Dimensional Crossover Research Articles

Feynman’s Classification of Natural Phenomena and Physical Aspects of 2014 Nobel Prize in Physiology or Medicine

This review article is devoted to the formulation of the Richard Feynman’s classification of three stages in the study of natural phenomena and the application of this classification to the amazing discovery of the hexagonal grid cells that constitute a positioning system in the brain which was awarded the 2014 Nobel Prize in Physiology and Medicine. The problem of grid cells in brain is considered with accounting for (a) the experimental studies that led to the emergence of hexagons in the human and animal brains, (b) discussion of the problem of generation and propagation of an action potential along nerve fibers, (c) physical parameters of the human brain and its medical applications in the method of hyperthermia for the treatment of malignant tumors, (d) theoretical considerations using a certain analogy between grid cells in brain and the Abrikosov vortex lattice in type II superconductors, and (e) hexagonal graphene and dimensional crossover.

Intrinsic exchange bias state in silicene and germanene materials EuX2.

2D magnets have recently emerged as a host for unconventional phases and related phenomena. The prominence of 2D magnetism stems from its high amenability to external stimuli and structural variations. The low dimensionality facilitates competition between magnetic orders which may give rise to exchange bias, in particular in magnetic heterostructures. Here, we propose a strategy for the search of exchange bias state in 2D individual compounds. We track the evolution of magnetic orders driven by the number of monolayers in a system exhibiting antiferromagnetism in the multilayer and ferromagnetism in the monolayer limit. The material, EuSi2, has the structure of multilayer silicene intercalated by Eu. A strong intrinsic exchange bias effect accompanies the dimensional crossover. Comparison with silicene-based GdSi2 and germanene-based EuGe2 suggests the competition between magnetic orders to be a common property of this class of materials that may be useful in spintronic applications.

Dimensional crossover of a Rabi-coupled two-component Bose–Einstein condensate in an optical lattice

Dimensionality is a central concept in developing the theory of low-dimensional physics. However, previous research on dimensional crossover in the context of a Bose–Einstein condensate (BEC) has focused on the single-component BEC. To our best knowledge, further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking. In this work, we are motivated to investigate the dimensional crossover in a three-dimensional (3D) Rabi-coupled two-component BEC. The spin degrees of freedom consist of the Rabi-like and inter- and intra- interaction coupling constants. The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively. Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations, with an emphasis on the separated effects of Rabi-like and inter- and intra- interaction coupling constants on the quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Emergent Pauli Blocking in a Weakly Interacting Bose Gas

The relationship between many-body interactions and dimensionality is integral to numerous emergent quantum phenomena. A striking example is the Bose gas, which upon confinement to one dimension (1D) obeys an infinite set of conservation laws, prohibiting thermalization and constraining dynamics. In our experiment, we demonstrate that such a 1D behavior can extend much further into the dimensional crossover toward 3D than expected. Starting from a weakly interacting Bose gas trapped in a highly elongated potential, we perform a quench to instigate the dynamics of a single density mode. Employing the theory of generalized hydrodynamics, we identify the dominant relaxation mechanism as the 1D dephasing of the relevant collective excitations of the system, the rapidities. Surprisingly, the dephasing remains dominant even for temperatures far exceeding conventional limits of one dimensionality where thermalization should occur. We attribute our observations to an emergent Pauli blocking of transverse excitations caused by the rapidities assuming fermionic statistics, despite the gas being purely bosonic. Thus, our study suggests that 1D physics is less fragile than previously thought, as it can persist even in the presence of significant perturbations. More broadly, by employing the exact Bethe ansatz solutions of the many-body system, we facilitate an interpretation of how the emergent macroscopic behavior arises from the microscopic interactions.5 MoreReceived 24 June 2022Accepted 15 November 2022DOI:https://doi.org/10.1103/PhysRevX.12.041032Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsQuantum quenchPhysical Systems1-dimensional systemsUltracold gasesCondensed Matter, Materials & Applied PhysicsStatistical Physics

Effective Fractal Dimension at 2d-3d Crossover

This article is aimed at reviewing and studying the effects of the 2d-3d crossover on the effective fractal and spatial dimensions, as well as on the critical exponents of the physical properties of bulk and bounded systems at criticality. Here we consider the following problems: (1) the two types of dimensional crossovers and the concept of the universality classes; (2) a smooth 2d-3d crossover and the calculation of the effective fractal and spatial dimensions, as well as the effective critical indices; (3) the fractal dimension, its connection with the random mean square order-parameter fluctuations and a new phase formation; (4) the fractal nuclei of a new phase and the medical consequences of carcinogenesis and nucleation isomorphism.

Complex Phase-Fluctuation Effects Correlated with Granularity in Superconducting NbN Nanofilms.

Superconducting nanofilms are tunable systems that can host a 3D-2D dimensional crossover leading to the Berezinskii-Kosterlitz-Thouless (BKT) superconducting transition approaching the 2D regime. Reducing the dimensionality further, from 2D to quasi-1D superconducting nanostructures with disorder, can generate quantum and thermal phase slips (PS) of the order parameter. Both BKT and PS are complex phase-fluctuation phenomena of difficult experiments. We characterized superconducting NbN nanofilms thinner than 15 nm, on different substrates, by temperature-dependent resistivity and current-voltage (I-V) characteristics. Our measurements evidence clear features related to the emergence of BKT transition and PS events. The contemporary observation in the same system of BKT transition and PS events, and their tunable evolution in temperature and thickness was explained as due to the nano-conducting paths forming in a granular NbN system. In one of the investigated samples, we were able to trace and characterize the continuous evolution in temperature from quantum to thermal PS. Our analysis established that the detected complex phase phenomena are strongly related to the interplay between the typical size of the nano-conductive paths and the superconducting coherence length.

Hierarchical dimensional crossover of an optically-trapped quantum gas with disorder

Dimensionality serves as an indispensable ingredient in any attempt to formulate low-dimensional physics, and studying the dimensional crossover at a fundamental level is challenging. The purpose of this work is to study the hierarchical dimensional crossovers, namely the crossover from three dimensions (3D) to quasi-2D and then to 1D. Our system consists of a 3D Bose–Einstein condensate trapped in an anisotropic 2D optical lattice characterized by the lattice depths V 1 along the x direction and V 2 along the y direction, respectively, where the hierarchical dimensional crossover is controlled via V 1 and V 2. We analytically derive the ground-state energy, quantum depletion and the superfluid density of the system. Our results demonstrate the 3D-quasi-2D-1D dimensional crossovers in the behavior of quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Linear nonsaturating magnetoresistance in kagome superconductor CsV3Sb5 thin flakes

Linear nonsaturating magnetoresistance (LMR) represents a class of anomalous resistivity response to external magnetic field that has been observed in a variety of materials including but not limited to topological semi-metals, high-T c superconductors and materials with charge density wave (CDW)/spin density wave orders. Here we report the observation of LMR in layered kagome superconductor and CDW material CsV3Sb5 thin flakes, as well as the dimensional crossover and temperature (T) crossover of such LMR. Specifically, in ultrathin CsV3Sb5 crystals, the magnetoresistance (MR) exhibits a crossover from LMR at low T to quadratic B dependence above the CDW transition temperature; the MR also exhibits a crossover from LMR to sublinear MR for sample thickness at around ∼20 nm at low T. We discuss several possible origins of the LMR and attribute the effect to two-dimensional CDW fluctuations. Our results may provide a new perspective for understanding the interactions between competing orders in kagome superconductors.

1H NMR study of dimensionality crossover in a two-dimensional antiferromagnet

1H NMR study of dimensionality crossover in a two-dimensional antiferromagnet

Quasi-Two-Dimensional Nature of High-T c Superconductivity in Iron-Based (Li,Fe)OHFeSe

The intercalated iron selenide (Li,Fe)OHFeSe has a strongly layered structure analogous to the quasi-two-dimensional (2D) bismuth cuprate superconductors, and exhibits both high-temperature (T c) and topological superconductivity. However, the issue of its superconductivity dimensionality has not yet been fully investigated so far. Here we report that the quasi-2D superconductivity features, including the high anisotropy γ = 151 and the associated quasi-2D vortices, are also revealed for (Li,Fe)OHFeSe, based on systematic experiments of the electrical transport and magnetization and model fittings. Thus, we establish a new vortex phase diagram for (Li,Fe)OHFeSe, which delineates an emergent quasi-2D vortex-liquid state, and a subsequent vortex-solid dimensional crossover from a pancake-like to a three-dimensional state with decreasing temperature and magnetic field. Furthermore, we find that all the quasi-2D characteristics revealed here for the high-T c iron selenide superconductor are very similar to those reported for high-T c bismuth cuprate superconductors.

Superatomic-Charge-Density-Wave in Cluster-Assembled Au6Te12Se8 Superconductors.

Superatomic crystals are a class of hierarchical materials composed of atomically precise clusters assembled via van der Waals or covalent-like interactions. Au6Te12Se8, an all-inorganic superatomic superconductor exhibiting superatomic-charge-density-wave (S-CDW), provides the first platform to study the response of its collective quantum phenomenon to the external pressure in superatomic crystals. We reveal a competition between S-CDW and superconductivity in an ultra-narrow pressure range. Distinct from conventional CDW ordering, S-CDW shows the lowest threshold (0.1 GPa) toward external pressure that is 1-2 orders of magnitude lower than other atomic compounds. Prominently, a second superconducting phase emerges above 7.3 GPa with a threefold enhancement in the transition temperature (Tc) to 8.5 K, indicating a switch of the conduction channel from the a- to b-axis. In situ synchrotron diffractions and theoretical calculations reveal a pressure-mediated mesoscopic slip of the superatoms and a 2D-3D transition of the Fermi surface topology, which well explains the observed dimensional crossover of conductivity and re-entrant superconductivity.

Crossing the superfluid-supersolid transition of an elongated dipolar condensate

We provide a theoretical characterization of the dynamical crossing of the superfluid-supersolid phase transition for a dipolar condensate confined in an elongated trap, as observed in the recent experiment by Biagioni et al. [G. Biagioni, N. Antolini, A. Ala\~na, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Modugno, Phys. Rev. X 12, 021019 (2022)]. By means of the extended Gross-Pitaevskii theory, which includes the Lee-Huang-Yang quantum fluctuation correction, we first analyze the ground-state configurations of the system as a function of the interparticle scattering length, for both trap configurations employed in the experiment. Then, we discuss the effects of the ramp velocity, by which the scattering length is tuned across the transition, on the collective excitations of the system in both the superfluid and supersolid phases. We find that, when the transverse confinement is sufficiently strong and the transition has a smooth (continuous) character, the system essentially displays a (quasi) one-dimensional behavior, its excitation dynamics being dominated by the axial breathing modes. Instead, for shallower transverse trapping, when the transition becomes discontinuous, the collective excitations of the supersolid display a coupling with the transverse modes, signaling the onset of a dimensional crossover.

Fluctuation magnetoconductivity in superconducting Ca10(Pt4As8)(Fe2As2)5 single crystal

Fluctuation-induced conductivity up to μ0H = 14 T for superconducting Ca10(Pt4As8)(Fe2As2)5 single crystal was evaluated from the measured in-plane electrical resistivity, and it was analyzed by Aslamazov-Larkin (AL) theory for zero magnetic field and Ullah and Dorsey (UD) scaling method for magnetic field. A dimensional crossover of superconducting fluctuations from low-temperature three-dimension to high-temperature two-dimension was observed. When the dimensional crossover occurs, a temperature region in which two-dimensional and three-dimensional fluctuations occur simultaneously was found in the intermediate temperature region.

Phase transition dimensionality crossover from two to three dimensions in a trapped ultracold atomic Bose gas

The equilibrium properties of a weakly interacting atomic Bose gas across the Berezinskii-Kosterlitz-Thouless (BKT) and Bose-Einstein condensation (BEC) phase transitions are numerically investigated through a dimensionality crossover from two to three dimensions. The crossover is realized by confining the gas in an experimentally feasible hybridized trap which provides homogeneity along the planar $xy$ directions through a box potential in tandem with a harmonic transverse potential along the transverse $z$ direction. The dimensionality is modified by varying the frequency of the harmonic trap from tight to loose transverse trapping. Our findings, based on a stochastic (projected) Gross-Pitaevskii equation, showcase a continuous shift in the character of the phase transition from BKT to BEC, and a monotonic increase of the identified critical temperature as a function of dimensionality, with the strongest variation exhibited for small chemical potential values up to approximately twice the transverse confining potential.

Coulomb Screening and Scattering in Atomically Thin Transistors across Dimensional Crossover.

Layered two-dimensional dichalcogenides are potential candidates for post-silicon electronics. Here, we report insightfully experimental and theoretical studies on the fundamental Coulomb screening and scattering effects in these correlated systems, in response to the changes of three crucial Coulomb factors, including electric permittivity, interaction distance, and density of Coulomb impurities. We systematically collect and analyze the trends of electron mobility with respect to the above factors, realized by synergic modulations on channel thicknesses and gating modes in dual-gated MoS2 transistors with asymmetric dielectric cleanliness. Strict configurative form factors are developed to capture the subtle parametric changes across dimensional crossover. A full diagram of the carrier scattering mechanisms, in particular on the pronounced Coulomb scattering, is unfolded. Moreover, we clarify the presence of up to 40% discrepancy in mobility by considering the permittivity modification across dimensional crossover. The understanding is useful for exploiting atomically thin body transistors for advanced electronics.

Dimensional crossover in self-intercalated antiferromagnetic V5S8 nanoflakes

Electronic and magnetic ordered states are strongly correlated to the dimensions of matter. Here we report a dimensional crossover in self-intercalated antiferromagnetic ${\mathrm{V}}_{5}{\mathrm{S}}_{8}$ nanoflakes. The transition of three-dimensional (3D) to two-dimensional (2D) transport, evidenced by thickness-independent conductivity, occurs when the thickness of ${\mathrm{V}}_{5}{\mathrm{S}}_{8}$ flakes is reduced to \ensuremath{\sim}7.3 nm. At low temperatures, 3D transport follows Fermi liquid behavior, but 2D transport suggests the emergence of Kondo physics with a logarithmic dependence on the temperature and a negative magnetoresistance of a 5.0 nm thick ${\mathrm{V}}_{5}{\mathrm{S}}_{8}$ flake at low temperatures for both in-plane and perpendicular magnetic fields. At temperatures higher than 6 K, the magnetoresistance is positive and parabolically dependent on the magnetic field, indicating suppression of the antiferromagnetic order. Based on a simple magnon gas model, a temperature-independent effective magnon moment $(\ensuremath{\sim}1g{\ensuremath{\mu}}_{B})$ is extracted from the Hall coefficient for all ${\mathrm{V}}_{5}{\mathrm{S}}_{8}$ flakes with different thicknesses. Our results reveal that dimensional crossover plays an important role in tuning the electronic properties in 2D metallic transition-metal dichalcogenides (TMDs).

Thermoelectric Hall Effect at High-Magnetic-Field Quantum Limit in Graphite as a Nodal-Line Semimetal

The high-magnetic-field thermoelectric effect in nodal-line semimetals with straight nodal lines was investigated. Three-dimensional (3D) Dirac/Weyl semimetals exhibit constant thermoelectric Hall conductivity at the high-magnetic-field quantum limit, resulting in a boundless linear increase of Seebeck coefficient. This is known as the quantized thermoelectric Hall effect (QTHE), and is expected to lead to high-performance thermoelectricity at low temperatures. Here, in addition to Dirac/Weyl semimetals, we demonstrated that 3D semimetals with straight nodal lines can also exhibit the QTHE under high magnetic fields. As a candidate material for experimental validation, we discussed the thermoelectric properties of bulk graphite. Furthermore, we investigated the dimensional crossover of thermoelectricity to two-dimensional behavior in thin-film graphite.

Resistance anomaly and linear magnetoresistance in thin flakes of itinerant ferromagnet Fe3GeTe2

Research interests in recent years have expanded into quantum materials that display novel magnetism incorporating strong correlations, topological effects, and dimensional crossovers. Fe3GeTe2 represents such a two-dimensional van der Waals platform exhibiting itinerant ferromagnetism with many intriguing properties. Up to date, most electronic transport studies on Fe3GeTe2 have been limited to its anomalous Hall responses while the longitudinal counterpart (such as magnetoresistance) remains largely unexplored. Here, we report a few unusual transport behaviors on thin flakes of Fe3GeTe2. Upon cooling to the base temperature, the sample develops a resistivity upturn that shows a crossover from a marginally –ln T to a –T 1/2 dependence, followed by a lower-temperature deviation. Moreover, we observe a negative and non-saturating linear magnetoresistance when the magnetization is parallel or antiparallel to the external magnetic field. The slope of the linear magnetoresistance also shows a nonmonotonic temperature dependence. We deduce an anomalous contribution to the magnetoresistance at low temperatures with a scaling function proportional –HT 1/2, as well as a temperature-independent linear term. Possible mechanisms that could account for our observations are discussed.

Anisotropic suppression of hyperuniformity of elastic systems in media with planar disorder

Disordered hyperuniform materials with vanishing long-wavelength density fluctuations are attracting attention due to their unique physical properties. In these systems, the large-scale density fluctuations are strongly suppressed as in a perfect crystal, even though the system can be disordered like a liquid. Yet, hyperuniformity can be affected by the different types of quenched disorder unavoidably present in the host medium where constituents are nucleated. Here, we use vortex matter in superconductors as a model elastic system to study how planar correlated disorder impacts the otherwise hyperuniform structure nucleated in samples with weak point disorder. Planes of defects suppress hyperuniformity in an anisotropic fashion: while in the transverse direction to defects the long-wavelength density fluctuations are non-vanishing, in the longitudinal direction they are smaller and the system can eventually recover hyperuniformity for sufficiently thick samples. Our findings stress the need of considering the nature of disorder and thickness-dependent dimensional crossovers in the search for novel hyperuniform materials.

Dimensional crossovers in the Gaussian critical fluctuations above Tc of two-layer and three-layer superconductors

By using a Ginzburg–Landau functional in the Gaussian approximation, we calculate the energy of superconducting fluctuations above the transition, at zero external magnetic field, of a system composed by a small number N of parallel two-dimensional superconducting planes, each of them Josephson coupled to its first neighbour, with special focus in the N = 2 and 3 cases. This allows us to obtain expressions for the critical contributions to various observables (fluctuation specific heat and magnetic susceptibility and Aslamazov–Larkin paraconductivity). Our results suggest that these systems may display deviations from pure 2D behaviour and interesting crossover effects, with both similitudes and differences to those known to occur in infinite-layers superconductors. Some challenges for future related research are also outlined.