a large increase in the magnetic susceptibility and saturation magnetization upon increasing Sn content. The observed bipolar doping induces a very interesting temperature-induced quantum electronic transition (Lifshitz transition), which is manifested by the presence of an anomalous peak in the resistivity curve simultaneously with a reversal of the sign of a majority of the charge carriers from hole-like to electron-like at the temperature of maximum resistivity. This study suggests that while there is a strong correlation between the overall magnetic moment and free carrier spin in FeSb_{2- x}Sn _xSe₄ FMSs, the magnitude of the Curie temperature strongly depends on the spatial separation between localized magnetic centers rather than the concentration of magnetic atoms or the density of itinerant carriers.

Many-Body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases

We demonstrate many-body multifractality of the Bose-Hubbard Hamiltonian's ground state in Fock space, for arbitrary values of the interparticle interaction. Generalized fractal dimensions unambiguously signal, even for small system sizes, the emergence of a Mott insulator that cannot, however, be naively identified with a localized phase in Fock space. We show that the scaling of the derivative of any generalized fractal dimension with respect to the interaction strength encodes the critical point of the superfluid to the Mott insulator transition, and provides an efficient way to accurately estimate its position. We further establish that the transition can be quantitatively characterized by one single wave function amplitude from the exponentially large Fock space.

Design and characterization of electrons in a fractal geometry

The dimensionality of an electronic quantum system is decisive for its properties. In one dimension electrons form a Luttinger liquid and in two dimensions they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in non-integer, or fractional dimensions1. Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu (111) surface2-4, and how these sites couple to form electronic Sierpiński fractals. We characterize the electron wave functions at different energies with scanning tunneling microscopy and spectroscopy and show that they inherit the fractional dimension. Wave functions delocalized over the Sierpiński structure decompose into self-similar parts at higher energy, and this scale invariance can also be retrieved in reciprocal space. Our results show that electronic quantum fractals can be artificially created by atomic manipulation in a scanning tunneling microscope. The same methodology will allow future study to address fundamental questions about the effects of spin-orbit interaction and a magnetic field on electrons in non-integer dimensions. Moreover, the rational concept of artificial atoms can readily be transferred to planar semiconductor electronics, allowing for the exploration of electrons in a well-defined fractal geometry, including interactions and external fields.

Disorder induced power-law gaps in an insulator-metal Mott transition

A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and a variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems. Theory predicts that disorder might play a role in driving a Mott insulator across an IMT, with the emergent metallic state hosting a power-law suppression of the density of states (with exponent close to 1; V-shaped gap) centered at the Fermi energy. Such V-shaped gaps have been observed in Mott systems, but their origins are as-yet unknown. To investigate this, we use scanning tunneling microscopy and spectroscopy to study isovalent Ru substitutions in Sr3(Ir1-xRux)2O7 (0 ≤ x ≤ 0.5) which drive the system into an antiferromagnetic, metallic state. Our experiments reveal that many core features of the IMT, such as power-law density of states, pinning of the Fermi energy with increasing disorder, and persistence of antiferromagnetism, can be understood as universal features of a disordered Mott system near an IMT and suggest that V-shaped gaps may be an inevitable consequence of disorder in doped Mott insulators.

Electronic phase separation in insulating (Ga, Mn) As with low compensation: super-paramagnetism and hopping conduction

In the present work, low compensated insulating (Ga,Mn)As with 0.7% Mn is obtained by ion implantation combined with pulsed laser melting. The sample shows variable-range hopping transport behavior with a Coulomb gap in the vicinity of the Fermi energy, and the activation energy is reduced by an external magnetic field. A blocking super-paramagnetism is observed rather than ferromagnetism. Below the blocking temperature, the sample exhibits a colossal negative magnetoresistance. Our studies confirm that the disorder-induced electronic phase separation occurs in (Ga,Mn)As samples with a Mn concentration in the insulator-metal transition regime, and it can account for the observed superparamagnetism and the colossal magnetoresistance.

Selective state spectroscopy and multifractality in disordered Bose-Einstein condensates: a numerical study

We propose to apply a modified version of the excitation scheme introduced by Volchkov et al. on bosons experiencing hyperfine state dependent disorder to address the critical state at the mobility edge of the Anderson localization transition, and to observe its intriguing multifractal structure. An optimally designed, spatially focused external radio frequency pulse can be applied to generate transitions to eigenstates in a narrow energy window close to the mobility edge, where critical scaling and multifractality emerge. Alternatively, two-photon laser scanning microscopy is proposed to address individual localized states even close to the transition. The projected image of the cloud is shown to inherit multifractality and to display universal density correlations. Interactions - unavoidably present - are taken into account by solving the Gross-Pitaevskii equations, and their destructive effect on the spectral resolution and the multifractal spectrum is analyzed. Time of flight images of the excited states are predicted to show interference fringes in the localized phase, while they allow one to map equal energy surfaces deep in the metallic phase.

Ultrafast current imaging by Bayesian inversion

Spectroscopic measurements of current–voltage curves in scanning probe microscopy is the earliest and one of the most common methods for characterizing local energy-dependent electronic properties, providing insight into superconductive, semiconductor, and memristive behaviors. However, the quasistatic nature of these measurements renders them extremely slow. Here, we demonstrate a fundamentally new approach for dynamic spectroscopic current imaging via full information capture and Bayesian inference. This general-mode I–V method allows three orders of magnitude faster measurement rates than presently possible. The technique is demonstrated by acquiring I–V curves in ferroelectric nanocapacitors, yielding >100,000 I–V curves in <20 min. This allows detection of switching currents in the nanoscale capacitors, as well as determination of the dielectric constant. These experiments show the potential for the use of full information capture and Bayesian inference toward extracting physics from rapid I–V measurements, and can be used for transport measurements in both atomic force and scanning tunneling microscopy.

Scanning probe microscopy is widely used to characterize material properties with atomic resolution, yet electronic property mapping is normally constrained by slow data acquisition. Somnath et al. show a current–voltage method, which enables fast electronic spectroscopy mapping over micrometer-sized areas.

A Two-Dimensional Manganese Gallium Nitride Surface Structure Showing Ferromagnetism at Room Temperature

Practical applications of semiconductor spintronic devices necessitate ferromagnetic behavior at or above room temperature. In this paper, we demonstrate a two-dimensional manganese gallium nitride surface structure (MnGaN-2D) which is atomically thin and shows ferromagnetic domain structure at room temperature as measured by spin-resolved scanning tunneling microscopy and spectroscopy. Application of small magnetic fields proves that the observed magnetic domains follow a hysteretic behavior. Two initially oppositely oriented MnGaN-2D domains are rotated into alignment with only 120 mT and remain mostly in alignment at remanence. The measurements are further supported by first-principles theoretical calculations which reveal highly spin-polarized and spin-split surface states with spin polarization of up to 95% for manganese local density of states.

Fractality in nonequilibrium steady states of quasiperiodic systems

We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular, we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a viable experimental technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen: generic length chains harbour qualitatively slower transport (different scaling exponent) than Fibonacci length chains, which is in turn slower than in the closed system. We conjecture that such fractal nonequilibrium steady states should arise in generic driven critical systems that have fractal properties.

First-Principles-Based Method for Electron Localization: Application to Monolayer Hexagonal Boron Nitride

We present a first-principles-based many-body typical medium dynamical cluster approximation and density function theory method for characterizing electron localization in disordered structures. This method applied to monolayer hexagonal boron nitride shows that the presence of boron vacancies could turn this wide-gap insulator into a correlated metal. Depending on the strength of the electron interactions, these calculations suggest that conduction could be obtained at a boron vacancy concentration as low as 1.0%. We also explore the distribution of the local density of states, a fingerprint of spatial variations, which allows localized and delocalized states to be distinguished. The presented method enables the study of disorder-driven insulator-metal transitions not only in h-BN but also in other physical materials.

Multiband One-Dimensional Electronic Structure and Spectroscopic Signature of Tomonaga-Luttinger Liquid Behavior in K_{2}Cr_{3}As_{3}

We present angle-resolved photoemission spectroscopy measurements of the quasi-one-dimensional superconductor K_{2}Cr_{3}As_{3}. We find that the Fermi surface contains two Fermi surface sheets, with linearly dispersing bands not displaying any significant band renormalizations. The one-dimensional band dispersions display a suppression of spectral intensity approaching the Fermi level according to a linear power law, over an energy range of ∼200  meV. This is interpreted as a signature of Tomonoga-Luttinger liquid physics, which provides a new perspective on the possibly unconventional superconductivity in this family of compounds.

Disorder-Driven Metal-Insulator Transitions in Deformable Lattices

We show that, in the presence of a deformable lattice potential, the nature of the disorder-driven metal-insulator transition is fundamentally changed with respect to the noninteracting (Anderson) scenario. For strong disorder, even a modest electron-phonon interaction is found to dramatically renormalize the random potential, opening a mobility gap at the Fermi energy. This process, which reflects disorder-enhanced polaron formation, is here given a microscopic basis by treating the lattice deformations and Anderson localization effects on the same footing. We identify an intermediate "bad insulator" transport regime which displays resistivity values exceeding the Mott-Ioffe-Regel limit and with a negative temperature coefficient, as often observed in strongly disordered metals. Our calculations reveal that this behavior originates from significant temperature-induced rearrangements of electronic states due to enhanced interaction effects close to the disorder-driven metal-insulator transition.

Quasiparticle Scattering off Defects and Possible Bound States in Charge-Ordered YBa_{2}Cu_{3}O_{y}

We report the NMR observation of a skewed distribution of ^{17}O Knight shifts when a magnetic field quenches superconductivity and induces long-range charge-density-wave (CDW) order in YBa_{2}Cu_{3}O_{y}. This distribution is explained by an inhomogeneous pattern of the local density of states N(E_{F}) arising from quasiparticle scattering off, yet unidentified, defects in the CDW state. We argue that the effect is most likely related to the formation of quasiparticle bound states, as is known to occur, under specific circumstances, in some metals and superconductors (but not in the CDW state, in general, except for very few cases in 1D materials). These observations should provide insight into the microscopic nature of the CDW, especially regarding the reconstructed band structure and the sensitivity to disorder.

The fractal heart - embracing mathematics in the cardiology clinic

For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care.

Electronic and optical properties of graphene nanoribbons in external fields

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

Fermi level position, Coulomb gap, and Dresselhaus splitting in (Ga,Mn)As

Carrier-induced nature of ferromagnetism in a ferromagnetic semiconductor, (Ga,Mn)As, offers a great opportunity to observe novel spin-related phenomena as well as to demonstrate new functionalities of spintronic devices. Here, we report on low-temperature angle-resolved photoemission studies of the valence band in this model compound. By a direct determination of the distance of the split-off band to the Fermi energy E_F we conclude that E_F is located within the heavy/light hole band. However, the bands are strongly perturbed by disorder and disorder-induced carrier correlations that lead to the Coulomb gap at E_F, which we resolve experimentally in a series of samples, and show that its depth and width enlarge when the Curie temperature decreases. Furthermore, we have detected surprising linear magnetic dichroism in photoemission spectra of the split-off band. By a quantitative theoretical analysis we demonstrate that it arises from the Dresselhaus-type spin-orbit term in zinc-blende crystals. The spectroscopic access to the magnitude of such asymmetric part of spin-orbit coupling is worthwhile, as they account for spin-orbit torque in spintronic devices of ferromagnets without inversion symmetry.

Quantum simulation of the Hubbard model with dopant atoms in silicon

In quantum simulation, many-body phenomena are probed in controllable quantum systems. Recently, simulation of Bose-Hubbard Hamiltonians using cold atoms revealed previously hidden local correlations. However, fermionic many-body Hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms. To date the required single-site measurements and cooling remain problematic, while only ensemble measurements have been achieved. Here we simulate a two-site Hubbard Hamiltonian at low effective temperatures with single-site resolution using subsurface dopants in silicon. We measure quasi-particle tunnelling maps of spin-resolved states with atomic resolution, finding interference processes from which the entanglement entropy and Hubbard interactions are quantified. Entanglement, determined by spin and orbital degrees of freedom, increases with increasing valence bond length. We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.

Multifractality of quantum wave functions in the presence of perturbations

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model, and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong-enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.

Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments

Motivated by the intrinsic non-Fermi-liquid behavior observed in the heavy-fermion quasicrystal Au51Al34Yb15, we study the low-temperature behavior of dilute magnetic impurities placed in metallic quasicrystals. We find that a large fraction of the magnetic moments are not quenched down to very low temperatures T, leading to a power-law distribution of Kondo temperatures P(T(K))∼T(K)(α-1), with a nonuniversal exponent α, in a remarkable similarity to the Kondo-disorder scenario found in disordered heavy-fermion metals. For α<1, the resulting singular P(T(K)) induces non-Fermi-liquid behavior with diverging thermodynamic responses as T→0.

Shot noise induced by nonequilibrium spin accumulation

When an electric current passes across a potential barrier, the partition process of electrons at the barrier gives rise to the shot noise, reflecting the discrete nature of the electric charge. Here we report the observation of excess shot noise connected with a spin current which is induced by a nonequilibrium spin accumulation in an all-semiconductor lateral spin-valve device. We find that this excess shot noise is proportional to the spin current. Additionally, we determine quantitatively the spin-injection-induced electron temperature by measuring the current noise. Our experiments show that spin accumulation driven shot noise provides a novel means of investigating nonequilibrium spin transport.

Two scenarios for quantum multifractality breakdown

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.

Global and local superconductivity in boron-doped granular diamond

Strong granularity-correlated and intragrain modulations of the superconducting order parameter are demonstrated in heavily boron-doped diamond situated not yet in the vicinity of the metal-insulator transition. These modulations at the superconducting state (SC) and at the global normal state (NS) above the resistive superconducting transition, reveal that local Cooper pairing sets in prior to the global phase coherence.

Facility for low-temperature spin-polarized-scanning tunneling microscopy studies of magnetic/spintronic materials prepared in situ by nitride molecular beam epitaxy

Based on the interest in, as well as exciting outlook for, nitride semiconductor based structures with regard to electronic, optoelectronic, and spintronic applications, it is compelling to investigate these systems using the powerful technique of spin-polarized scanning tunneling microscopy (STM), a technique capable of achieving magnetic resolution down to the atomic scale. However, the delicate surfaces of these materials are easily corrupted by in-air transfers, making it unfeasible to study them in stand-alone ultra-high vacuum STM facilities. Therefore, we have carried out the development of a hybrid system including a nitrogen plasma assisted molecular beam epitaxy/pulsed laser epitaxy facility for sample growth combined with a low-temperature, spin-polarized scanning tunneling microscope system. The custom-designed molecular beam epitaxy growth system supports up to eight sources, including up to seven effusion cells plus a radio frequency nitrogen plasma source, for epitaxially growing a variety of materials, such as nitride semiconductors, magnetic materials, and their hetero-structures, and also incorporating in situ reflection high energy electron diffraction. The growth system also enables integration of pulsed laser epitaxy. The STM unit has a modular design, consisting of an upper body and a lower body. The upper body contains the coarse approach mechanism and the scanner unit, while the lower body accepts molecular beam epitaxy grown samples using compression springs and sample skis. The design of the system employs two stages of vibration isolation as well as a layer of acoustic noise isolation in order to reduce noise during STM measurements. This isolation allows the system to effectively acquire STM data in a typical lab space, which during its construction had no special and highly costly elements included, (such as isolated slabs) which would lower the environmental noise. The design further enables tip exchange and tip coating without breaking vacuum, and convenient visual access to the sample and tip inside a superconducting magnet cryostat. A sample/tip handling system is optimized for both the molecular beam epitaxy growth system and the scanning tunneling microscope system. The sample/tip handing system enables in situ STM studies on epitaxially grown samples, and tip exchange in the superconducting magnet cryostat. The hybrid molecular beam epitaxy and low temperature scanning tunneling microscopy system is capable of growing semiconductor-based hetero-structures with controlled accuracy down to a single atomic-layer and imaging them down to atomic resolution.

Metal oxide resistive switching: evolution of the density of states across the metal-insulator transition

We report the study of gold-SrTiO3 (STO)-gold memristors where the doping concentration in STO can be fine-tuned through electric field migration of oxygen vacancies. In this tunnel junction device, the evolution of the density of states (DOS) can be followed continuously across the metal-insulator transition (MIT). At very low dopant concentration, the junction displays characteristic signatures of discrete dopant levels. As the dopant concentration increases, the semiconductor band gap fills in but a soft Coulomb gap remains. At even higher doping, a transition to a metallic state occurs where the DOS at the Fermi level becomes finite and Altshuler-Aronov corrections to the DOS are observed. At the critical point of the MIT, the DOS scales linearly with energy N(ϵ)∼ϵ, the possible signature of multifractality.

Identifying the electronic character and role of the Mn states in the valence band of (Ga,Mn)As

We report high-resolution hard x-ray photoemission spectroscopy results on (Ga,Mn)As films as a function of Mn doping. Supported by theoretical calculations we identify, for both low (1%) and high (13%) Mn doping values, the electronic character of the states near the top of the valence band. Magnetization and temperature-dependent core-level photoemission spectra reveal how the delocalized character of the Mn states enables the bulk ferromagnetic properties of (Ga,Mn)As.

Multifractality at Anderson transitions with Coulomb interaction

We explore mesoscopic fluctuations and correlations of the local density of states (LDOS) near localization transition in a disordered interacting electronic system. It is shown that the LDOS multifractality survives in the presence of the Coulomb interaction. We calculate the spectrum of multifractal dimensions in 2+ϵ spatial dimensions and show that it differs from that in the absence of interaction. The multifractal character of fluctuations and correlations of the LDOS can be studied experimentally by scanning tunneling microscopy of two-dimensional and three-dimensional disordered structures.

A 10 mK scanning tunneling microscope operating in ultra high vacuum and high magnetic fields

We present design and performance of a scanning tunneling microscope (STM) that operates at temperatures down to 10 mK providing ultimate energy resolution on the atomic scale. The STM is attached to a dilution refrigerator with direct access to an ultra high vacuum chamber allowing in situ sample preparation. High magnetic fields of up to 14 T perpendicular and up to 0.5 T parallel to the sample surface can be applied. Temperature sensors mounted directly at the tip and sample position verified the base temperature within a small error margin. Using a superconducting Al tip and a metallic Cu(111) sample, we determined an effective temperature of 38 ± 1 mK from the thermal broadening observed in the tunneling spectra. This results in an upper limit for the energy resolution of ΔE = 3.5 kBT = 11.4 ± 0.3 μeV. The stability between tip and sample is 4 pm at a temperature of 15 mK as demonstrated by topography measurements on a Cu(111) surface.

Multifractality of quantum wave packets

We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, which is different from the multifractality of eigenvectors but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems.