Weyl semimetals represent a significant class of topological gapless materials in three dimensions and have been shown to exhibit three-dimensional quantum Hall effect. However, existing research mainly focuses on scenarios without interactions. Recent studies suggest that the fractional quantum Hall effect can arise in a Weyl semimetal with a one-third filled Landau level under a magnetic field. However, it remains unclear whether more exotic states, such as composite Fermi liquid and MooreRead states, can appear at half filling. Here we surprisingly find the existence of composite Fermi liquid, Moore-Read states and charge density waves in the same Weyl-orbit-based Landau level of a Weyl semimetal and their transitions induced by varying the distance between Weyl points. We attribute these transitions to a significant change in the single-particle wave functions of the Landau level as the distance between Weyl points is varied. Finally, we demonstrate that a transition from composite Fermi liquid to Moore-Read states can be induced by tuning the direction of a magnetic field, a process that is more experimentally accessible.
We use conformal field theory to construct model wavefunctions for a gapless interface between lattice versions of a bosonic Laughlin state and a fermionic Moore-Read state, both at $ν=1/2$. The properties of the resulting model state, such as particle density, correlation function and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wavefunctions also for anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some any…
We develop a proposal to realise a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings $ν=\pm 3+1/2$ and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band…
We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for so…
We study a quantum Hall bilayer system of bosons at total filling factor $ν= 1$, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys.~Rev.~Lett.~{\bf 108}, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and de…
The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured that these modes are superpartners of each other and described by a supersymmetric conformal field theory [1]. We propose a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective spin-3/2 field in the bulk. After breaking supersymmetry through a Goldstino, the spin-3/2 field becomes massive and can be seen as…
Non-Abelian excitations are an interesting feature of many fractional quantum Hall phases, including those phases described by the Moore-Read (or Pfaffian) wave function. However, the detection of the non-Abelian quasiparticles is challenging. Here, we consider a system described by the Moore-Read wave function, and assume that impurity particles bind to its quasiholes. Then, the angular momentum of the impurities, reflected also by the impurity density, provides a useful witness of the physics of the non-Abelian excitations. By demanding that the impurities are constrained to the lowest Landa…
Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
我们研究了半填充双层结构中最低两个朗道能级中分数量子霍尔效应（Fractional quantum Hall effect，FQHE）的量子相图，它是隧穿强度和层间距的函数，即，我们重新审视最低朗道能级填充因子1/2双层问题并做出涉及半填充的第二朗道能级中的双层的新预测（即，填充因子5/2）。使用数值精确对角化，我们调查的重要问题，这个系统是否支持由非阿贝尔摩尔-里德Pfweian状态描述的强隧穿制度的一个非对称性。在最低的朗道水平，我们发现，虽然在原则上，增加（递减）隧穿强度（层分离）可以导致从阿贝尔双组分Halperin 331到非阿贝尔单组分Moore-Read Pfperin状态的转变，在朗道能级最低的Pfronan区域，OHE激发能隙相对较小--我们建立了迄今为止观察到的所有OHE态的一半--填充的最低朗道能级双层最可能由阿贝尔Halperin 331状态描述。在第二个朗道水平，我们作出预测，双层结构将表现出两个不同的分支不可压缩的ECOHE对应的阿贝尔331状态（在中等到低的隧道和大的层分离）和非阿贝尔摩尔-里德Pfavian状态（在大隧道和小的层分离）。这两个分支的观测和它们之间可能的量子相变将是令人信服的证据，支持在第二朗道能级的非阿贝尔Moore-Read Pfronan状态的存在。我们讨论我们的结果在现有的实验和理论工作的背景下。
We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall s…
We present a method for the exact construction of the fully particle-hole symmetric PH-Pfaffian ground state and its charged excitations on a sphere. We adopt the Moore-Read state, but with a nonholomorphic pairing component as in previous studies, and project it to the lowest Landau level. We study the energetics as well as other properties of these states and find that in a pure system interacting with the Coulomb forces the PH-Pfaffian cannot compete with either the Moore-Read state or its particle-hole conjugate, the anti-Pfaffian state, as an explanation for the 5/2-effect.
We study thermodynamic manifestations of the chiral anomaly in disordered Weyl semimetals. We focus, in particular, on the effect which we call 'adiabatic dechiralization,' the phenomenon in which a change in temperature and/or an absorption or release of heat results from applying parallel electric and magnetic fields that change the imbalance of quasiparticles with different chiralities (at different Weyl nodes). This effect is similar to that of adiabatic demagnetization, which is commonly used as a method of low-temperature refrigeration. We describe this phenomenon quantitatively and disc…
The recently discovered type-II Weyl points appear at the boundary between electron and hole pockets. Type-II Weyl semimetals that host such points are predicted to exhibit a new type of chiral anomaly and possess thermodynamic properties very different from their type-I counterparts. In this Letter, we describe the prediction of a type-II Weyl semimetal phase in the transition metal diphosphides MoP$_2$ and WP$_2$. These materials are characterized by relatively simple band structures with four pairs of type-II Weyl points. Neighboring Weyl points have the same chirality, which makes the pred…
On the basis of Chern-Simons field-theoretical description we propose a simple method for derivation of model interactions for Pfaffian paired states. We verify the method in the case of Pfaffian (i.e. Moore - Read) state, and derive a general form of the model interaction in the case of PH Pfaffian. More than one Landau level is needed to establish the correlations of the PH Pfaffian, and we present the values of relevant three-body pseudo-potentials for two Landau levels.
We propose a new topological quantum state of matter---the two-dimensional (2D) Weyl half semimetal (WHS), which features 2D Weyl points at Fermi level belonging to a single spin channel, such that the low-energy electrons are described by fully spin-polarized 2D Weyl fermions. We predict its realization in the ground state of monolayer PtCl$_3$. We show that the material is a half metal with an in-plane magnetization, and its Fermi surface consists of a pair of fully spin-polarized Weyl points protected by a mirror symmetry, which are robust against spin-orbit coupling. Remarkably, we show th…
The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics
