States In Two-dimensional Systems Research Articles

Three-dimensional higher-order saddle-point-induced flatbands in Co-based kagome metals

The saddle point (Van Hove singularity) exhibits a divergent density of states in two-dimensional systems, leading to fascinating phenomena such as strong correlations and unconventional superconductivity, yet it is seldom observed in three-dimensional (3D) systems. In this work we find two types of 3D higher-order saddle points (HOSPs) in emerging 3D kagome metals YbCo6Ge6 and MgCo6Ge6. Both HOSPs exhibit a singularity in their density of states, which is significantly enhanced compared to the ordinary saddle point. The HOSP near the Fermi energy generates a flatband extending a large area in the Brillouin zone, potentially amplifying the correlation effect and fostering electronic instabilities. Two types of HOSPs exhibit distinct robustness upon element substitution and lattice distortions in these kagome compounds. Our work paves the way for engineering exotic band structures, such as saddle points and flatbands, and exploring interesting phenomena in Co-based kagome materials. Published by the American Physical Society 2024

Power-law correlation in the homogeneous disordered state of anisotropically self-propelled systems

Self-propelled particles display unique collective phenomena, due to the intrinsic coupling of density and polarity. For instance, the giant number fluctuation appears in the orientationally ordered state, and the motility-induced phase separation appears in systems with repulsion. Effects of strong noise typically lead to a homogeneous disordered state, in which the coupling of density and polarity can still play a significant role. Here we study universal properties of the homogeneous disordered state in two-dimensional systems with uniaxially anisotropic self-propulsion. Using hydrodynamic arguments, we propose that the density correlation and polarity correlation generically exhibit power-law decay with distinct exponents (−2 and −4, respectively) through the coupling of density and polarity. Simulations of self-propelled lattice gas models indeed show the predicted power-law correlations, regardless of whether the interaction type is repulsion or alignment. Further, by mapping the model to a two-component boson system and employing non-Hermitian perturbation theory, we obtain the analytical expression for the structure factors, the Fourier transform of the correlation functions. This reveals that even the first order of the interaction strength induces the power-law correlations. Published by the American Physical Society 2024

Droplet-mediated long-range interfacial correlations. Exact field theory for entropic repulsion effects

We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify.

Multifractally-Enhanced Superconductivity in Two-Dimensional Systems with Spin–Orbit Coupling

The interplay of Anderson localization and electron-electron interactions is known to lead to enhancement of superconductivity due to multifractality of electron wave functions. We develop the theory of multifractally-enhanced superconducting states in two-dimensional systems in the presence of spin-orbit coupling. Using the Finkel'stein nonlinear sigma model, we derive the modified Usadel and gap equations that take into account renormalizations caused by the interplay of disorder and interactions. Multifractal correlations induce energy dependence of the superconducting spectral gap. We determine the superconducting transition temperature and the superconducting spectral gap in the case of Ising and strong spin orbit couplings. In the latter case the energy dependence of superconducting spectral gap is convex whereas in the former case (as well as in the absence of spin-orbit coupling) it is concave. Multifractality enhances not only the transition temperature but, in the same way, the spectral gap at zero temperature. Also we study mesoscopic fluctuations of the local density of states in the superconducting state. Similarly to the case of normal metal, spin-orbit coupling reduce the amplitude of fluctuations.

Flat bands and related novel quantum states in two-dimensional systems

In flat bands of two-dimensional materials, the mass of charge carriers increases dramatically and the Coulomb energy of the charge carriers can be much larger than the quenched kinetic energy. When the flat band is partially filled, electron-electron interactions can drive electrons to form exotic correlated phases, such as quantum Hall ferromagnetism, fractional quantum Hall effect, superconductivity, and quantum anomalous Hall effect. Therefore, flat bands in two-dimensional materials have attracted much attention very recently. In the past few years, the strongly correlated phenomena in flat bands have become a hot topic in community of condensed matter physics. There are several different methods, such as using a perpendicular magnetic field, introducing strained structures, and introducing a twist angle, to realize the flat bands in two-dimensional materials. In this review article, we summarize the methods to realize flat bands in two-dimensional systems and introduce the related novel electronic states when the flat band is partially filled.

Multipoint correlation functions at phase separation. Exact results from field theory

We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary n-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.

Quantum metric and correlated states in two-dimensional systems

The recent realization of twisted, two-dimensional, bilayers exhibiting strongly correlated states has created a platform in which the relation between the properties of the electronic bands and the nature of the correlated states can be studied in unprecedented ways. The reason is that these systems allow extraordinary control of the electronic bands’ properties, for example by varying the relative twist angle between the layers forming the system. In particular, in twisted bilayers the low energy bands can be tuned to be very flat and with a nontrivial quantum metric. This allows the quantitative and experimental exploration of the relation between the metric of Bloch quantum states and the properties of correlated states. In this work we first review the general connection between quantum metric and the properties of correlated states that break a continuous symmetry. We then discuss the specific case when the correlated state is a superfluid and show how the quantum metric is related to its superfluid stiffness. To exemplify such relation we show results for the case of superconductivity in magic angle twisted bilayer graphene. We conclude by discussing possible research directions to further elucidate the connection between quantum metric and correlated states’ properties.

Light-induced bound electron states in two-dimensional systems: Contribution to electron transport

In two-dimensional (2D) electron systems, an off-resonant high-frequency circularly polarized electromagnetic field can induce the quasi-stationary bound electron states of repulsive scatterers. As a consequence, the resonant scattering of conduction electrons through the quasi-stationary states and the capture of conduction electrons by the states appear. The present theory describes the transport properties of 2D electron gas irradiated by a circularly polarized light, which are modified by these processes. Particularly, it is demonstrated that irradiation of 2D electron systems by the off-resonant field results in the quantum correction to conductivity of resonant kind.

Twist-projected two-dimensional acoustic topological insulators

Acoustic analogs of electronic or photonic topological insulators provide unique approaches to manipulate sound wave propagation. Inspired by twist-induced topological photonic insulators, here we propose a type of two-dimensional acoustic topological insulator (TI) via projecting a section of a three-dimensional twisting structure to a plane, assembling the projected meta-atoms into metamolecules, and arranging the metamolecules into unit cells to form a honeycomb lattice. It follows that in this acoustic TI, topological phases mimic pseudospin-up and pseudospin-down states, and the pseudospin-orbital couplings are tuned via changing the rotation angles of the meta-atoms, which eventually leads to band inversion. By calculating acoustic band structures, pressure field distributions, and spin Chern numbers of bands, we verify that the topological phase transition occurs around the double Dirac cone and present the topological phase diagram as a function of the rotation angle of the meta-atoms. Once the coupling between adjacent metamolecules is sufficiently strong, mode inversion of topological states emerges. Furthermore, we numerically demonstrate the existence of topologically protected edge states. It is shown that robust pseudospin-dependent one-way transmission is immune to defects at the edge of topological distinct regions, which can be applied to acoustic wave transmissions and communications. Our approach in acoustic systems provides a strategy to explore abundant topological states in two-dimensional systems.

Spin effects in edge transport in two-dimensional topological insulators

Investigations of topological insulators, which are two- and three-dimensional systems with a gap in the bulk spectrum and topologically protected gapless edge states, are of considerable fundamental interest at present. The experiments confirming the presence of the edge states in two-dimensional systems with inverted bands and problems of determining the nature of such states in these experiments are reviewed. Special attention is focused on spin-sensitive experiments since the topological edge states have a nontrivial spin structure.

Stationary states in two-dimensional systems driven by bivariate Lévy noises.

Systems driven by α-stable noises could be very different from their Gaussian counterparts. Stationary states in single-well potentials can be multimodal. Moreover, a potential well needs to be steep enough in order to produce stationary states. Here it is demonstrated that two-dimensional (2D) systems driven by bivariate α-stable noises are even more surprising than their 1D analogs. In 2D systems, intriguing properties of stationary states originate not only due to heavy tails of noise pulses, which are distributed according to α-stable densities, but also because of properties of spectral measures. Consequently, 2D systems are described by a whole family of Langevin and fractional diffusion equations. Solutions of these equations bear some common properties, but also can be very different. It is demonstrated that also for 2D systems potential wells need to be steep enough in order to produce bounded states. Moreover, stationary states can have local minima at the origin. The shape of stationary states reflects symmetries of the underlying noise, i.e., its spectral measure. Finally, marginal densities in power-law potentials also have power-law asymptotics.

Dimensional Crossover of the Fulde–Ferrell–Larkin–Ovchinnikov State in Strongly Pauli-Limited Quasi-One-Dimensional Superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is examined in quasi-one-dimensional s-wave and d-wave superconductors with particular attention paid to the effect of the Fermi-surface anisotropy. The upper critical field $H_{c2}(T)$ is found to exhibit a qualitatively different behavior depending on the ratio of the hopping energies $t_b/t_a$ and the direction of the FFLO modulation vector q, where $t_a$ and $t_b$ are the intra- and interchain hopping energies, respectively. In particular, when $t_b/t_a < 0.1$ and $\mathbf{q} \parallel \mathbf{a}$, we find a novel dimensional crossover of $H_{c2}(T)$ from one dimension to two dimensions, where a is the lattice vector of the most conductive chain. Just below the tricritical temperature $T^*$, the upper critical field $H_{c2}(T)$ increases steeply as in one-dimensional systems, but when the temperature decreases, the rate of increase in $H_{c2}(T)$ diminishes and a shoulder appears. Near $T = 0$, $H_{c2}(T)$ shows a behavior typical of the FFLO state in two-dimensional systems, i.e., an upturn with a finite field at $T = 0$. When the angle between $\mathbf{q}$ and $\mathbf{a}$ is large, the upper critical field curve is convex upward at low temperatures, as in three-dimensional systems, but the magnitude is much larger than that of a three-dimensional isotropic system. For $t_b/t_a > 0.15$, the upper critical fields exhibit a two-dimensional behavior, except for a slight shoulder in the range of $0.2 > t_b/t_a > 0.15$. The upper critical field is maximum for $\mathbf{q} \parallel \mathbf{a}$ both for s-wave and d-wave pairings, while it is only slightly larger than the Pauli paramagnetic limit for $\mathbf{q} \perp \mathbf{a}$. The relevance of the present results to the organic superconductor ${\rm (TMTSF)_2ClO_4}$ is discussed.

Exact theory of intermediate phases in two dimensions

We show how field theory yields the exact description of intermediate phases in the scaling limit of two-dimensional statistical systems at a first order phase transition point. The ability of a third phase to form an intermediate wetting layer or only isolated bubbles is explicitly related to the spectrum of excitations of the field theory. The order parameter profiles are determined and interface properties such as passage probabilities and internal structure are deduced from them. The theory is illustrated through the application to the q-state Potts model and the Ashkin–Teller model. The latter is shown to provide the first exact solution of a bulk wetting transition.

On a symmetry topological classification of edge states in crystalline spin-Hall insulators with the time reversal invariance

Symmetry analysis reveals all types of singularities of the edge states in two-dimensional systems with a boundary (2D → 1D systems), which are invariant under time reversal. Symmetry reasons also provide the matching condition for material functions parameterizing the Hamiltonian at various points of the Brillouin zone. The unified parameterization of the Hamiltonian makes it possible to construct the mapping of trajectories closed in the quasimomentum k in the Brillouin zone into the SU(2) topological group. There are only two equivalence classes of Hamiltonians, which are given by the elements of the first fundamental group Open image in new window . The first type of surface states corresponds to a normal insulator and the second type corresponds to a topological spin-Hall insulator. Comparison with the Open image in new window classification based on the Pfaffian method is performed.

Control and managing of localized states in two-dimensional systems with periodic forcing

We study the formation of localized structures in two-dimensional systems with periodic forcing, showing that these types of systems provide an adequate framework for the study and control of localized structures. Theoretically, we introduce a dissipative ϕ 4 model as a prototype for a bistable spatially forced system, and we show that with different spatial forcings of small amplitudes, such as square or hexagonal grids, this model exhibits a family of localized structures. By changing the forcing parameters, we control the bistability between the various induced patterns. Experimentally, based on an optical feedback with spatially amplitude-modulated beam, we set-up a two-dimensional forced experiment in a nematic liquid crystal cell. By changing the forcing parameters, the system exhibits a family of localized structures that are confirmed by numerical simulations for the average liquid crystal tilt angle.

Microwave magnetoabsorption in two-dimensional electron systems

Magnetoabsorption, microwave-induced resistance oscillations, and zero resistance states in two-dimensional systems are calculated in the framework of the same theory: the microwave driven Larmor orbit model. On one hand, this theory allows to obtain resistance oscillations with multiple peaks, depending on the microwave frequency. On the other hand, it also permits to calculate the microwave magnetoabsorption yielding only one broad peak at the cyclotron resonance condition.

Impurity-related polarizability and photoionization-cross section in [formula omitted] double quantum wells under electric fields and hydrostatic pressure

Double quantum well heterostructures are quite important for the exploration of correlated electron states in two-dimensional systems. By using the variational procedure, within the effective-mass and parabolic-band approximations, the effects of both electric field and hydrostatic pressure on the shallow-donor-impurity related polarizability and photoionization cross-section in GaAs–Ga 1− x Al x As double asymmetric quantum wells are presented. The electric field is considered to be applied along the growth direction. It is found that the impurity binding energy and polarizability can be tuned by means of an applied external electric field or hydrostatic pressure in asymmetric double quantum wells, a behavior which could be used in the design and construction of semiconductor devices. The photoionization cross-section magnitude increases as the pressure and applied electric field are increased, except beyond the Γ – X crossover in the barrier material, where a decrease of the photoionization cross-section is expected due the smaller confinement of the impurity wave function.

Statistics of harmonic measure and winding of critical curves from conformal field theory

Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals. We show how these characteristics are related to local operators of conformal field theory and how they can be computed using conformal invariance of critical systems with central charge c ⩽ 1.

SLE in self-dual critical [formula omitted] spin systems: CFT predictions

The Schramm–Loewner evolution (SLE) describes the continuum limit of domain walls at phase transitions in two-dimensional statistical systems. We consider here the SLE in Z ( N ) spin models at their self-dual critical point. For N = 2 and N = 3 these models correspond to the Ising and three-state Potts model. For N ⩾ 4 the critical self-dual Z ( N ) spin models are described in the continuum limit by non-minimal conformal field theories with central charge c ⩾ 1 . By studying the representations of the corresponding chiral algebra, we show that two particular operators satisfy a two level null vector condition which, for N ⩾ 4 , presents an additional term coming from the extra symmetry currents action. For N = 2 , 3 these operators correspond to the boundary conditions changing operators associated to the SLE 16 / 3 (Ising model) and to the SLE 24 / 5 and SLE 10 / 3 (three-state Potts model). We suggest a definition of the interfaces within the Z ( N ) lattice models. The scaling limit of these interfaces is expected to be described at the self-dual critical point and for N ⩾ 4 by the SLE 4 ( N + 1 ) / ( N + 2 ) and SLE 4 ( N + 2 ) / ( N + 1 ) processes.

Growth of GaNAs/GaAs Multiple Quantum Well by Molecular Beam Epitaxy Using Modulated N Radical Beam Source

GaNAs/GaAs multiple quantum well (MQW) structures have been grown on GaAs(001) substrates by molecular beam epitaxy (MBE) using modulated N radical beam source under optimized conditions, wherein the amount of N2 gas flow, RF-power and shutter sequence are systematically controlled. Clear and flat GaNAs/GaAs interfaces were observed in the cross-sectional transmission electron microscopy (TEM) measurements. Fine MQW structures originating from the precise control of the modulated N radical beam have been demonstrated as clear satellite peaks from the X-ray diffraction (XRD) measurements and sharp photoluminescence (PL) peaks. The step-like behaviors in the absorption spectra which reflect the density of state in two-dimensional systems, were clearly observed for all MQW samples.