arXiv subjects

P. Lederer

Publications and source records attributed to P. Lederer.

16 recordsLinked to original sources

arXiv2008

Entanglement Skyrmions in multicomponent quantum Hall systems

We discuss charged topological spin textures in quantum Hall ferromagnets in which the electrons carry a pseudospin as well as the usual spin degree of freedom, as is the case in bilayer GaAs or monolayer graphene samples. We develop a theory which treats spin and pseudospin on a manifestly equal footing, which may also be of help in visualizing the relevant spin textures. We in particular consider the entanglement of spin and pseudospin in the presence of realistic anisotropies. An entanglement operator is introduced which generates families of degenerate Skyrmions with differing entanglement properties. We propose a local characterization of the latter, and touch on the role entangled Skyrmions play in the nuclear relaxation time of quantum Hall ferromagnets.

cond-mat.mes-hall↗

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↗

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↗

arXiv2002

Tomonaga-Luttinger liquid with reservoirs in a multi-terminal geometry

We propose a formalism which uses boundary conditions imposed on the Luttinger liquid (LL) to describe the transport properties of a LL coupled to reservoirs. The various boundary conditions completely determine linear transport in the joint system reservoirs+LL. As an illustration we consider an exactly solvable microscopic model in a multi-terminal geometry for which such boundary conditions can be explicitly derived; in this model the Landauer-Büttiker formalism fails: if it were valid, the relation between the conductance matrix elements and the reflection and transmission coefficients could yield negative probabilities. We then apply our formalism to a discussion of shot noise through an impurity in a LL connected to two reservoirs.

cond-mat.mes-hall↗

arXiv2002

Conductance of one-dimensional quantum wires

We discuss the conductance of quantum wires (QW) in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of the standard two-terminal (2T) conductance measurement depend on the coupling of TLL with the reservoirs and can be interpreted as different boundary conditions at the interfaces. We propose a three-terminal (3T) geometry in which the third contact is connected weakly to the bulk of TLL subjected to a large bias current. We develop a renormalization group (RG) analysis for this problem by taking explicitly into account the splitting of the injected electronic charge into two chiral irrational charges. We study in the presence of {\it bulk} contact the leading order corrections to the conductance for two different boundary conditions, which reproduce in the absence of {\it bulk} contact, respectively, the standard 2T source-drain (SD) conductance $G_{\rm SD}^{(2)}=e^2/h$ and $G_{\rm SD}^{(2)}=ge^2/h$, where $g$ is the TLL charge interaction parameter. We find that under these two boundary conditions for the {\it end} contacts the 3T SD conductance $G_{\rm SD}^{(3)}$ shows an UV-relevant deviation from the above two values, suggesting new fixed points in the ohmic limit. Non-trivial scaling exponents are predicted as a result of electron fractionalization.

cond-mat.mes-hall↗

arXiv2000

Fractional excitations in the Luttinger liquid

We reconsider the spectrum of the Luttinger liquid (LL) usually understood in terms of phonons (density fluctuations), and within the context of bosonization we give an alternative representation in terms of fractional states. This allows to make contact with Bethe Ansatz which predicts similar fractional states. As an example we study the spinon operator in the absence of spin rotational invariance and derive it from first principles: we find that it is not a semion in general; a trial Jastrow wavefunction is also given for that spinon state. Our construction of the new spectroscopy based on fractional states leads to several new physical insights: in the low-energy limit, we find that the $S_{z}=0$ continuum of gapless spin chains is due to pairs of fractional quasiparticle-quasihole states which are the 1D counterpart of the Laughlin FQHE quasiparticles. The holon operator for the Luttinger liquid with spin is also derived. In the presence of a magnetic field, spin-charge separation is not realized any longer in a LL: the holon and the spinon are then replaced by new fractional states which we are able to describe.

cond-mat.str-el↗

arXiv1999

Wavefunctions for the Luttinger liquid

Standard bosonization techniques lead to phonon-like excitations in a Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these systems. Yet in addition to the above excitations some LL are known to possess solitonic states carrying fractional quantum numbers (e.g. the spin 1/2 Heisenberg chain). We have reconsidered the zero modes in the low-energy spectrum of the gaussian boson LL hamiltonian both for fermionic and bosonic LL: in the spinless case we find that two elementary excitations carrying fractional quantum numbers allow to generate all the charge and current excited states of the LL. We explicitly compute the wavefunctions of these two objects and show that one of them can be identified with the 1D version of the Laughlin quasiparticle introduced in the context of the Fractional Quantum Hall effect. For bosons, the other quasiparticle corresponds to a spinon excitation. The eigenfunctions of Wen's chiral LL hamiltonian are also derived: they are quite simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions.

cond-mat.str-el↗

arXiv1998

Jastrow-Luttinger Fractional Liquids

In this paper, we present a description of Haldane's Luttinger liquid which parallels Laughlin's theory of the Fractional Quantum Hall (FQH) incompressible fluid, both exhibiting similar ground states as well as fractional excitations. These two non-Fermi liquids are instances of a generic structure for low-dimensional quantum liquids which we propose to dub Jastrow-Luttinger Fractional Liquids. An important feature of such liquids is the complete fractionalization of the parent particle. In particular, in both one and two dimensions spin-charge separation can be achieved and is indeed suggested to occur for unpolarized quantum Hall systems both at the edge and in the bulk.

cond-mat.str-el↗

arXiv1995

On the Spin Gap Phase of Strongly-Correlated Electrons

We discuss the possible existence of a spin-gap phase in the low-doping regime of strongly-correlated two-dimensional electrons within the gauge field description of the t-J model. The spin-gap phase was recently shown by Ubbens and Lee to be destroyed by gauge field quantum fluctuations for a single-layer 2D system in the absence of disorder and for a full gap. We show that the same conclusion applies both in the dirty limit and for the case of a gapless spinon condensate.

cond-mat↗