Quantum Hall ferromagnetic phases in the Landau level N=0 of a graphene bilayer

In a Bernal-stacked graphene bilayer, an electronic state in Landau level $N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $\xi =\pm K,\sigma =\pm 1,$ and $n=0,1.$ When Coulomb interaction is taken into account, the chiral two-dimensional electron gas (C2DEG) in this system can support a variety of quantum Hall ferromagnetic (QHF)\ ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space. In this work, we give a comprehensive account of the phase diagram of the C2DEG at integer filling factors $\nu \in [-3,3]$ in Landau level N=0 when an electrical potential difference $\Delta_{B}$ between the two layers is varied. We consider states with or without layer, spin, or orbital coherence. For each phase, we discuss the behavior of the transport gap as a function of $\Delta_{B},$ the spectrum of collective excitations and the optical absorption due to orbital pseudospin-wave modes. We also study the effect of an external in-plane electric field on a coherent state that has both valley and spin coherence and show that it is possible, in such a state, to control the spin polarization by varying the strength of the external in-plane electric field.Comment: 21 pages, 13 eps figure

Many-body dynamics of Rydberg excitation using the Ω\Omega-expansion

We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $\Omega$. In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $\Omega^4$, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions.Comment: 9 pages, 3 figures, 1 tabl

Zeeman coupling and screening corrections to skyrmion excitations in graphene

At half filling of the fourfold degenerate Landau levels |n| \geq 1 in graphene, the ground states are spin polarized quantum Hall states that support spin skyrmion excitations for |n| =1,2,3. Working in the Hartree-Fock approximation, we compute the excitation energy of an unbound spin skyrmion-antiskyrmion excitation as a function of the Zeeman coupling strength for these Landau levels. We find for both the bare and screened Coulomb interactions that the spin skyrmion-antiskyrmion excitation energy is lower than the excitation energy of an unbound spin 1/2 electron-hole pair in a finite range of Zeeman coupling in Landau levels |n| =1,2,3. This range decreases rapidly for increasing Landau level index and is extremely small for |n| =3. For valley skyrmions which should be present at 1/4 and 3/4 fillings of the Landau levels |n| =1,2,3, we show that screening corrections are more important in the latter case. It follows that an unbound valley skyrmion-antiskyrmion excitation has lower energy at 3/4 filling than at 1/4. We compare our results with recent experiments on spin and valley skyrmion excitations in graphene.Comment: 15 pages with 11 eps figure

Jost function description of near threshold resonances for coupled-channel scattering

We study the effect of resonances near the threshold of low energy ($\varepsilon$) reactive scattering processes, and find an anomalous behavior of the $s$-wave cross sections. For reaction and inelastic processes, the cross section exhibits the energy dependence $\sigma\sim\varepsilon^{-3/2}$ instead of the standard Wigner's law threshold behavior $\sigma\sim\varepsilon^{-1/2}$. Wigner's law is still valid as $\varepsilon\rightarrow 0$, but in a narrow range of energies. We illustrate these effects with two reactive systems, a low-reactive system (H$_2$ + Cl) and a more reactive one (H$_2$ + F). We provide analytical expressions, and explain this anomalous behavior using the properties of the Jost functions. We also discuss the implication of the reaction rate coefficients behaving as $K\sim 1/T$ at low temperatures, instead of the expected constant rate of the Wigner regime in ultracold physics and chemistry.Comment: 15 pages, 12 figure

RD-NMR spectra of the crystal states of the two-dimensional electron gas in a quantizing magnetic field

Transport experiments on the two-dimensional electron gas (2DEG) confined into a semiconductor quantum well and subjected to a quantizing magnetic field have uncovered a rich variety of uniform and nonuniform phases such as the Laughlin liquids, the Wigner, bubble and Skyrme crystals and the quantum Hall stripe state. Optically pumped nuclear magnetic resonance (OP-NMR) has also been extremely useful in studying the magnetization and dynamics of electron solids with exotic spin textures such as the Skyrme crystal. Recently, it has been demonstrated that a related technique, resistively-detected nuclear magnetic resonance (RD-NMR), could be a good tool to study the topography of the electron solids in the fractional and integer quantum Hall regimes. In this work, we compute theoretically the RD-NMR line shapes of various crystal phases of the 2DEG and study the relation between their spin density and texture and their NMR spectra. This allows us to evaluate the ability of the RD-NMR to discriminate between the various types of crystal states.Comment: 12 pages, 8 figure

Charge density wave with meronlike spin texture induced by a lateral superlattice in a two-dimensional electron gas

The combined effect of a lateral square superlattice potential and the Coulomb interaction on the ground state of a two-dimensional electron gas in a perpendicular magnetic field is studied for different rational values of $\Gamma$, the inverse of the number of flux quanta per unit cell of the external potential, at filling factor $\nu =1$ in Landau level $N=0.$ When Landau level mixing and disorder effects are neglected, increasing the strength $W_{0}$ of the potential induces a transition, at a critical strength $W_{0}^{\left( c\right) },$ from a uniform and fully spin polarized state to a two-dimensional charge density wave (CDW) with a meronlike spin texture at each maximum and minimum of the CDW. The collective excitations of this vortex-CDW are similar to those of the Skyrme crystal that is expected to be the ground state near filling factor $\nu =1$. In particular, a broken U(1) symmetry in the vortex-CDW results in an extra gapless phase mode that could provide a fast channel for the relaxation of nuclear spins. The average spin polarization $S_{z}$ changes in a continuous or discontinuous manner as $W_{0}$ is increased depending on whether $\Gamma \in \left[ 1/2,1\right]$ or $\Gamma \in \left[ 0,1/2\right] .$ The phase mode and the meronlike spin texture disappear at large value of $W_{0},$ leaving as the ground state a partially spin-polarized CDW if $\Gamma \neq 1/2$ or a spin-unpolarized CDW if $\Gamma =1/2.$Comment: 11 pages with 9 eps figure

Nuclear magnetic resonance line shapes of Wigner crystals in 13^{13}C-enriched graphene

Assuming that the nuclear magnetic resonance (NMR) signal from a $^{13}$C isotope enriched layer of graphene can be made sufficiently intense to be measured, we compute the NMR\ lineshape of the different crystals ground states that are expected to occur in graphene in a strong magnetic field. We first show that in nonuniform states, there is, in addition to the frequency shift due to the spin hyperfine interaction, a second contribution of equal importance from the coupling between the orbital motion of the electrons and the nuclei. We then show that, if the linewidth of the bare signal can be made sufficiently small, the Wigner and bubble crystals have line shapes that differ qualitatively from that of the uniform state at the same density while crystal states that have spin or valley pseudospin textures do not. Finally, we find that a relatively small value of the bare linewidth is sufficient to wash out the distinctive signature of the crystal states in the NMR line shape.Comment: 12 pages with 6 eps figure

Electromagnetic absorption and Kerr effect in quantum Hall ferromagnetic states of bilayer graphene

In a quantizing magnetic field, the chiral two-dimensional electron gas in Landau level $N=0$ of bilayer graphene goes through a series of phase transitions at integer filling factors $\nu \in \left[ -3,3\right]$ when the strength of an electric field applied perpendicularly to the layers is increased. At filling factor $\nu =3,$ the electron gas can described by a simple two-level system where layer and spin degrees of freedom are frozen. The gas then behaves as an orbital quantum Hall ferromagnet. A Coulomb-induced Dzyaloshinskii-Moriya term in the orbital pseudospin Hamiltonian is responsible for a series of transitions first to a Wigner crystal state and then to a spiral state as the electric field is increased. Both states have a non trivial orbital pseudospin texture. In this work, we study how the phase diagram at $\nu =3$ is modified by an electric field applied in the plane of the layers and then derive several experimental signatures of the uniform and nonuniform states in the phase diagram. In addition to the transport gap, we study the electromagnetic absorption and the Kerr rotation due to the excitations of the orbital pseudospin-wave modes in the broken-symmetry states.Comment: 15 pages and 13 figure

Phase-amplitude formalism for ultra-narrow shape resonances

We apply Milne's phase-amplitude representation [W. E. Milne, Phys. Rev. 35, 863 (1930)] to a scattering problem involving disjoint classically allowed regions separated by a barrier. Specifically, we develop a formalism employing different sets of amplitude and phase functions --- each set of solutions optimized for a separate region --- and we use these locally adapted solutions to obtain the true value of the scattering phase shift and accurate tunneling rates for ultra-narrow shape resonances. We show results for an illustrative example of an attractive potential with a large centrifugal barrier.Comment: 6 figure

Threshold resonance effects in reactive processes

We investigate the effect of near threshold resonances in reactive scattering at low energy. We find a general type of anomalous behavior of the cross sections, and illustrate it with a real system (H$_2$ + Cl). For inelastic processes, the anomalous energy dependence of the total cross sections is given by $\sigma\sim\varepsilon^{-3/2}$. The standard threshold behavior given by Wigner's law ($\sigma\sim\varepsilon^{-1/2}$) is eventually recovered at vanishing energies, but its validity is now limited to a much narrower range of energies. The universal anomalous behavior leads to reaction rate coefficients behaving as $K\sim 1/T$ at low temperatures, instead of the expected constant rate of the Wigner regime. We also provide analytical expressions for s-wave cross sections, and discuss the implication in ultracold physics and chemistry.Comment: 5 figure