Search Results (20)

Three-dimensional topological insulators possess surface-conducting states in the bulk energy gap, which are topologically protected and can be well described as helical 2 + 1 Dirac fermions. The electromagnetic response is given by axion electrodynamics in the bulk, leading to a Maxwell–Chern–Simons theory at the boundary, which is the source of the Hall conductivity. In this paper, we extend the formulation of axion electrodynamics such that it captures higher-derivative corrections to the Hall conductivity. Using the underlying 2 + 1 quantum field theory at the boundary, we employ thermal field theory techniques to compute the vacuum polarization tensor at finite chemical potential in the zero-temperature limit. Applying the derivative expansion method, we obtain higher-order derivative corrections to the Chern–Simons term in 2 + 1 dimensions. To first order the corrections, we find that the Hall conductivity receives contributions proportional to ${\omega }^2$ and ${\mathbf{k}}^2$ from the higher-derivative Chern–Simons term. Finally, we discuss the electrodynamic consequences of these terms on the topological Faraday and Kerr rotations of light, as well as on the image monopole effect. Full article

In the low-energy regime, baryons with $N_f\ge 2$ have long been constructed as skyrmions or through bag models, but such constructions for $N_f=1$ are hindered by the trivial topological structure of the meson field. Recent proposals suggest that one-flavor baryons can instead be interpreted as quantum Hall droplets on the ${\eta }^{\prime }$ domain wall, providing a potential link to quark–hadron continuity at high density. In retrospect, the qualitative or semi-qualitative construction of one-flavor baryons on the ${\eta }^{\prime }$ domain wall reveals that these baryons can be described as quantum Hall droplets, resembling topological solitons akin to skyrmions. Using an effective theory on the ${\eta }^{\prime }$ domain wall, which is conjectured to be the Chern–Simons–Higgs theory, it is discussed that its vortex solution with unit baryon numbers naturally has a spin of $N_c/2$, and thus can be interpreted as a baryon or multi-baryon structure. The particle–vortex duality suggests that quarks carry a fractional topological charge of $1/N_c$ and obey fractional statistics. In terms of chiral bag models, confinement can be attributed to the monopoles confined within the bag, and the vector meson fields on the bag surface are essential for ensuring the correct baryon number in the chiral bag framework, thereby providing deeper insights into baryons as non-trivial topological structures of the meson field. In this paper, we review the progress in this development, with a special focus on the ${\eta }^{\prime }$ domain wall dynamics. Naive extensions to $N_f\ge 2$ are also discussed. Full article

The spin Hall effect for the model Hamiltonian of graphene with Rashba spin–orbit coupling is analyzed by means of a recently derived quantum kinetic theory of the linear response for multi-band electron systems. The latter expresses the interband part of the density matrix in terms of the intraband occupation numbers, which can be obtained as solutions of a Boltzmann transport equation. The analysis, which, in the case of the model here considered, can be carried out in a completely analytical way, thus provides an effective pedagogical illustration of the general theory. While our results agree with those previously obtained with alternative approaches for the same model, our comparatively simpler and more physically transparent derivation illustrates the advantages of our formalism when dealing with non trivial multi-band Hamiltonians. Full article

Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and the EM fields (through which they interact) live in different dimensions. Pseudo-Quantum Electrodynamics (PQED) is a U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM interaction of charged particles confined to a plane. PQED is completely different from QED(2 + 1), namely, Quantum Electrodynamics of a planar gauge field. It produces, for instance, the correct $1/r$ Coulomb potential between static charges, whereas QED(2 + 1) produces $lnr$ potential. In spite of possessing a nonlocal Lagrangian, it has been shown that PQED preserves both causality and unitarity, as well as the Huygens principle. PQED has been applied successfully to describe the EM interaction of numerous systems containing charged particles constrained to move on a plane. Among these are p-electrons in graphene, silicene, and transition-metal dichalcogenides; systems exhibiting the Valley Quantum Hall Effect; systems inside cavities; and bosonization in (2 + 1)D. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics). Full article

Magnetizing the surface states of topological insulators without damaging their topological features is a crucial step for realizing the quantum anomalous Hall (QAH) effect and remains a challenging task. The TI–ferromagnetic material interface system was constructed and studied by the density functional theory (DFT). A two-dimensional magnetic semiconductor CrWI₆ has been proven to effectively magnetize topological surface states (TSSs) via the magnetic proximity effect. The non-trivial phase was identified in the Bi₂Se₃ (BS) films with six quantum layers (QL) within the CrWI₆/BS/CrWI₆ heterostructure. BS thin films exhibit the generation of spin splitting near the TSSs, and a band gap of approximately 2.9 meV is observed at the Γ in the Brillouin zone; by adjusting the interface distance of the heterostructure, we increased the non-trivial band gap to 7.9 meV, indicating that applying external pressure is conducive to realizing the QAH effect. Furthermore, the topological non-triviality of CrWI₆/6QL-BS/CrWI₆ is confirmed by the nonzero Chern number. This study furnishes a valuable guideline for the implementation of the QAH effect at elevated temperatures within heterostructures comprising two-dimensional (2D) magnetic monolayers (MLs) and topological insulators. Full article

The loss of any symmetry in a system leads to quantum problems that are typically very difficult to solve. Such a situation arises for particles with anisotropic mass, like electrons in various semiconductor host materials, where it is known that they may have an anisotropic effective mass. In this work, we consider the quantum problem of a spinless charged particle with anisotropic mass in two dimensions and study the resulting energy and eigenstate spectrum in a uniform constant perpendicular magnetic field when a Landau gauge is adopted. The exact analytic solution to the problem is obtained for arbitrary values of the anisotropic mass using a mathematical technique that relies on the scaling of the original coordinates. The characteristic features of the energy spectrum and corresponding eigenstate wave functions are analyzed. The results of this study are expected to be of interest to quantum Hall effect theory. Full article

The fractional quantum Hall effect was experimentally discovered in 1982. It was observed that the Hall conductivity ${\sigma }_{yx}$ of a two-dimensional electron system is quantized, ${\sigma }_{yx}=e^2/3h$, in the vicinity of the Landau level filling factor $\nu =1/3$. In 1983, Laughlin proposed a trial many-body wave function, which he claimed described a “new state of matter”—a homogeneous incompressible liquid with fractionally charged quasiparticles. Here, I develop an exact diagonalization theory that allows one to calculate the energy and other physical properties of the ground and excited states of a system of N two-dimensional Coulomb interacting electrons in a strong magnetic field. I analyze the energies, electron densities, and other physical properties of the systems with $N\le 7$ electrons continuously as a function of magnetic field in the range $1/4\lesssim \nu <1$. The results show that both the ground and excited states of the system resemble a sliding Wigner crystal whose parameters are influenced by the magnetic field. Energy gaps in the many-particle spectra appear and disappear as the magnetic field changes. I also calculate the physical properties of the $\nu =1/3$ Laughlin state for $N\le 8$ and compare the results with the exact ones. This comparison, as well as an analysis of some other statements published in the literature, show that the Laughlin state and its fractionally charged excitations do not describe the physical reality, neither at small N nor in the thermodynamic limit. The results obtained shed new light on the nature of the ground and excited states in the fractional quantum Hall effect. Full article

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble. Full article

Layered honeycomb magnets with strong atomic spin–orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. $\alpha$-RuCl${}_3$ has been the most promising candidate, and there have been several reports on the realization of sibling compounds $\alpha$-RuBr${}_3$ and $\alpha$-RuI${}_3$ with the same crystal structure. Here, we investigate correlated electronic structures of $\alpha$-RuCl${}_3$ and $\alpha$-RuI${}_3$ by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of $\alpha$-RuI${}_3$, and suggests a potential realization of correlated flat bands with strong spin–orbit coupling and a quantum spin-Hall insulating phase in $\alpha$-RuI${}_3$. Full article

The theory of open quantum systems is applied to study galvano-, thermo-magnetic, and magnetization phenomena in axial symmetric two-dimensional systems. Charge carriers are considered as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is affected by the average collision time that takes effectively into account two-body effects. The functional dependencies of the average collision time on the external uniform magnetic field, concentration and temperature are phenomenologically treated. Analytical expressions are obtained for the tensors of electric and thermal conductivity and/or resistivity. The developed theory is applied to describe the Shubnikov-de Haas oscillations and quantum Hall effect in graphene and GaAs/Al${}_x$Ga${}_{1-x}$As heterostructure. The dependencies of magnetization and thermal conductivity on the magnetic field are also predicted. Full article

Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons. This is a continuous topological parameter space bearing the homotopy of a torus. Since the base localization space has the homotopy of a torus, if we vary the quasi-momentum in a direction, when the edge of the zone is reached, we obtain a closed path. Then, if we lift this loop from the base space to the sections of the sheaf-theoretic fibration induced by the localization of the energy eigenfunctions, we obtain a global topological phase factor which encodes the topological structure of the Brillouin zone. Because it is homotopically equivalent to a torus, the global phase factor turns out to be quantized, taking integer values. The experimental significance of this model stems from the recent discovery that there are observable global topological phase factors in fairly ordinary materials. In this communication, we show that it is the unitary representation theory of the discrete Heisenberg group in terms of commutative modular symplectic variables, giving rise to a joint commutative representation space endowed with an integral and ${\mathbb{Z}}_2$-invariant symplectic form that articulates the specific form of the topological conditions characterizing both the quantum Hall effect and the spin quantum Hall effect under a unified sheaf-theoretic cohomological framework. Full article

The connectivity and inherent frustration of the kagome lattice can produce interesting electronic structures and behaviors in compounds containing this structural motif. Here we report the properties of Pt${}_3$X${}_2$ (X = In and Tl) that adopt a double-layer kagome net structure related to that of the topologically nontrivial high-temperature ferromagnet Fe₃Sn₂ and the density wave hosting compound V₃Sb₂. We examined the structural and physical properties of single crystal Pt₃Tl₂ and polycrystalline Pt₃In₂ using X-ray and neutron diffraction, magnetic susceptibility, heat capacity, and electrical transport measurements, along with density functional theory calculations of the electronic structure. Our calculations show that Fermi levels lie in pseudogaps in the densities of states with several bands contributing to transport, and this is consistent with our Hall effect, magnetic susceptibility, and heat capacity measurements. Although electronic dispersions, characteristic of simple kagome nets with nearest-neighbor hopping, are not clearly seen, likely due to the extended nature of the Pt $5d$ states, we do observe moderately large and non-saturating magnetoresistance values and quantum oscillations in the magnetoresistance and magnetization associated with the kagome nets of Pt. Full article

We introduce and prove the “root theorem”, which establishes a condition for families of operators to annihilate all root states associated with zero modes of a given positive semi-definite k-body Hamiltonian chosen from a large class. This class is motivated by fractional quantum Hall and related problems, and features generally long-ranged, one-dimensional, dipole-conserving terms. Our theorem streamlines analysis of zero-modes in contexts where “generalized” or “entangled” Pauli principles apply. One major application of the theorem is to parent Hamiltonians for mixed Landau-level wave functions, such as unprojected composite fermion or parton-like states that were recently discussed in the literature, where it is difficult to rigorously establish a complete set of zero modes with traditional polynomial techniques. As a simple application, we show that a modified $V_1$ pseudo-potential, obtained via retention of only half the terms, stabilizes the $\nu =1/2$ Tao–Thouless state as the unique densest ground state. Full article

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are “local flavor symmetry” of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden “quantum scale symmetry” with an IR fixed point with a “genuine dilaton (GD)” characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for $N_f\ge 2$ baryons and the fractional quantum Hall (FQH) droplet topology for $N_f=1$ baryons are unified in the “homogeneous/hidden” Wess–Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless. Full article

In this paper, we consider the topological abelian BF theory with radial boundary on a generic 3D manifold, as we were motivated by the recently discovered accelerated edge modes on certain Hall systems. Our aim was to research if, where, and how the boundary keeps the memory of the details of the background metrics. We discovered that some features were topologically protected and did not depend on the bulk metric. The outcome was that these edge excitations were $accelerated$, as a direct consequence of the non-flat nature of the bulk spacetime. We found three possibilities for the motion of the edge quasiparticles: same directions, opposite directions, and a single-moving mode. However, requiring that the Hamiltonian of the 2D theory is bounded by below, the case of the edge modes moving in the same direction was ruled out. Systems involving parallel Hall currents (for instance, a fractional quantum Hall effect with $\nu =2/5$) cannot be described by a BF theory with the boundary, independently from the geometry of the bulk spacetime, because of positive energy considerations. Thus, we were left with physical situations characterized by edge excitations moving with opposite velocities (for example, the fractional quantum Hall effect with $\nu =1-1/n$, with the n positive integer, and the helical Luttinger liquids phenomena) or a single-moving mode (quantum anomalous Hall). A strong restriction was obtained by requiring time reversal symmetry, which uniquely identifies modes with equal and opposite velocities, and we know that this is the case of topological insulators. The novelty, with respect to the flat bulk background, is that the modes have local velocities, which correspond to topological insulators with $accelerated$ edge modes. Full article