The Halperin $(m,m',n)$ bilayer quantum Hall states are studied on thin cylinders. In this limit, charge density wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the $(331)$ state and the non-abelian Moore-Read state in the thin cylinder limit.
Inspired by the four-fold spin-valley symmetry of relativistic electrons in graphene, we investigate a possible SU(4) fractional quantum Hall effect, which may also arise in bilayer semiconductor quantum Hall systems with small Zeeman gap. SU(4) generalizations of Halperin's wave functions [Helv. Phys. Acta 56, 75 (1983)], which may break differently the original SU(4) symmetry, are studied analytically and compared, at nu=2/3, to exact-diagonalization studies.
We study bilayer Fractional Quantum Hall State also known as Halperin state. We prove that for any filling fractions (positive rational numbers), there are infinite solutions that imply that infinite topological states are corresponding to any given filling fraction. Our results can apply to any charge vectors.
We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at ν=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.
We present a field theory of Jain's composite fermion model as generalised to the bilayer quantum Hall systems. We define operators which create composite fermions and write the Hamiltonian exactly in terms of these operators. This is seen to be a complexified version of the familiar Chern Simons theory. In the mean-field approximation, the composite fermions feel a modified effective magnetic field exactly as happens in usual Chern Simons theories, and plateaus are predicted at the same values of filling factors as Lopez and Fradkin and Halperin . But unlike normal Chern Simons theories, we o…
We study the fractional quantum Hall effect in a bilayer with charge-distribution imbalance induced, for instance, by a bias gate voltage. The bilayer can either be intrinsic or it can be formed spontaneously in wide quantum wells, due to the Coulomb repulsion between electrons. We focus on fractional quantum Hall effect in asymmetric bilayer systems at filling factor nu=4/11 and show that an asymmetric Halperin-like trial wavefunction gives a valid description of the ground state of the system.
The natures of the ground state in a $ν_{\rm T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the Halperin's (1,1,1) state is not relevant in the incompressible regime near the incompressible to compressible transition point in which the Josephson-like effect was observed. The two-particle correlation function shows the deflated correlation hole at this regime. An effective model that can give a good approximation to the ground state is proposed. A connecti…
We consider a fully spin-polarized quantum Hall system with no interlayer tunneling at total filling factor $ν=1/k$ (where $k$ is an odd integer) using the Chern-Simons-Ginzburg-Landau theory. Exploiting particle-vortex duality and the concept of quantum disordering, we find a large number of possible compressible and incompressible ground states, some of which may have relevance to recent experiments of Spielman {\it et.al.}. We find interlayer coherent compressible states without Hall quantization and interlayer-incoherent incompressible with Hall quantization in addition to the usual $(k,k,…
We examine the quantum phase diagram of the fractional quantum Hall effect in the lowest Landau level in half-filled bilayer structures as a function of tunneling strength and layer separation. Using numerical exact diagonalization we investigate the important question of whether this system supports a fractional quantum Hall effect described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. We find that, although it is in principle possible, it is unlikely that the non-Abelian FQHE exists in the lowest Landau level. We establish that all so far observed FQHE states …
We examine the quantum phase diagram of the fractional quantum Hall effect (FQHE) in the lowest two Landau levels in half-filled bilayer structures as a function of tunneling strength and layer separation, i.e., we revisit the lowest Landau level filling factor 1/2 bilayer problem and make new predictions involving bilayers in the half-filled second Landau level (i.e., filling factor 5/2). Using numerical exact diagonalization we investigate the important question of whether this system supports a FQHE described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. In th…
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $ν=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is li…
Half state at $ν_{tot}$ = -1/2 and its transition in Decoupled Twisted Double Bilayer Graphene
Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Research Center for Functional Materials, National Institute for Materials Science（物质材料研究机构功能材料研究中心）；International Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究机构国际纳米材料架构中心）；Center for Quantum Science and Engineering (QSE Center), École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）
Based on the construction of generalized Halperin wave functions, we predict the possible existence of a large class of broken spin symmetry states in bilayer quantum Hall structures, generalizing the recently suggested canted antiferromgnetic phase to many fractional fillings. We develop the appropriate Chern-Simons theory, and establish explicitly that the low-lying neutral excitation is a Goldstone mode and that the charged excitations are bimerons with continuously tunable (through the canted antiferromagnetic order parameter) electric charge on the individual merons.
Transitions from a paired quantum Hall state to another quantum Hall state in bilayer systems are discussed in the framework of the edge theory. Starting from the edge theory for the Haldane-Rezayi state, it is shown that the charging effect of a bilayer system which breaks the SU(2) symmetry of the pseudo-spin shifts the central charge and the conformal dimensions of the fermionic fields which describe the pseudo-spin sector in the edge theory. This corresponds to the transition from Haldane-Rezayi state to Halperin's 331 state, or singlet d-wave to triplet p-wave ABM type paired state in the…
We study the bilayer quantum Hall system at total filling factor ν_T = 1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation firstly assuming that only one momentum Q0 is macroscopically occupied and later we consider t…
We derive the effective Hamiltonian for the composite fermion in double-layer quantum Hall systems with inter-layer tunneling at total Landau-level filling factor $ν=1/m$, where $m$ is an integer. We find that the ground state is the triplet p-wave BCS pairing state of the composite fermions. At $ν=1/2$, the ground state of the system evolves from the Halperin $(3,3,1)$-state toward the Pfaffian-state with increasing the tunneling amplitude. On the other hand, at $ν=1$, the pairing state is uniquely determined independent of tunneling amplitude.
We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331 Halperin states and include their fractional descendants at lower filling factors; the former is easily realized experimentally while the latter is a candidate for the experimentally observed quantum Hall state at a total filling factor of 1/2 in bilayers. We discuss the experimentally interesting observables that involve just one chiral edge of the sample and th…
Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe$_2$
We examine the possibility of creating the Moore-Read Pfaffian in the lowest Landau level when the multicomponent Halperin 331 state (believed to describe quantum Hall bilayers and wide quantum wells at the filling factor $ν=1/2$) is destroyed by the increase of tunneling. Using exact diagonalization of the bilayer Hamiltonian with short-range and long-range (Coulomb) interactions in spherical and periodic rectangular geometries, we establish that tunneling is a perturbation that drives the 331 state into a compressible composite Fermi liquid, with the possibility for an intermediate critical …
We investigate, with the help of Monte-Carlo and exact-diagonalization calculations in the spherical geometry, several compressible and incompressible candidate wave functions for the recently observed quantum Hall state at the filling factor $ν=1/4$ in a wide quantum well. The quantum well is modeled as a two-component system by retaining its two lowest subbands. We make a direct connection with the phenomenological effective-bilayer model, which is commonly used in the description of a wide quantum well, and we compare our findings with the established results at $ν=1/2$ in the lowest Landau…
We consider a number of strongly-correlated quantum Hall states which are likely to be realized in bilayer quantum Hall systems at total Landau level filling fraction ${ν_T}=1$. One state, the $(3,3,-1)$ state, can occur as an instability of a compressible state in the large $d/l_B$ limit, where $d$ and $l_B$ are the interlayer distance and magnetic length, respectively. This state has a hierarchical descendent which is interlayer coherent. Another interlayer coherent state, which is expected in the small $d/l_B$ limit is the well-known Halperin $(1,1,1)$ state. Using the concept of composite …
Two-component fractional quantum Hall systems are providing a major motivation for a large section of the physics community. Here we study two-component fractional quantum Hall systems in the spin-polarized half-filled lowest Landau level (filling factor 1/2) and second Landau level (filling factor 5/2) with exact diagonalization utilizing both the spherical and torus geometries. The two distinct two-component systems we consider are the true bilayer and effective bilayers (wide-quantum-well). In each model (bilayer and wide-quantum-well) we completely take into account inter-layer tunneling a…
Critical Majorana fermion at a topological quantum Hall bilayer transition
School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学学院）；Institute of Natural Sciences, Westlake Institute for Advanced Study（西湖高等研究院自然科学研究院）；Department of Physics, School of Science, Westlake University（西湖大学理学院物理系）；Center for Computational Quantum Physics, Flatiron Institute（西蒙斯平坦研究所计算量子物理中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学校物理实验室，ENS，PSL大学，法国国家科学研究中心，索邦大学，巴黎第七大学，索邦巴黎城）
We observe fractional quantum Hall effect (FQHE) at the even-denominator Landau level filling factor $ν=1/2$ in two-dimensional hole systems confined to GaAs quantum wells of width 30 to 50 nm and having bilayer-like charge distributions. The $ν=1/2$ FQHE is stable when the charge distribution is symmetric and only in a range of intermediate densities, qualitatively similar to what is seen in two-dimensional electron systems confined to approximately twice wider GaAs quantum wells. Despite the complexity of the hole Landau level structure, originating from the coexistence and mixing of the hea…
Using the parton construction, we build a three-dimensional (3D) multilayer fractional quantum Hall state with average filling ν= 1/3 per layer that is qualitatively distinct from a stacking of weakly coupled Laughlin states. The state supports gapped charge e/3 fermionic quasiparticles that can propagate both within and between the layers, in contrast to the quasiparticles in a multilayer Laughlin state which are confined within each layer. Moreover, the state has gapless neutral collective modes, a manifestation of an emergent "photon", which is minimally coupled to the fermionic quasipartic…
Sum rules and density-wave modes in spin-singlet fractional quantum Hall fluids
Institute of Mathematical Sciences（数学科学研究所）；Department of Physics, Indian Institute of Technology Bombay（印度理工学院孟买分校物理系）；Institute for Interdisciplinary Research in Science and Education, ICISE（科学与教育跨学科研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）
Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of …
