Influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors
B. A. Piot, D. K. Maude, M. Henini, Z. R. Wasilewski, J. A. Gupta, K. J. Friedland, R. Hey, K. H. Ploog, U. Gennser, A. Cavanna, D. Mailly, R. Airey, G. Hill
In a recent paper [B. A. Piot et al., Phys. Rev. B 72, 245325 (2005)], we have shown that the lifting of the electron spin degeneracy in the integer quantum Hall effect at high filling factors should be interpreted as a magnetic-field-induced Stoner transition. In this work, we extend the analysis to investigate the influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors. The single-particle Zeeman energy is tuned through the application of an additional in-plane magnetic field. Both the evolution of the spin polarization of the system and the critical magnetic field for spin splitting are well described as a function of the tilt angle of the sample in the magnetic field.
We present the phase diagram of a ferromagnetic quantum Hall effect liquid in a narrow quantum well with vanishing single-particle Zeeman splitting, $ε_{\rm Z}$ and pronounced spin-orbit coupling. Upon decreasing $ε_{\rm Z}$, the spin-polarization field of a liquid takes, first, the easy-axis configuration, followed by the formation of a helical state, which affects the transport and NMR properties of a liquid and the form of topological defects in it. The analysis is extended over high odd integer filling factors.
Skyrmions in the FQHE at filling fractions above ν=1/3 are studied within the anyon model and by exact diagonalization. Relations to the composite fermion theory are pointed out. We find that unpolarized quasiparticles above ν=1/3 are stable below B\approx 0.02T. At low Zeeman energy the polarization in the range ν=8/5 ... 5/3 is found to be a linear function of the filling factor. We also reexamine the energy and wave function of skyrmions at ν=1 by a new method.
We study the charged excitations of a double layer at filling factor 2 in the ferromagnetic regime. In a wide range of Zeeman and tunneling splittings we find that the low energy charged excitations are spin-isospin textures with the charge mostly located in one of the layers. As tunneling increases, the parent spin texture in one layer becomes larger and it induces, in the other layer, a shadow spin texture antiferromagnetically coupled to the parent texture. These new quasiparticles should be observable by measuring the strong dependence of its spin on tunneling and Zeeman couplings.
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 rang…
We present an exact diagonalisation study of bilayer quantum Hall systems at a filling factor of two in the spherical geometry. We find the high-Zeeman-coupling phase boundary of the broken symmetry canted antiferromagnet is given exactly by previous Hartree-Fock mean-field theories, but that the state's stability at weak Zeeman coupling has been qualitatively overestimated. In the absence of interlayer tunneling, degeneracies occur between total spin multiplets due to the Hamiltonian's invariance under independent spin-rotations in top and bottom two-dimensional electron layers.
We investigate the competition between pairing correlations and ferromagnetism in small metallic grains in the presence of a Zeeman field. Our analysis is based on the universal Hamiltonian, valid in the limit of large Thouless conductance. We show that the coexistence regime of superconducting and ferromagnetic correlations can be made experimentally accessible by tuning an external Zeeman field. We compare the exact solution of the model with a mean-field theory and find that the latter cannot describe pairing correlations in the intermediate regime. We also study the occurrence of spin jump…
The inversion of a spin valve device is proposed. Opposite to a conventional spin valve of a non-magnetic spacer sandwiched between two ferromagnetic metals, an inverse spin valve is a ferromagnet sandwiched between two non-magnetic metals. It is predicted that, under a bias, the chemical potentials of spin-up and spin-down electrons in the metals split at metal-ferromagnet interfaces, a dynamical Zeeman effect. This split is of the order of an applied bias. Thus, there should be no problem of generating an $eV$ split that is not possible to be realized on the earth by the usual Zeeman effect.
Opposite spin Landau levels in a quantum well can be brought into coincidence by tilting the magnetic field away from normal orientation. We demonstrate that the magnetotransport anomaly at integer filling factors that was recently discovered by Pan {\it et al} is due to such a coincidence. By performing exact diagonalization calculations using microscopically evaluated effective electron-electron interactions, we are able to establish that the electronic ground state at coincidence is an Ising quantum Hall ferromagnet and that the low energy excitations correspond to the formation of a domain…
We study the charged excitations of quantum Hall systems at integer filling fractions $ν=2n+1$, for a force-law that takes account of the finite width of the electron gas. For typical values of this width, in the limit of vanishing Zeeman energy we find that the low-energy excitations are ``skyrmions'' not only at $ν=1$ but also at higher filling fractions. Our results lead to the prediction that, in typical samples, abrupt transitions to charged excitations with very large spins should be observable at filling fractions higher than $ν=1$ if the Zeeman energy is reduced sufficiently.
The nuclear spin-lattice relaxation time T1 of the nu = 2 quantum Hall ferromagnet (QHF) formed in a gate-controlled InSb two-dimensional electron gas has been characterized using a pump-probe technique. In contrast to a long T1 of quantum Hall states around nu = 1 that possesses a Korringa-type temperature dependence, the temperature-independent short T1 of the nu = 2 QHF suggests the presence of low energy collective spin excitations in a domain wall. Furthermore, T1 of this ferromagnetic state is also found to be filling- and current-independent. The interpretation of these results as compa…
We report on a study of the charged-skyrmion or spin-texture excitations which occur in quantum Hall ferromagnets near odd Landau level filling factors. Particle-hole symmetry is used to relate the spin-quantum numbers of charged particle and hole excitations and neutral particle-hole pair excitations. Hartree-Fock theory is used to provide quantitative estimates of the energies of these excitations and their dependence on Zeeman coupling strength, Landau level quantum numbers, and the thicknesses of the two-dimensional electron layers. For the case of $ν$ near three we suggest the possibility…
We consider the possibility to employ a quantum wire realized in a two-dimensional electron gas (2DEG) as a spin ratchet. We show that a net spin current without accompanying net charge transport can be induced in the nonlinear regime by an unbiased external driving via an ac voltage applied between the contacts at the ends of the quantum wire. To achieve this we make use of the coupling of the electron spin to inhomogenous magnetic fields created by ferromagnetic stripes patterned on the semiconductor heterostructure that harbours the 2DEG. Using recursive Green function techniques we numeric…
We report on magneto-transport measurements of a two-dimensional electron gas confined in a Cd$_{0.997}$Mn$_{0.003}$Te quantum well structure under conditions of vanishing Zeeman energy. The electron Zeeman energy has been tuned via the $s-d$ exchange interaction in order to probe different quantum Hall states associated with metallic and insulating phases. We have observed that reducing Zeeman energy to zero does not necessary imply the disappearing of quantum Hall states, i.e. a closing of the spin gap. The spin gap value under vanishing Zeeman energy conditions is shown to be dependent on t…
We develop a theory of cavity quantum electrodynamics for a two-dimensional electron gas in the presence of Rashba spin-orbit and Zeeman couplings and perpendicular magnetic field, coupled to a spatially nonuniform quantum photon field. We show that the superradiant quantum phase transition (SQPT), also known as photon condensation, can in principle occur through a pure in-plane Zeeman coupling, but it requires extremely small (unrealistic) quantum well widths or extremely fine tuning of the effective Landé factor which makes two Landau levels coincide. Landau level crossings can also be induc…
Measurements on a multilayer two-dimensional electron system (2DES) near Landau level filling $ν$=1 reveal the disappearance of the nuclear spin contribution to the heat capacity as the ratio $\tilde{g}$ between the Zeeman and Coulomb energies exceeds a critical value $\tilde{g}_c \approx$0.04. This disappearance suggests the vanishing of the Skyrmion-mediated coupling between the lattice and the nuclear spins as the spin excitations of the 2DES make a transition from Skyrmions to single spin-flips above $\tilde{g}_c$. Our experimental $\tilde{g}_c$ is smaller than the calculated $\tilde{g}_c$…
Deformation of the easy-axis ferromagnetic state in asymmetric bilayer systems are investigated numerically. Using the exact diagonalization the easy-axis to easy-plane ferromagnetic transition at total filling factor 3 or 4 is investigated. At still higher filling, novel stripe state in which stripes are aligned in the vertical direction occurs. The Hartree-Fock energies of relevant ordered states are calculated and compared.
We study the recently observed graphene fractional quantum Hall state at a filling factor $ν_G=1/3$ using a four-component trial wave function and exact diagonalization calculations. Although it is adiabatically connected to a 1/3 Laughlin state in the upper spin branch, with SU(2) valley-isospin ferromagnetic ordering and a completely filled lower spin branch, it reveals physical properties beyond such a state that is the natural ground state for a large Zeeman effect. Most saliently, it possesses at experimentally relevant values of the Zeeman gap low-energy spin-flip excitations that may be…
The electronic excitations at the edges of a Hall bar not much wider than a few magnetic lengths are studied theoretically at filling $ν= 2$. Both mean-field theory and Luttinger liquid theory techniques are employed for the case of a null Zeeman energy splitting. The first calculation yields a stable spin-density wave state along the bar, while the second one predicts dominant Wigner-crystal correlations along the edges of the bar. We propose an antiferromagnetic Wigner-crystal groundstate for the edge electrons that reconciles the two results. A net Zeeman splitting is found to produce canti…
Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor $ν=1$ and at very low temperatures($\sim40$ mK). A small change in filling factor ($δν\approx\pm0.01$) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at $ν=1$ is surprisingly fragile against increasing temperature, or against small changes in filling factor.
Microwave pinning-mode resonances found around integer quantum Hall effects, are a signature of crystallized quasiparticles or holes. Application of in-plane magnetic field to these crystals, increasing the Zeeman energy, has negligible effect on the resonances just below Landau level filling $ν=2$, but increases the pinning frequencies near $ν=1$, particularly for smaller quasiparticle/hole densities. The charge dynamics near $ν=1$, characteristic of a crystal order, are affected by spin, in a manner consistent with a Skyrme crystal.
Quantum Hall ferromagnetic transitions are typically achieved by increasing the Zeeman energy through in-situ sample rotation, while transitions in systems with pseudo-spin indices can be induced by gate control. We report here a gate-controlled quantum Hall ferromagnetic transition between two real spin states in a conventional two-dimensional system without any in-plane magnetic field. We show that the ratio of the Zeeman splitting to the cyclotron gap in a Ge two-dimensional hole system increases with decreasing density owing to inter-carrier interactions. Below a critical density of $\sim2…
In this work we study the properties of a two-subband quasi-two-dimensional electron system in a strong magnetic field when the electron filling factor is equal to four. When the cyclotron energy is close to the intersubband splitting the system can be mapped onto a four-level electron system with an effective filling factor of two. The ground state is either a ferromagnetic state or a spin-singlet state, depending on the values of the inter-level splitting and Zeeman energy. The boundaries between these phases are strongly influenced by the inter-electron interaction. A significant exchange-m…
We suggest a single-mode spin injection scheme in non-ferromagnetic quantum channels utilizing perpendicular strong Rashba spin-orbit and Zeeman fields. By applying a positive top-gate potential in order to inject electrons from the spin-orbit gap to the low-energy regime, we observe coherent destruction of transport signatures of a hole-like quasi-bound state, an electron-like quasi-bound state, or a hole-like bound state features that are sensitive to the selection of the top-gate length along the transport direction.
We investigate the possiblity of creating directed spin-polarized currents in a two-dimensional electron gas (2DEG) subject to an asymmetric magnetic field and an external adiabatic driving. We thereby generalize concepts of quantum charge ratchets to the case with spin. Due to the Zeeman term in the Hamiltonian, spin-up and -down electrons experience different effective potentials, which can be tailored to achieve net spin currents without corresponding charge currents. We consider ballistic, coherent transport in waveguides defined in a 2DEG, where the magnetic field modulation is induced by…
Magnetic tunnel junctions comprising of an insulator sandwiched between two ferromagnetic films are the simplest spintronic devices. Theoretically, these can be modeled by a metallic Hamiltonian in both the lattice and the continuum with an addition of Zeeman field. We calculate conductance at arbitrary orientations of the easy axes of the two ferromagnets. When mapped, the lattice and the continuum models show a discrepancy in conductance in the limit of a large Zeeman field. We resolve the discrepancy by modeling the continuum theory in an appropriate way.
Graphene exhibits quantum Hall ferromagnetism in which an approximate SU(4) symmetry involving spin and valley degrees of freedom is spontaneously broken. We construct a set of integer and fractional quantum Hall states that break the SU(4) spin/valley symmetry, and study their neutral and charged excitations. Several properties of these ferromagnets can be evaluated analytically in the SU(4) symmetric limit, including the full collective mode spectrum at integer fillings. By constructing explicit wave functions we show that the lowest energy skyrmion states carry charge $\pm 1$ for {\em any} …
The differential resistance of submicron-size ferromagnet/superconductor interface structures shows asymmetries as a function of the current through the ferromagnet/superconductor interface. These asymmetries are a consequence of spin-polarized electron transport from the ferromagnet to the superconductor, coupled with the Zeeman-splitting of the superconducting quasiparticle density of states. They are sensitive to the orientation of the magnetization of the ferromagnet, as the magnetic field required to spin-split the quasiparticle density of states can be provided by the ferromagnetic eleme…
We study the magnetotransport of high-mobility electrons in monolayer and bilayer MoSe$_2$, which show Shubnikov-de Haas (SdH) oscillations and quantum Hall states in high magnetic fields. An electron effective mass of 0.8$m_e$ is extracted from the SdH oscillations' temperature dependence; $m_e$ is the bare electron mass. At a fixed electron density the longitudinal resistance shows minima at filling factors (FFs) that are either predominantly odd, or predominantly even, with a parity that changes as the density is tuned. The SdH oscillations are insensitive to an in-plane magnetic field, con…
Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb interactions dominate against disorder broadening, quantum Hall ferromagnetic states realize at integer fillings. Extending the quantum Hall ferromagnetism to the fractional filling case of massless Dirac fermions, we study the elementally charge excitations which couple with the valley degrees of freedom (so-called valley skyrmions). With the use of the density matrix renomalization group (DMRG) method, the excitation gaps are calculated and extr…
The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for fractional quantum Hall states by including correlation effects. A transition of the direction of the spin-polarization is predicted at specific values of the Zeeman energy. We show that these values can be expressed in terms of the pair-correlation function, and thus provide information about the microscopic ground state. We examine the particular examples of the Laughlin wavefunctions and the 5/2-Pfaffian state. We also include effects of the nuclear bath.
In this paper we study fractional quantum Hall composite fermion wavefunctions at filling fractions ν= 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations, depending on how many spin-up or spin-down composite fermion Landau levels are occupied. We calculate the energy of the possible composite fermion wavefunctions and we predict transitions between ground states of different spin polarizations as the ratio of Zeeman energy to Coulomb energy is varied. Previously, several experiments have observed such transitions be…
Two-dimensional (2D) van der Waals heterostructures serve as a promising platform to exploit various physical phenomena in a diverse range of novel spintronic device applications. The efficient spin injection is the prerequisite for these devices. The recent discovery of magnetic 2D materials leads to the possibility of fully 2D van der Waals spintronics devices by implementing spin injection through magnetic proximity effect (MPE). Here, we report the investigation of magnetic proximity effect in 2D CrBr3/graphene van der Waals heterostructures, which is probed by Zeeman spin Hall effect thro…
Detecting magnetic order at the nanoscale is of central interest for the study of quantum magnetism in general, and the emerging field of moiré magnets in particular. Here, we analyze the exciton band structure that arises from a periodic modulation of the valley Zeeman effect. Despite long-range electron-hole exchange interactions, we find a sizable splitting in the energy of the bright circularly-polarized exciton Umklapp resonances, which serves as a direct optical probe of magnetic order. We first analyze quantum moiré magnets realized by periodic ordering of electron spins in Mott-Wigner …
Current understanding of spin injection tells us that a metal ferromagnet can inject spin into a semiconductor with 100% efficiency if either the ferromagnet is an ideal half metal with 100% spin polarization, or there exists a suitable tunnel barrier at the interface. In this paper, we show that, at absolute zero temperature, 100% spin injection efficiency from a non-ideal metal ferromagnet into a semiconductor quantum wire can be reached at certain injection energies, without a tunnel barrier, provided there is an axial magnetic field along the direction of current flow as well as a spin orb…
We apply polarization resolved photoluminescence spectroscopy to measure the spin polarization of a two dimensional electron gas in perpendicular magnetic field. In the vicinity of filling factor nu=5/2, we observe a sharp discontinuity in the energy of the zero Landau level emission line. We find that the splitting between the two circular polarizations exhibits a sharp drop at nu=5/2 and is equal to the bare Zeeman energy, which resembles the behavior at even filling factors. We show that this behavior is consistent with filling factor nu=5/2 being unpolarized.
We report spin-dependent quantum coherent oscillations (ringing) and beats of the total and spin currents flowing through a quantum dot with Zeeman split levels. The spin dependent transport is calculated via nonequilibrium Green function in the transient after a bias voltage is turned on at t=0. The dot is coupled to two electrodes that can be ferromagnetic or nonmagnetic. In the ferromagnetic case both parallel and antiparallel alignments are considered. The coherent oscillation and beat frequencies are controlled via the Zeeman energy E_Z. In particular, for E_Z=0 no beats are observed and …
We observed the coulomb blockade phenomena in ferromagnetic contacting single wall semiconducting carbon nanotube devices. No obvious Coulomb peaks shift was observed with existing only the Zeeman splitting at 4K. Combining with other effects, the ferromagnetic leads prevent the orbital spin states splitting with magnetic field up to 2 Tesla at 4K. With increasing magnetic field further, both positive or negative coulomb peaks shift slopes are observed associating with clockwise and anticlockwise orbital state splitting. The strongly suppressed/enhanced of the conductance has been observed ass…
The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseud…
A coherent superposition of many nuclear spin states can be prepared and manipulated via the hyperfine interaction with the electronic spins by varying the Landau level filling factor through the gate voltage in appropriately designed Quantum Hall Ferromagnet. During the manipulation periods the 2D electron system forms spatially large Skyrmionic spin textures, where many nuclear spins follow locally the electron spin polarization. It is shown that the collective spin rotation of a single spin texture is gapless in the limit of zero Zeeman splitting, and may dominate the nuclear spins relaxati…
We study the spin filling of a semiconductor quantum dot using excited-state spectroscopy in a strong magnetic field. The field is oriented in the plane of the two-dimensional electron gas in which the dot is electrostatically defined. By combining the observation of Zeeman splitting with our knowledge of the absolute number of electrons, we are able to determine the ground state spin configuration for one to five electrons occupying the dot. For four electrons, we find a ground state spin configuration with total spin S=1, in agreement with Hund's first rule. The electron g-factor is observed…
A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG)\ in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\pm 1,\pm 2,...$ While Landau level $N=0$ is eighfold degenerate, higher Landau levels ($ \left\vert N\right\vert \geq 1$) are fourfold degenerate when counting spin and valley degrees of freedom. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $ \widetilde{ν}=1,2,3$ of these higher Landau levels. At these filling factors, the C2DEG…
A microscopic description of (baby)skyrmions in quantum Hall ferromagnets is derived from a scattering theory of collective (neutral) spin modes by a bare quasiparticle. We start by mapping the low lying spectrum of spin waves in the uniform ferromagnet onto that of free moving spin excitons, and then we study their scattering by the defect of charge. In the presence of this disturbance, the local spin stiffness varies in space, and we translate it into an inhomogeneus metric in the Hilbert space supporting the excitons. An attractive potencial is then required to preserve the symmetry under g…
Recent experiments on the role of electron-electron interactions in fractal Dirac systems have revealed a host of interesting effects, in particular, the unique nature of the magnetic field dependence of butterfly gaps in graphene. The novel gap structure observed in the integer quantum Hall effect is quite intriguing [Nat. Phys. 10, 525 (2014)], where one observes a suppression of the ferromagnetic state at one value of the commensurable flux but a reentrant ferromagnetic state at another. Our present work that includes the interplay between the electron-electron interaction and the periodic …
The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored first-order topological insulators described by the Z_2 index. However, most recently, a proposal asserts that a significant bridge can be established between the HOTIs and the Z_2 topological insulators. When subject to an in-plane Zeeman field, the corner states, the signature of the HOTIs, can be induced in a Z_2 topological insulator. Such Zeeman field can be prod…
We investigate theoretically the non-local conductance through a superconducting wire in tunnel contact with normal and ferromagnetic leads. In the presence of an in-plane magnetic field, the superconducting density of states is spin-split, and the current injected from the normal lead is spin-polarized. A non-local conductance that is antisymmetric with the applied voltage can be measured with a ferromagnetic lead. It persists for a distance between the contacts that is larger than both the charge-imbalance relaxation length and the normal-state spin relaxation length. We determine its amplit…
We study spin and charge striped states at the half-filled high Landau level in the zero Zeeman energy limit using a Hartree-Fock approximation. It is shown that a ferromagnetic striped Hall state is more stable than the antiferromagnetic striped state or charge striped state. We calculate the collective excitations using the single mode approximation.
We study non-equilibrium electronic transport through a quantum dot or impurity weakly coupled to ferromagnetic leads. Based on the rate equation formalism we derive noise spectra for the transport current. We show that due to quantum interference between different spin components of the current the spectrum develops a peak or a dip at the frequency corresponding to Zeeman splitting in the quantum dot. The detailed analysis of the spectral structure of the current is carried out for noninteracting electrons as well as in the regime of Coulomb blockade.
We report on a study of the classical field theory description of charged skyrmions in quantum Hall ferromagnets. The appropriate field theory is a non-linear $σ$ model generalized to include Coulomb and Zeeman interaction terms. We have tested the range of validity of the classical field theory by comparing with microscopic descriptions of the single skyrmion state based on the Hartree-Fock approximation, exact diagonalization calculations, and many-body trial wavefunctions. We find that the field theory description is accurate for skyrmions with moderate spin quantum numbers ($\gtrsim 10$) a…
Spin splitting in the integer quantum Hall effect is investigated for a series of Al$_{x}$Ga$_{1-x}$As/GaAs heterojunctions and quantum wells. Magnetoresistance measurements are performed at mK temperature to characterize the electronic density of states and estimate the strength of many body interactions. A simple model with no free parameters correctly predicts the magnetic field required to observe spin splitting confirming that the appearance of spin splitting is a result of a competition between the disorder induced energy cost of flipping spins and the exchange energy gain associated wit…
The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $ν_{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavio…
The two-dimensional electron gas in a bilayer graphene in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N=0 at integer filling factors $ν\in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $ν=-1,3$, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias where \textit{electric} dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that by further increasing t…
We study the splitting between the right-hand and left-hand circularly polarized luminescence lines in a quantum dot under relatively weak confinement regime and resonant high-power excitation. When the dot is populated with an even number of electron-hole pairs (biexciton and higher excitations), the splitting measures basically the Zeeman energy. However, in the odd number of pairs case, we have, in addition to the Zeeman and Overhauser shifts, a contribution to the splitting coming from Coulomb interactions. This contribution is of the order of a few meV, and shows distinct signatures of sh…
In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can spontaneously break this symmetry, manifesting as additional integer quantum Hall plateaus outside the normal sequence. Here we report the observation of a large number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using temperature-dependent tilted field magnetotransport. The large measured activation gaps confirm the Coulomb origin…
When two Landau levels are brought to a close coincidence between them and with the chemical potential in the Integer Quantum Hall regime, the two Landau levels can just cross or collapse while the external or pseudospin field that induces the alignment changes. In this work, all possible crossings are analyzed theoretically for the particular case of semiconductor trilayer systems, using a variational Hartree-Fock approximation. The model includes tunneling between neighboring layers, bias, intra-layer and inter-layer Coulomb interaction among the electrons. We have found that the general pse…
