Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs

We present a microscopic theory for the recently observed reentrant integral quantum Hall effect in the n=1 and n=2 Landau levels. Our energy investigations indicate an alternating sequence of M-electron-bubble and quantum-liquid ground states in a certain range of the partial filling factor of the n-th level. Whereas the quantum-liquid states display the fractional quantum Hall effect, the bubble phases are insulating, and the Hall resistance is thus quantized at integral values of the total filling factor.Comment: 4 pages, 4 figures; minor corrections include

Competition between quantum-liquid and electron-solid phases in intermediate Landau levels

On the basis of energy calculations we investigate the competition between quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a function of their partial filling factor. Whereas the quantum-liquid phases are stable only in the vicinity of quantized values 1/(2s+1) of the partial filling factor, an electron solid in the form of a triangular lattice of clusters with a few number of electrons (bubble phase) is energetically favorable between these fillings. This alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains a recently observed reentrance of the integral quantum Hall effect in the Landau levels n=1 and 2. Around half-filling of the last Landau level, a uni-directional charge density wave (stripe phase) has a lower energy than the bubble phase.Comment: 12 pages, 9 figures; calculation of exact exchange potential for n=1,2,3 included, energies of electron-solid phases now calculated with the help of the exact potential, and discussion of approximation include

A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal

We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac cones from an insulating phase with a gap. We calculate the density of states and the specific heat. The spectrum in a magnetic field B is related to the resolution of a Schrodinger equation in a double well potential. They obey the general scaling law e_n \propto B^{2/3} f_n(Delta /B^{2/3}. They evolve continuously from a sqrt{n B} to a linear (n+1/2)B dependence, with a [(n+1/2)B]^{2/3} dependence at the transition. The spectrum in the vicinity of the topological transition is very well described by a semiclassical quantization rule. This model describes continuously the coupling between valleys associated with the two Dirac points, when approaching the transition. It is applied to the tight-binding model of graphene and its generalization when one hopping parameter is varied. It remarkably reproduces the low field part of the Rammal-Hofstadter spectrum for the honeycomb lattice.Comment: 18 pages, 15 figure

Energy scale of Dirac electrons in Cd3As2

Cadmium arsenide (Cd3As2) has recently became conspicuous in solid-state physics due to several reports proposing that it hosts a pair of symmetry-protected 3D Dirac cones. Despite vast investigations, a solid experimental insight into the band structure of this material is still missing. Here we fill one of the existing gaps in our understanding of Cd3As2, and based on our Landau-level spectroscopy study, we provide an estimate for the energy scale of 3D Dirac electrons in this system. We find that the appearance of such charge carriers is limited-contrary to a widespread belief in the solid-state community-to a relatively small energy scale (below 40 meV)

Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States

We present an effective Chern-Simons theory for the bulk fully polarized fractional quantum Hall (FQH) hierarchical states constructed as daughters of general states of the Jain series, {\it i. e.} as FQH states of the quasi-particles or quasi-holes of Jain states. We discuss the stability of these new states and present two reasonable stability criteria. We discuss the theory of their edge states which follows naturally from this bulk theory. We construct the operators that create elementary excitations, and discuss the scaling behavior of the tunneling conductance in different situations. Under the assumption that the edge states of these fully polarized hierarchical states are unreconstructed and unresolved, we find that the differential conductance $G$ for tunneling of electrons from a Fermi liquid into {\em any} hierarchical Jain FQH states has the scaling behavior $G\sim V^\alpha$ with the universal exponent $\alpha=1/\nu$, where $\nu$ is the filling fraction of the hierarchical state. Finally, we explore alternative ways of constructing FQH states with the same filling fractions as partially polarized states, and conclude that this is not possible within our approach.Comment: 10 pages, 50 references, no figures; formerly known as "Composite Fermions: The Next Generation(s)" (title changed by the PRB thought police). This version has more references and a discussion of the stability of the new states. Published version. One erroneous reference is correcte

Magneto-optical signatures of Volkov-Pankratov states in topological insulators

International audienceIn addition to the usual chiral surface states, massive surface states can arise at a smooth interface between a topological and a trivial bulk insulator. While not subject to topological protection as the chiral states, these massive states, theorized by Volkov and Pankratov in the 1980s, reflect nevertheless emergent Dirac physics at the interface. We study theoretically the magneto-optical response of these surface states, which is strikingly different from that of the bulk states. Most saliently, we show that these states can be identified clearly in the presence of a magnetic field and its orientation with respect to the interface

Exciton spectrum in two-dimensional transition metal dichalcogenides: The role of Diracness

10.1088/1742-6596/864/1/012033Journal of Physics: Conference Series86411203

Novel composite-fermion phases: Crystals, stripes, and higher generations

Residual interactions between composite fermions, the quasi-particles responsible for the fractional quantum Hall effect, may be neglected at the Landau-level filling factors $\nu=p/(2sp+1)$, at which most fractional quantum Hall states are observed. However, they become relevant at fillings in between states of this series. We have derived the form of the interaction potential of composite fermions within a recently developed Hamiltonian formalism, and we show how these residual interaction may give rise to novel phases, such as crystals and stripes of composite fermions, as well as higher-generation states. The latter may be responsible for a recently observed fractional quantum Hall effect at $\nu=4/11$

Quantum electronic phases in partially filled Landau levels

On the basis of energy calculations, we investigate the competition between quantum-liquid and electron-solid phases in intermediate Landau levels as a function of their partial filling factor. An alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains an observed reentrance of the integral quantum Hall effect. The phase transitions are identified as first-order. Recent transport measurements under micro-wave irradiation reveal the crystalline origin of the reentrant points, and a mixed phase of a coexisting Wigner crystal and a 2-electron bubble phase is found in a Landau-level filling-factor range $4.15{\lesssim} \nu {\lesssim} 4.26$, as expected from our calculations