Phase Transitions In Two-dimensional Systems Research Articles

Polarization jumps across topological phase transitions in two-dimensional systems

Polarization jumps across topological phase transitions in two-dimensional systems

Systematic study for two-dimensional Z2 topological phase transitions at high-symmetry points in all layer groups

We construct a general theory of $Z_2$ topological phase transitions in two-dimensional systems with time-reversal symmetry. We investigate the possibilities of $Z_2$ topological phase transitions at band inversions at all high-symmetry points in $k$-space in all the 80 layer groups. We exclude the layer groups with inversion symmetry because the $Z_2$ topological phase transition is known to be associated with band inversions with an exchange of parities. Among the other layer groups, we find 21 layer groups with insulator-to-insulator transitions with band inversion, and this problem is finally reduced to five point groups $C_3, C_4, C_6, S_4$, and $C_{3h}$. We show how the change of the $Z_2$ topological invariant at a band inversion is entirely determined by the irreps of occupied and unoccupied bands at the high-symmetry point. For example, in the case of $C_3$, we show that the $Z_2$ topological invariants change whenever the band inversion occurs between two Kramers pairs whose $C_3$ eigenvalues are $\{e^{\pi i / 3}, e^{-\pi i / 3}\}$ and $\{-1, -1\}$. These results are not included in the theory of symmetry-based indicators or topological quantum chemistry.

Phase Transitions in Two-Dimensional Systems of Janus-like Particles on a Triangular Lattice.

We studied the phase behavior of two-dimensional systems of Janus-like particles on a triangular lattice using Monte Carlo methods. The model assumes that each particle can take on one of the six orientations with respect to the lattice, and the interactions between neighboring particles were weighted depending on the degree to which their A and B halves overlap. In this work, we assumed that the AA interaction was fixed and attractive, while the AB and BB interactions varied. We demonstrated that the phase behavior of the systems considered strongly depended on the magnitude of the interaction energies between the AB and BB halves. Here, we considered systems with non-repulsive interactions only and determined phase diagrams for several systems. We demonstrated that the phase diagram topology depends on the temperature at which the close-packed systems undergo the orientational order–disorder transition.

A Career in Physics

Over the course of my career, I have had the opportunity to work on a wide variety of problems in condensed matter physics, benefiting from superb collaborators and environments full of inspiring colleagues. I review here some highlights of my journey so far. Subjects include theories of dynamic critical phenomena, phase transitions in two-dimensional systems, systems with strong disorder, quantum physics of mesoscopic systems, one-dimensional quantum systems, and the quantum Hall effects.

The Berezinskii–Kosterlitz–Thouless Transition and Melting Scenarios of Two-Dimensional Systems

The paper discusses current theories of melting of two-dimensional systems that are mainly based on the concepts of the Berezinskii–Kosterlitz–Thouless (BKT) theory of phase transitions in two-dimensional systems with continuous symmetry. At present there are three basic scenarios of melting of two-dimensional crystals that as shown by computer simulation are implemented in the two-dimensional system of Hertzian spheres used to describe the behavior of a number of soft matter systems. The system demonstrates complex phase behavior with the presence of all three melting scenarios in the various parts of the phase diagram.

Boundary criticality of topological quantum phase transitions in two-dimensional systems

We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: i. the quantum phase transition between a $2d$ $Z_2$ topological order and an ordered phase with spontaneous symmetry breaking; ii. the continuous quantum phase transition between metal and a particular type of Mott insulator (U(1) spin liquid). This theoretical study could be relevant to many purely $2d$ systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.

Liquid-hexatic-solid phase transition of a hard-core lattice gas with third neighbor exclusion.

The determination of phase behavior and, in particular, the nature of phase transitions in two-dimensional systems is often clouded by finite size effects and by access to the appropriate thermodynamic regime. We address these issues using an alternative route to deriving the equation of state of a two-dimensional hard-core particle system, based on kinetic arguments and the Gibbs adsorption isotherm, by the use of the random sequential adsorption with a surface diffusion model. Insight into coexistence regions and phase transitions is obtained through direct visualization of the system at any fractional surface coverage via local bond orientation order. The analysis of the bond orientation correlation function for each individual configuration confirms that first-order phase transition occurs in a two-step liquid-hexatic-solid transition at high surface coverage.

Metal–insulator transition in a transition metal dichalcogenide: Dependence on metal contacts

Transition metal dichalcogenides are promising layered materials for realizing novel nanoelectronic and nano-optoelectronic devices. Molybdenum disulfide (MoS2), a typical transition metal dichalcogenide, has been extensively investigated due to the presence of a sizable band gap, which enables the use of MoS2 as a channel material in field-effect transistors (FET). The gate-voltage-tunable metal–insulator transition and superconductivity using MoS2 have been demonstrated in previous studies. These interesting phenomena can be considered as quantum phase transitions in two-dimensional systems. In this study, we observed that the transport properties of thin MoS2 flakes in FET geometry significantly depend on metal contacts. On comparing Ti/Au with Al contacts, it was found that the threshold voltages for FET switching and metal–insulator transition were considerably lower for the device with Al contacts. This result indicated the significant influence of the Al contacts on the properties of MoS2 devices.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry.

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z_{2} topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Commentary on ‘Ordering, metastability and phase transitions in two-dimensional systems’ J M Kosterlitz and D J Thouless (1973 J. Phys. C: Solid State Phys. 6 1181–203)—the early basis of the successful Kosterlitz–Thouless theory

Commentary on ‘Ordering, metastability and phase transitions in two-dimensional systems’ J M Kosterlitz and D J Thouless (1973 J. Phys. C: Solid State Phys. 6 1181–203)—the early basis of the successful Kosterlitz–Thouless theory

Quantitative Characterization of Hexagonal Packings in Nanoporous Alumina Arrays: A Case Study

Herein is presented a methodology to quantify the degree of hexagonal order in nanoporous alumina arrays (NAA). The approach is inspired by the theory of two-dimensional melting, developed to describe phase transitions in two-dimensional systems that present liquid-crystal-like structures. A local order parameter (LOP) is defined to quantify the degree of hexagonal order of each pore without any arbitrary parameters. Using this LOP, three main qualitative and quantitative analytical tools were developed: (i) a color code to create a map of the LOP, which is a visual tool to identify the degree of order; (ii) quantitative measurements of the average hexagonal order of the sample by measuring the distribution of the LOP and the distribution of the number of neighbors of each pore, and (iii) a quantification of the spatial correlation of the LOP, which indicates how far the hexagonal order is spread in a sample. Because this approach has a strong support on tools developed in statistical mechanics, one can go beyond a simple characterization and interpret the results in terms of phases, as in other physical systems. This may help to unveil the mechanisms behind the self-organization process and long-range order observed in NAA. Moreover, this approach can be trivially extended to characterize other physical systems that form hexagonal packings.

Fazovie perehodi v dvumernih sistemah s neprerivnim virozhdeniem

We discuss the nature and sequence of phase transitions in two-dimensional systems with continuous degeneracy, in which other factors must be taken into account in addition to the interaction of point-like topological excitations, namely, the existence of an additional discrete degeneracy (which leads to the possibility of domain wall formation), the removal of accidental degeneracy by fluctuations, the formation of solitons, and the presence of a random potential acting on vortices. Formally, we discuss various modifications of the two-dimensional XY model, while physical objects that can be described by such models are various arrays of superconducting junctions and noncollinear planar antiferromagnets.

Structural phase transitions in two-dimensional systems: Pb/Ge(111) and Sn/Ge(111)

Abstract The adsorption systems Pb/Ge(111) and Sn/Ge(111) exhibit temperature induced structural phase transitions. We report here a phenomenological analysis of these phase transitions starting from Landau theory. On the basis of symmetry arguments, we show that essential differences are expected theoretically for the critical behav ior of the two interfaces. The influence of hopping defects in these systems is treated using a Landau-like approach. This approach gives us a consistent and general manner to interpret the existing experimental data for these interfaces.

Nematic phase transitions in two-dimensional systems

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an $O(2)$ vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles or correlation functions. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results, while the value of the correlation function exponent at the deconfining transition seems controversial.

Counter-ion condensation and Kosterlitz–Thouless transition

The similarity between counter-ion condensations in polyelectrolyte rod systems andKosterlitz–Thouless phase transitions in two-dimensional systems is discussed at the levelof mean-field theory. Based on the similarity, the renormalization group theory is applied topolyelectrolyte liquid systems aligned in parallel. It is found that the critical separationbetween monovalent charges for the counter-ion condensation is renormalized inpolyelectrolyte liquid systems and becomes shorter than the Bjerrum length which is thecritical separation predicted by the mean-field theory for a dilute solution of polyelectrolyterods.

Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional systems with internal symmetries

The Berezinskii-Kosterlitz-Thouless (BKT) phase transitions in two-dimensional systems with internal continuous Abelian symmetries are investigated. In order for phase transitions to occur, the kinetic part of the action of the system must have conformal invariance, and the vacuum manifold must be degenerate and have a discrete Abelian homotopy group π 1. In this case topological excitations have a logarithmically divergent energy and can be described by effective theories that generalize the two-dimensional Euclidean sine-Gordon theory, which is an effective theory of the original XY model. In particular, the effective actions are found for chiral models on the maximal Abelian tori T G of the simple compact Lie groups G. The critical properties of the possible effective theories are found, and it is shown that they are characterized by the Coxeter numbers h G of lattices of the \(\mathbb{A},\mathbb{D},\mathbb{E}\) and ℤ series and can be interpreted as properties of conformal theories with an integer central charge C=n, where n is the rank of the groups π 1 and G. The possibility of reconstructing the complete symmetry of G in the massive phase is also discussed.

Classification of line tension

The classification of line tension has been given distinguishing between the mechanical line tension and the thermodynamic one as related to the excess mechanical stress at the phase linear boundary and the specific work of formation of a new linear phase boundary, respectively. Three types of line tension are characterised: the line tension in two-dimensional heterogeneous systems, the line tension at the three phase contact line, and the effective line tension in the presence of deformation along the three phase contact line. Phase transitions in two-dimensional systems, the effect of roughness of the three phase contact line and the anisotropy of the contact angle on deformed elastomeric surfaces have been discussed.

Wetting controlled phase transitions in two-dimensional systems of colloids

The phase behavior of disk colloids, embedded in a two-dimensional fluid matrix that undergoes a first-order phase transition, is studied in the complete wetting regime where the thermodynamically metastable fluid phase is stabilized at the surface of the disks. In dilute collections of disks, the tendency to minimize the extent of the fluid-fluid interface and the extent of the unfavorable wetting phase in the system gives rise to aggregation phenomena and to separation of large domains of disks that have the characteristics of bulk colloidal phases. The conditions for phase transitions among cluster gas, liquid, and solid phases of the disk colloids are determined from the corresponding values of the disk chemical potential within an analytic representation of the grand partition function for the excess energy associated with a gas of disk clusters in the low-disk-density limit. The wetting effective-interface potential is combined with the disk interaction potential in associating an internal energy with each one of the clusters. The theory can thus be applied to any type of interaction potential among disks, provided that the free energy associated with the corresponding bulk colloidal phases is available. A phase diagram is calculated explicitly for the case of hard disks on the basis of an analytical approximation for the free energy of the hard disk fluid phase and the generalized effective liquid approximation for the free energy of the hard disk solid phase.

Theory of phase transitions in two-dimensional systems

A detailed description of phase transitions in two dimensions is presented based on the two-dimensional classical XY model. After describing the basic physics of topological ordering, the starting model Hamiltonian is constructed for a detailed study. Following this, a direct space renormalization programme is presented. The obtained phase transition is analysed in detail based on the scaling equations. The systematic renormalization group calculation up to third order based on field-theoretical techniques is also presented. The notion of topological excitations from the viewpoint of the dual model is analysed in detail. The D > 2 cases are analysed through the three-dimensional XY model and layered systems. This article is pedagogical in nature and is intended to be accessible to any graduate student or physicist who is not an expert in this field.

Phase transitions and critical phenomena in strongly chemisorbed adlayers: Influence of defects

Phase diagrams and, more severely, critical properties of continuous phase transitions in two-dimensional systems can strongly be changed by the presence of defects on the surface. We focus on the example of adsorbed atomic hydrogen on Ni(111). Although strongly chemisorbed, the phase diagram of this system is sensitive to isotopic mixtures. Finite energies of mixing and changes of the order-disorder phase transition of the (2 × 2) phase from continuous to first order were found. The critical properities of this order-disorder transition are changed by the presence of preadsorbed oxygen concentrations of 0.3% to 3% of a monolayer. The result is a crossover from 4-state Potts exponents far away from T c to Ising-like exponents closer to T c . These effects can well be separated from finite size effects, which are present in addition. The influence of steps on the critical properties is particularly interesting, if the order of the adsorbate is not interupted by steps. In this case, a similar change of critical exponents is seen, as for O/Ru(0001)−p(2 × 2). These results are discussed in the framework of random disorder.