Landau Level Research Articles

General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity while insulators with zero Chern number present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry, which can be identified as a new type of multiferroic coupling. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the integer quantum Hall effect.

Second Landau level projection of antiholomorphic Pfaffian wave functions

We propose a new state described by the second Landau level (SLL) projection of a generalized Moore-Read Pfaffian wavefunction with an antiholomorphic pairing component. Unlike the PH-Pfaffian state which is described by the lowest Landau level (LLL) projection of the same antiholomorphic Pfaffian wavefunction, we find the proposed state, which we call the SLL PH-Pfaffian, represents a gapped, incompressible phase, and provides an excellent description for the exact ground state of finite-size SLL Coulomb-interacting electrons over a range of the short distance interaction strength. We also find the SLL PH-Pfaffian, when mapped to the LLL, has a very large overlap and the same low-energy orbital entanglement spectrum structures with the anti-Pfaffian state. We discuss possible interpretations of our results on the nature of the topological order of both states.

Magnetosonics with Landau levels in GaAs semiconductor systems

The propagation of low frequency electromagnetic magnetosonic waves in a quantum magneto electron–hole plasma is investigated. Both of the semiconductor plasma species are magnetically quantized at equilibrium. The quantization is included through recoil effect and Landau effects on applying quantum hydrodynamic model (QHD). Analytical results of quantum hydrodynamical model are then verified numerically for GaAs plasma system.

Chiral Separation Effect in a Quark–Gluon Plasma

An expression for the chiral separation effect in a quark–gluon plasma has been derived using the method of field correlators by expanding in Landau levels.

Ideal unconventional charge-2 Dirac fermions in an ultralightweight chiral crystal

When topology meets chirality, it is of great interest to search for possible topological properties in chiral crystals, thereby achieving the effect of making $1+1$ greater than 2. Here, we accomplish a complete list of topological charge-2 (C-2) Dirac fermions based on 65 S\"ohncke space groups. Such emergent fermions occurring in chiral crystals enjoy a higher topological charge number and exhibit more unique characteristics compared to C-0 cases, including multiple Fermi arcs extending to most of the Brillouin zone. For material realization, we propose that an ultralightweight chiral crystal ${\mathrm{N}}_{4}\mathrm{Cl}$ is a high-quality C-2 Dirac semimetal, where the seductive nodal points reside at the Fermi level and exhibit a large linear energy range to overcome the interruption of irrelevant bands. More interestingly, the doubly degenerate Landau levels are described by a Kramers-like degeneracy in such a C-2 Dirac fermion, featuring a doubly degenerate zero mode. Furthermore, the topological phase transitions from Dirac to Weyl states of ${\mathrm{N}}_{4}\mathrm{Cl}$ can be manipulated by applying shear strains. These fascinating findings will certainly evoke continued exploration of unconventional Dirac semimetals, in turn leading to extensive application prospects and uncommon insights.

Entanglement entropy and hyperuniformity of Ginibre and Weyl–Heisenberg ensembles

We show that, for a class of planar determinantal point processes (DPP) {mathcal {X}}, the growth of the entanglement entropy S({mathcal {X}}(Omega )) of {mathcal {X}} on a compact region Omega subset {mathbb {R}}^{2d}, is related to the variance {mathbb {V}}left( {mathcal {X}}(Omega )right) as follows: VX(Ω)≲SX(Ω)≲VX(Ω).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} {\\mathbb {V}}\\left( {\\mathcal {X}}(\\Omega )\\right) \\lesssim S\\left( \\mathcal {X(} \\Omega \\mathcal {)}\\right) \\lesssim {\\mathbb {V}}\\left( {\\mathcal {X}}(\\Omega )\\right) . \\end{aligned}$$\\end{document}Therefore, such DPPs satisfy an area lawSleft( {mathcal {X}}_{g} mathcal {(}Omega mathcal {)}right) lesssim left| partial {Omega } right| , where partial {Omega } is the boundary of Omega if they are of Class I hyperuniformity ({mathbb {V}}left( {mathcal {X}} (Omega )right) lesssim left| partial {Omega }right| ), while the area law is violated if they are of Class II hyperuniformity (as Lrightarrow infty , {mathbb {V}}left( {mathcal {X}} (LOmega )right) sim C_{Omega }L^{d-1}log L). As a result, the entanglement entropy of Weyl–Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity.

Fermi-Arc Metals.

We predict a novel metallic state of matter that emerges in a Weyl-semimetal superstructure withspatially varying Weyl-node positions. In the new state, the Weyl nodes are stretched into extended, anisotropic Fermi surfaces, which can be understood as being built from Fermi arclike states. This "Fermi-arc metal" exhibits the chiral anomaly of the parental Weyl semimetal. However, unlike in the parental Weyl semimetal, in the Fermi-arc metal the "ultraquantum state," in which the anomalous chiral Landau level is the only state at the Fermi energy, is already reached for a finite energy window at zero magnetic field. Thedominance of the ultraquantum state implies a universal low-field ballistic magnetoconductance and the absence of quantum oscillations, making the Fermi surface "invisible" to de Haas-van Alphen and Shubnikov-de Haas effects, although it signifies its presence in other response properties.

Quantum oscillations in field-induced correlated insulators of a moiré superlattice

We report an observation of quantum oscillations (QOs) in the correlated insulators with valley anisotropy of twisted double bilayer graphene (TDBG). The anomalous QOs are best captured in the magneto resistivity oscillations of the insulators at v = −2, with a period of 1/B and an oscillation amplitude as high as 150 kΩ. The QOs can survive up to ∼10 K, and above 12 K, the insulating behaviors are dominant. The QOs of the insulator are strongly D dependent: the carrier density extracted from the 1/B periodicity decreases almost linearly with D from −0.7 to −1.1 V/nm, suggesting a reduced Fermi surface; the effective mass from Lifshitz-Kosevich analysis depends nonlinearly on D, reaching a minimal value of 0.1 me at D = ∼ −1.0 V/nm. Similar observations of QOs are also found at v = 2, as well as in other devices without graphite gate. We interpret the D sensitive QOs of the correlated insulators in the picture of band inversion. By reconstructing an inverted band model with the measured effective mass and Fermi surface, the density of state at the gap, calculated from thermal broadened Landau levels, agrees qualitatively with the observed QOs in the insulators. While more theoretical understandings are needed in the future to fully account for the anomalous QOs in this moiré system, our study suggests that TDBG is an excellent platform to discover exotic phases where correlation and topology are at play.

Zeeman-Stark problem in a two-dimensional disk

Under a perpendicular magnetic field, electrons in two-dimensional disks occupy quantum-confined Landau levels. By analyzing the electric polarizability of such states, we reveal an extreme sensitivity to confinement. Hence, an exponential increase with magnetic field or disk size is found and ascribed to the linear Zeeman effect. In contrast, if the balance between linear and quadratic Zeeman terms is slightly reduced, due to, e.g., addition of a nonmagnetic parabolic potential, the polarizability varies nonmonotonically with field strength and eventually vanishes. The analysis is based on a compact exact expression for the polarizability valid for arbitrary magnetic field, disk size, and linear Zeeman strength.

Noncommutative $$SO(2,3)_{\star }$$ gauge theory of gravity

Topological gravity (in the sense that it is metric-independent) in a 2n-dimensional spacetime can be formulated as a gauge field theory for the AdS gauge group $$SO(2,2n-1)$$ by adding a multiplet of scalar fields. These scalars can break the gauge invariance of the topological gravity action, thus making a connection with Einstein’s gravity. This review is about a noncommutative (NC) star-product deformation of the four-dimensional AdS gauge theory of gravity, including Dirac spinors and the Yang–Mills field. In general, NC actions can be expanded in powers of the canonical noncommutativity parameter $$\theta$$ using the Seiberg–Witten map. The leading-order term of the expansion is the classical action, while the higher-order $$\theta$$ -dependent terms are interpreted as new types of coupling between classical fields due to spacetime noncommutativity. We study how these perturbative NC corrections affect the field equations of motion and derive some phenomenological consequences, such as NC-deformed Landau levels of an electron. Finally, we discuss how topological gravity in four dimensions (both classical and noncommutative) appears as a low-energy sector of five-dimensional Chern–Simons gauge theory in the sense of Kaluza–Klein reduction.

Field-induced chiral transitions in the Weyl semimetal TaP

The chiral anomaly effect has been regarded as a hallmark of Weyl semimetals. While most research focuses on the change of electrical conductivity due to the chiral charge-pumping effect, these transport measurements are accompanied by other effects such as weak antilocalization which are difficult to exclude. Also, the magnetic field intensity at which the energy dispersion of the Landau level starts to display the chiral anomaly effect is hard to identify. Here, we report the evolutionary process of the energy dispersion of the zeroth Landau level under increasing magnetic fields, and we elucidate the relationship between the chiral Landau level and the Fermi level via magneto-optical measurements in Weyl semimetal TaP. Two series of Landau-level transitions have been extracted and fitted well to a massless Weyl fermion model and a classical semiconductor model, respectively. The field-induced chiral Landau-level transition is obtained from a comparison between the spectra under Voigt geometry and Faraday geometry in an increasing magnetic field. The chiral nature of the zeroth Landau level is found to enhance with the increase of magnetic field and clearly manifests in the magneto-optical spectrum above 13 T. The state transition of the zeroth Landau level can be explained by the strength of the field-induced chiral anomaly effect and the position of the Fermi level. These magneto-optical results unveil the chiral Landau-level transitions in TaP, which serves as an ideal material platform to analyze the chiral anomaly effect.

Composite Fermion Pairing Induced by Landau Level Mixing.

Pairing of composite fermions provides a possible mechanism for fractional quantum Hall effect at even denominator fractions and is believed to serve as a platform for realizing quasiparticles with non-Abelian braiding statistics. We present results from fixed-phase diffusion MonteCarlo calculations which predict that substantial Landau level mixing can induce a pairing of composite fermions at filling factors ν=1/2 and ν=1/4 in the l=-3 relative angular momentum channel, thereby destabilizing the composite-fermion Fermi seas to produce non-Abelian fractional quantum Hall states.

Chiral Separation Effect in a Quark–Gluon Plasma

An expression for the chiral separation effect in a quark–gluon plasma has been derived using the method of field correlators by expanding in Landau levels.

De Haas–van Alphen effect under rotation

We explored the interplay between magnetic field and rotation in the de Hass--van Alphen oscillation. The effect is found to be reduced because of the reweighting of different angular momentum states within the same Landau level by rotation energy. The implications of our results on high energy physics and condensed matter physics are discussed.

Medium effect on anisotropic surface tension of magnetized quark matter

The thermodynamics of finite size quark matter in the quasiparticle model is self-consistently constructed by an effective bag function, which presents the medium effect to the confinement. We obtained completely analytic surface tension in the strong magnetic field with the multiple reflection expansion. The anisotropic structure is demonstrated by the splitting of the longitudinal and transverse surface tensions. The anisotropy of the surface tension could be enhanced by an increase of the magnetic field. The analytical surface tension is modified by an additional term related to the bag function. For strong enough magnetic fields, the increase of the longitudinal surface tension is proportional to the magnetic field.On the contrary, the transverse component vanishes due to all quarks locating in the lowest landau level.

Modification of Landau Levels in a 2D Ring Due to Rotation Effects and Edge States

AbstractThe properties of a 2D quantum ring under rotating and external magnetic field effects are investigated. The Landau levels and their inertial effects on them are initially analyzed. Among the results obtained, it is emphasized that the rotation lifted the degeneracy of Landau levels. The second part deals with the electronic confinement in a 2D ring modeled by a hard wall potential. The eigenstates are described by Landau states as long as they are not too close to the ring edges. On the other hand, near the ring edges, the energies increase monotonically. These states are known as edge states. Edge states have a significant role in the physical properties of the ring. Thus, the Fermi energy and magnetization are analyzed. In the specific case of magnetization, two approaches are considered. In the first approach, an analytical result for magnetization is obtained but without considering rotation. Numerical results show the de Haas‐Van Alphen (dHvA) oscillations. In the second approach, rotating effects are considered. In addition to the dHvA oscillations, the Aharonov–Bohm‐type (AB) oscillations are verified, which are associated with the presence of edge states. The effects of rotation on the results are discussed and it is found that rotation is responsible for inducing AB oscillations.

Dynamically screened strongly quantized electron transport in binary neutron-star merger

We examine electron-transport coefficients in magnetized hot and dense electron-ion plasma relevant in binary neutron star merger simulation. We calculate electrical and thermal conductivities in low density, high temperature, highly magnetized plasma of binary neutron star mergers where quantum oscillatory behavior of electrons emerge. For pronounced thermodynamic effects, we consider zeroth Landau level population of electrons for the calculation of conductivity. We solve Boltzmann equation in presence of magnetic field to obtain the dissipative components of electrical and thermal conductivities. The dissipative coefficients are formulated considering frequency dependent dynamical screening in the quantized electron-ion scattering rate. Numerical estimations show that the effect of dynamical screening of photon propagator on electrical and thermal conductivities is pronounced. We observe that dynamical screening reduces the maxima of both the electrical and thermal conductivities by factors of thirty one and twenty respectively leading to a reduction in the corresponding time scales of these coefficients. The common scaling factor between electrical and thermal conductivity is also observed to follow cubic relationship with temperature violating Wiedemann–Franz law.

Geometric fluctuation of conformal Hilbert spaces and multiple graviton modes in fractional quantum Hall effect

Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.

The affine ensemble: determinantal point processes associated with the $ax + b$ group

We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane $\mathbb{C}^{+}$ associated with the $ax + b$ (affine) group, depending on an admissible Hardy function $\psi$. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set $\Omega \subset \mathbb{C}^{+}$. As a special case one recovers the DPP related to the weighted Bergman kernel. When $\psi$ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.

Dipole representation of half-filled Landau level

We introduce a variant of a dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under an exchange of particles and holes. This is implemented by a special constraint on a composite fermion and a composite hole degree of freedom (of an enlarged space), which makes the resulting composite particle (dipole) a symmetric object. We study an effective Hamiltonian that commutes with the constraint on the physical space and fulfills the requirement for boost invariance on the Fermi level. The calculated Fermi liquid parameter ${F}_{2}$ is in good agreement with numerical investigations in Phys. Rev. Lett. 121, 147601 (2018).