Phases In Two-dimensional Systems Research Articles

Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study

Coupled-wire constructions have been widely applied to quantum Hall systems and symmetry-protected topological (SPT) phases. In this Letter, we use the coupled one-dimensional nonchiral Luttinger liquids with domain-wall structured mass terms as quantum wires to construct the crystalline higher-order topological superconductors (HOTSC) in two-dimensional interacting fermionic systems by two representative examples: $D_4$-symmetric class-D HOTSC and $C_4$-symmetric class-BD\1 HOTSC, with Majorana corner modes on the edge. Furthermore, based on the coupled-wire constructions, the quantum phase transition between different phases of 2D HOTSC by tuning the inter-wire couplings is investigated in a straightforward way.

Valley-polarized quantum anomalous Hall phase in bilayer graphene with layer-dependent proximity effects

Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by reversing the sign of the exchange interaction. By performing quantum transport calculations in disordered systems, the chirality and resilience of the valley-polarized edge state are demonstrated. Our findings provide a promising route to engineer a topological phase that could enable low-power electronic devices and valleytronic applications as well as putting forward layer-dependent proximity effects in bilayer graphene as a way to create versatile topological states of matter.

Real-space observation of topological invariants in 2D photonic systems.

Topological materials are capable of inherently robust transport and propagation of physical fields against disorder and perturbations, holding the promise of revolutionary technologies in a wide spectrum. Higher-order topological insulators are recently predicted as topological phases beyond the standard bulk-edge correspondence principle, however, their topological invariants have been proven very challenging to observe, even not possible yet by indirect ways. Here, we demonstrate theoretically and experimentally that the topological invariants in two-dimensional systems can be directly revealed in real space by measuring single-photon bulk dynamics. By freely writing photonic lattices with femtosecond laser, we construct and identify the predicted second-order topological insulators, as well as first-order topological insulators with fractional topological winding number. Furthermore, we show that the accumulation and statistics on individual single-particle registrations can eventually lead to the same results of light waves, despite the fact that the development of topological physics was originally based on wave theories, sharing the same spirit of wave-particle nature in quantum mechanics. Our results offer a direct fashion of observing topological phases in two-dimensional systems and may inspire topologically protected artificial devices in high-order topology, high-dimension and quantum regime.

Sequential phase transitions and transient structured fluctuations in two-dimensional systems with a high-density Kagome lattice phase.

We report studies of (i) the isothermal density dependent sequences of phases in two-dimensional systems of particles with repulsive pair potentials devised by Truskett [J. Chem. Phys. 145, 054901 (2016)] and Torquato [Phys. Rev. E 88, 042309 (2013)] to support a high-density Kagome lattice phase and (ii) transient structured fluctuations close to a transition to a Kagome lattice. The commonalities in the sequences of phases in these systems and other 2D systems suggest the existence of a universal mechanism driving all to favor similar packing arrangements as the density is increased, but the simulations also show that the only such general rule proposed, namely, the Süto theorem, is not a necessary condition for the support of multiple distinct lattice structures by a particular pair potential. The transient fluctuations in the liquid close to the liquid-to-Kagome phase transition have Kagome symmetry, whereas deeper in the liquid phase, the fluctuations have hexagonal symmetry. When the transition is string-to-Kagome phase, the transient structured fluctuations in the string phase have both six-fold and other than six-fold symmetries. The path of the string-to-Kagome transition in the Truskett system involves intermediate honeycomb configurations that subsequently buckle to form a Kagome lattice. The path of the string-to-Kagome transition in the Torquato system suggests that the Kagome phase is formed by coiled strings merging together; increasing density generates a Kagome phase with imperfections such as 8-particle rings.

Topological defects in the two-dimensional melting

The melting of crystal phases in two-dimensional systems has been the subject of a large amount of theoretical, numerical and experimental works. Several mechanisms to describe the melting in two dimensions were proposed, e.g., the KTHNY theory and the melting induced by formation of grains boundaries. There are strong evidence that the melting in two dimensions depends crucially on the form and range of the interaction potentials between particles. We report extensive Monte Carlo studies of the melting of the classical two-dimensional crystal for systems of point particles interacting via the potential for and 3; the long ranged interaction is taken into account with the Ewald method. In this contribution, we focus on the statistical analysis of topological defects and of the unbinding transitions of the dislocations and disclinations pairs which permits to obtain a better description of the two-dimensional melting.

Topological superconductivity in a phase-controlled Josephson junction.

Topological superconductors can support localized Majorana states at their boundaries1-5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8-21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

We explore the possibility of a Berezinskii-Kosterlitz-Thouless-like critical phase for the charge degrees of freedom in the intermediate-temperature regime between the charge-ordered and disordered phases in two-dimensional systems with competing short-range Coulomb repulsion. As the simplest example, we investigate the extended Hubbard model with on-site and nearest-neighbor Coulomb interactions on a triangular lattice at half filling in the atomic limit by using a classical Monte Carlo method, and find a critical phase, characterized by algebraic decay of the charge correlation function, belonging to the universality class of the two-dimensional XY model with a $\mathbb{Z}_6$ anisotropy. Based on the results, we discuss possible conditions for the critical phase in materials.

Transformation between spin-Peierls and incommensurate fluctuating phases of Sc-doped TiOCl

Single crystals of ${\mathrm{Sc}}_{x}$${\mathrm{Ti}}_{1\ensuremath{-}x}\text{OCl}(x=0.005)$ have been grown by the vapor phase transport technique. Specific heat measurements prove the absence of phase transitions for 4--200 K. Instead, an excess entropy is observed over a range of temperatures that encompasses the incommensurate phase transition at 90 K and the spin-Peierls transition at 67 K of pure TiOCl. Temperature-dependent x-ray diffraction on ${\mathrm{Sc}}_{x}$${\mathrm{Ti}}_{1\ensuremath{-}x}$OCl gives broadened diffraction maxima at incommensurate positions between ${T}_{c1}=61.5\phantom{\rule{0.16em}{0ex}}(3)$ and $\ensuremath{\sim}90$ K, and at commensurate positions below 61.5 K. These results are interpreted as due to the presence of an incommensurate phase without long-range order at intermediate temperatures, and of a highly disturbed commensurate phase without long-range order at low temperatures. The commensurate phase is attributed to a fluctuating spin-Peierls state on an orthorhombic lattice. The monoclinic symmetry and local structure of the fluctuations are equal to the symmetry and structure of the ordered spin-Peierls state of TiOCl. A novel feature of ${\mathrm{Sc}}_{x}$${\mathrm{Ti}}_{1\ensuremath{-}x}\text{OCl}(x=0.005)$ is a transformation from one fluctuating phase (the incommensurate phase at intermediate temperatures) to another fluctuating phase (the spin-Peierls-like phase). This transformation is not a phase transition occurring at a critical temperature, but it proceeds gradually over a temperature range of $\ensuremath{\sim}10$ K wide. The destruction of long-range order requires much lower levels of doping in TiOCl than in other low-dimensional electronic crystals, like the canonical spin-Peierls compound ${\mathrm{CuGeO}}_{3}$. An explanation for the higher sensitivity to doping has not been found, but it is noticed that it may be the result of an increased two-dimensional character of the doped magnetic system. The observed fluctuating states with long correlation lengths are reminiscent of Kosterlitz--Thouless-type phases in two-dimensional systems.

Tetratic order in the phase behavior of a hard-rectangle system

Previous Monte Carlo investigations by Wojciechowski et al. have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy $1.79{k}_{B}$ per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.