We have studied the formation of Hall-qubit (LLL state) in Quantum Hall effect due to the Aharonov-Bhom oscillation of quasiparticles.The spin echo method plays the key role in the topological entanglement of qubits. The proper ratio of fluxes for maximally entangling qubits has also been pointed out. The generation of higher Quantum Hall state may be possible with the help of quantum teleportation.
The topological Hall effect (THE) of electrons in skyrmion crystals is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the skyrmion crystal (THE) or of the corre…
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free bulk-edge effective actions in any dimension. I then present the case of QHE on complex projective spaces and focus on the entanglement entropy for integer QHE in even spatial dimensions. In the case of $ν=1$, a semiclassical analysis shows that the entanglement entropy is proportional to the phase-space area of the entangling surface with a universal overall co…
For weakly disordered fractional quantum Hall phases, the non linear photoconductivity is related to the charge susceptibility of the clean system by a Floquet boost. Thus, it may be possible to probe collective charge modes at finite wavevectors by electrical transport. Incompressible phases, irradiated at slightly above the magneto-roton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields. Non linear conductivity can probe composite fermions' charge excitations in compressible filling factors.
The hallmark of a skyrmion crystal (SkX) is the topological Hall effect (THE). In this Article, we predict and explain an unconventional behavior of the topological Hall conductivity in SkXs. In simple terms, the spin texture of the skyrmions causes an inhomogeneous emergent magnetic field whose associated Lorentz force acts on the electrons. By making the emergent field homogeneous, the THE is mapped onto the quantum Hall effect (QHE). Consequently, each electronic band of the SkX is assigned to a Landau level. This correspondence of THE and QHE allows to explain the unconventional behavior o…
Unconventional fermions with high degeneracies in three dimensions beyond Weyl and Dirac fermions have sparked tremendous interest in condensed matter physics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D) unconventional fermion system with a pair of gapped spin-1 fermions. We find that the original unlimited number of zero energy Landau levels (LLs) in the gapless case develop into a series of bands, leading to a novel QHE phenomenon that the Hall conductance first decreases (or increases) to zero and then revives as an infinite ladder of fine staircase when the Fermi s…
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。
Particle-hole symmetry breaking in the fractional quantum Hall effect has recently been studied both theoretically and experimentally with most works focusing on non-Abelian states in the second electronic Landau level. In this work, we theoretically investigate particle-hole symmetry breaking of incompressible fractional quantum Hall states in the lowest Landau level under the influence of the realistic effect of a finite magnetic field strength. A finite magnetic field induces Landau level and sub-band mixing which are known to break particle-hole symmetry at the level of the Hamiltonian. We…
We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $ν=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in two-dimensional guiding center space emerges from these internal geometric modes. Using the Dirac bracket method, we find that this quantum geometric field theory is a topological non-commutative Chern-Simons theory.Topological indices, such as the guiding center angular momentum (also called the shift) and the guiding center spin, which characterize the fractional qua…
Valley Degenerate 2D Electrons in the Lowest Landau Level
我们报道了在H-终端Si（111）表面上的高迁移率（μ= 325，000 cm ^2/V sec）二维电子系统的低温磁输运测量。当低磁场数据表明一个六重谷简并系统时，我们在所有填充因子ν<=6时观察到积分量子霍尔效应，并发现ν=2在异常窄的温度范围内发展。在ν=3/2附近出现了一个扩展的、完全偶分子的分数量子霍尔体系，与双重谷简并复合费米子（CF）相一致。我们确定活化能和估计CF质量。
We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and non-dissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a non-dissipative Hall viscosity.
We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved background. Using the symmetries of the microscopic electron theory in this massless limit we find a number of constraints on any low-energy effective theory. We find that any low-energy description must couple to a geometry which exhibits nontrivial curvature even on flat space-times. Any composite fermion must have an electric dipole moment proportional an…
We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $π$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau level mixing. For this purpose, we consider a simple mo…
Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time dependent variational approach to quantify these dynamics and give intuitive arguments…
We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermi…
Quantum Hall systems offer the most familiar setting where strong inter-particle interactions combine with the topology of single particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to to develop a microscopic theory capturing both their universal and non-universal properties, when the Hamiltonian is restricted to the non-commutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings $ν={p\over p+1}$. Building on a lowest Landau level desc…
We consider the integer QH state on Riemann surfaces with conical singularities, with the main objective of detecting the effect of the gravitational anomaly directly from the form of the wave function on a singular geometry. We suggest the formula expressing the normalisation factor of the holomorphic state in terms of the regularized zeta determinant on conical surfaces and check this relation for some model geometries. We also comment on possible extensions of this result to the fractional QH states.
Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field form degenerate energy bands, the Landau levels. We discuss the unitary correspondence between states in higher Landau levels and those in the lowest Landau level, where wave functions are holomorphic. We apply this correspondence to many-body systems, in particular we represent effective Hamiltonians and particle densities in higher Landau levels by corresponding quantities in the lowest Landau level.
We study the electronic transport in the lowest Landau level of disordered two-dimensional semimetals placed in a homogeneous perpendicular magnetic field. The material system is modeled by the Bernevig-Hughes-Zhang Hamiltonian, which has zero energy Landau modes due to the material's intrinsic Berry curvature. These turn out to be crucially important for the density of states and the static conductivity of the disordered system. We develop an analytical approach to the diffusion and conductivity based on a self-consistent equation of motion for the mean squared displacement. The obtained valu…
The equivalence between neutral particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. In their quantum descriptions, translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. Here, we exploit the ability to squeeze non-commuting variables to dynamically create a Bose-Einstein condensate occupying a single Landau gauge wavefunction in the lowest Landau level. We directly resolve the extent of the zero-point cycl…
We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH-conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states …
A "modified" variant of the Weierstrass sigma, zeta, and elliptic functions is proposed whereby the zeta function is redefined by $ζ(z)$ $\mapsto$ $\tilde ζ(z)$ $\equiv$ $ζ(z) - γ_2z$, where $γ_2$ is a lattice invariant related to the almost-holomorphic modular invariant of the quasi-modular-invariant weight-2 Eisenstein series. If $ω_i$ is a primitive half-period, $\tildeζ(ω_i)$ = $πω_i^*/A$, where $A$ is the area of the primitive cell of the lattice. The quasiperiodicity of the modified sigma function is much simpler than that of the original, and it becomes the building block for the modula…
