arXiv subjects

M. O. Goerbig

Publications and source records attributed to M. O. Goerbig.

66 records · Page 4Linked to original sources

arXiv2005

Spin-excitations of the quantum Hall ferromagnet of composite fermions

The spin-excitations of a fractional quantum Hall system are evaluated within a bosonization approach. In a first step, we generalize Murthy and Shankar's Hamiltonian theory of the fractional quantum Hall effect to the case of composite fermions with an extra discrete degree of freedom. Here, we mainly investigate the spin degrees of freedom, but the proposed formalism may be useful also in the study of bilayer quantum-Hall systems, where the layer index may formally be treated as an isospin. In a second step, we apply a bosonization scheme, recently developed for the study of the two-dimensional electron gas, to the interacting composite-fermion Hamiltonian. The dispersion of the bosons, which represent quasiparticle-quasihole excitations, is analytically evaluated for fractional quantum Hall systems at ν= 1/3 and ν= 1/5. The finite width of the two-dimensional electron gas is also taken into account explicitly. In addition, we consider the interacting bosonic model and calculate the lowest-energy state for two bosons. Besides a continuum describing scattering states, we find a bound-state of two bosons. This state is interpreted as a pair excitation, which consists of a skyrmion of composite fermions and an antiskyrmion of composite fermions. The dispersion relation of the two-boson state is evaluated for ν= 1/3 and ν= 1/5. Finally, we show that our theory provides the microscopic basis for a phenomenological non-linear sigma-model for studying the skyrmion of composite fermions.

cond-mat.mtrl-sci↗

arXiv2005

Quantum dimer models and effective Hamiltonians on the pyrochlore lattice

We study a large-N deformation of the S=1/2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading non-trivial order. In this limit, the ground state manifold -- while extensively degenerate -- breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the 1/N expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-field ground states of the effective Hamiltonian which exhibit translational symmetry breaking. The entire scenario offers a new perspective on previous treatments of the SU(2) problem not controlled by a small parameter, in particular showing that a mean-field state considered previously encodes the physics of a maximally flippable dimer configuration. We also comment on the difficulties of extending our results to the SU(2) case, and note implications for classical dimer models.

cond-mat.str-el↗

arXiv2004

Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level

In the framework of a recently developed model of interacting composite fermions, we calculate the energy of different solid and Laughlin-type liquid phases of spin-polarized composite fermions. The liquid phases have a lower energy than the competing solids around the electronic filling factors nu=4/11,6/17, and 4/19 and may thus be responsible for the fractional quantum Hall effect at nu=4/11. The alternation between solid and liquid phases when varying the magnetic field may lead to reentrance phenomena in analogy with the observed reentrant integral quantum Hall effect.

cond-mat.mes-hall↗

arXiv2004

Second Generation of Composite Fermions and the Self-Similarity of the Fractional Quantum Hall Effect

A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted in terms of second-generation composite fermions and which may be responsible for the fractional quantum Hall states observed at unusual filling factors, such as nu=4/11. Projection of the composite-fermion dynamics to a single level, involved in the derivation of the Hamiltonian of interacting composite fermions, reveals the underlying self-similarity of the model.

cond-mat.mes-hall↗

arXiv2004

Second Generation of Composite Fermions in the Hamiltonian Theory

In the framework of a recently developed model of interacting composite fermions restricted to a single level, we calculate the activation gaps of a second generation of spin-polarized composite fermions. These composite particles consist each of a composite fermion of the first generation and a vortex-like excitation and may be responsible for the recently observed fractional quantum Hall states at unusual filling factors such as nu=4/11,5/13,5/17, and 6/17. Because the gaps of composite fermions of the second generation are found to be more than one order of magnitude smaller than those of the first generation, these states are less visible than the usual states observed at filling factors nu=p/(2ps+1). Their stability is discussed in the context of a pseudopotential expansion of the composite-fermion interaction potential.

cond-mat.mes-hall↗

arXiv2004

Quantum Phases in Partially Filled Landau Levels

We compare the energies of different electron solids, such as bubble crystals with triangular and square symmetry and stripe phases, to those of correlated quantum liquids in partially filled intermediate Landau levels. Multiple transitions between these phases when varying the filling of the top-most partially filled Landau level explain the observed reentrance of the integer quantum Hall effect. The phase transitions are identified as first-order. This leads to a variety of measurable phenomena such as the phase coexistence between a Wigner crystal and a two-electron bubble phase in a Landau-level filling-factor range $4.15 < nu < 4.26$, which has recently been observed in transport measurements under micro-wave irradiation.

cond-mat.mes-hall↗

arXiv2004

On the self-similarity in quantum Hall systems

The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this fractal structure emerges naturally in the Hamiltonian formulation of composite fermions. After a set of transformations on the electronic model, we show that the model, which describes interacting composite fermions in a partially filled energy level, is self-similar. This mathematical property allows for the construction of a basis of higher generations of composite fermions. The collective-excitation dispersion of the recently observed 4/11 fractional-quantum-Hall state is discussed within the present formalism.

cond-mat.mes-hall↗

arXiv2003

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.

cond-mat.mes-hall↗

arXiv2003

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.

cond-mat.mes-hall↗

arXiv2003

Comment faire fondre un cristal d'electrons bidimensionnel sous champ magnetique

C'est un phenomene connu de la vie quotidienne : si l'on augmente la temperature, la glace fond. Ceci est le paradigme d'une transition de phase solide-liquide, qu'on observe egalement dans d'autres materiaux : tout cristal fond a temperature suffisamment elevee. Or de telles transitions de phase existent aussi dans des structures moins bien connues a temperature zero, ou l'on fait varier un parametre physique different de la temperature. C'est le cas par exemple dans un systeme d'electrons dont le mouvement est contraint dans un plan sous champ magnetique perpendiculaire. Nous avons montre qu'une partie de ces electrons peut faire une telle transition de phase solide-liquide. Le parametre que l'on varie est le champ magnetique meme, et l'on observe un phenomene etrange : quand on augmente le champ magnetique, un cristal d'electrons fond pour former un liquide electronique. Contrairement a notre intuition acquise par la fusion de la glace en la chauffant, les electrons liquides forment a nouveau un cristal si l'on augmente davantage le champ magnetique. Une telle alternance de phases en fonction du champ a ete recemment observee dans des experiences par Eisenstein et al. au California Institute of Technology.

cond-mat.mes-hall↗

arXiv2003

Scaling Approach to the Phase Diagram of Quantum Hall Systems

We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This classification, and a criterion for the validity of the mean-field approximation in the charge-density-wave phase, is based on scaling arguments concerning the effective interaction potential of electrons restricted to an arbitrary Landau level. Finite-temperature effects are investigated within the same formalism, and a good agreement with recent experiments is obtained.

cond-mat.mes-hall↗

arXiv2002

Magnetoroton instabilities and static susceptibilities in higher Landau levels

We present analytical results concerning the magneto-roton instability in higher Landau levels evaluated in the single mode approximation. The roton gap appears at a finite wave vector, which is approximately independent of the LL index n, in agreement with numerical calculations in the composite-fermion picture. However, a large maximum in the static susceptibility indicates a charge density modulation with wave vectors $q_0(n)\sim 1/\sqrt{2n+1}$, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LLs.

cond-mat.mes-hall↗