Occupation Of Landau Levels Research Articles

Size scaling of the exchange interaction in the quantum Hall effect regime

We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall effect (IQHE) regime in terms of many-body physics at higher Landau levels (LLs). We investigate the dependence of many-particle interactions on the lateral size of the electron system. We use the exchange enhancement of the $g$-factor for spin-polarized Landau levels as an indicator for the strength of the exchange interaction. The driving force for the $g$-factor enhancement is a Hund's rule behavior for the occupation of spin-split Landau levels that lowers the many-particle ground state energy by arranging as many spins in parallel as possible. By increasing the total number of electrons and total number of available states per LL, it can therefore be expected that the exchange-enhanced spin gap should increase as well. In contrast to the dependence on the magnetic field, an increase of the total number of states by simply increasing the system size at constant magnetic field shows a clear saturation behavior above a lateral system size of 1000 nm. The importance of this result is underlined by an extended introduction, which demonstrates the permanent dominance of many-body interactions in all transport regimes of the IQHE. A modeling of IQHE systems therefore has to include many-body interactions, and our results open a pathway towards many-body modeling of quantum Hall systems of macroscopic size.

Seebeck effect in a thermal QCD medium in the presence of strong magnetic field

The strongly interacting partonic medium created post ultrarelativistic heavy ion collision experiments exhibits a significant temperature-gradient between the central and peripheral regions of the collisions, which in turn, is capable of inducing an electric field in the medium; a phenomenon known as Seebeck effect. The effect is quantified by the magnitude of the induced electric field per unit temperature-gradient - the Seebeck coefficient ($S$). We study the coefficient, $S$ in the relativistic Boltzmann transport equation in relaxation-time approximation, as a function of temperature ($T$) and chemical potential ($\mu$), wherein we find that with current quark masses, the magnitude of $S$ for individual flavours as well as that for the medium as a whole decreases with $T$ and increases with $\mu$, with the electric charge of the flavour deciding the sign of $S$. The emergence of a strong magnetic field ($B$) in the non-central collisions at heavy-ion collider experiments motivates us to study the effect of $B$ on Seebeck effect. The strong $B$ affects $S$ in multifold ways, via : a) modification of phase-space due to the dimensional reduction, b) dispersion relation in lowest Landau level (occupation probability), and c) relaxation-time. We find that a strong $B$ not only decreases the magnitudes of $S$'s of individual species, it also flips their signs. This leads to a faster reduction of the magnitude of $S$ of the medium than its counterpart at $B=0$. We then explore how the interactions among partons in perturbative thermal QCD in the quasiparticle framework affect Seebeck effect, where we find that even in strong B, there is no more a flip of the sign of $S$ for individual species and an enhancement of the magnitudes of $S$ of individual species as well as that of the medium, compared to current quark mass description at either $B=0$ or $B \neq 0$.

Gauge-invariant variables reveal the quantum geometry of fractional quantum Hall states

Herein, we introduce the framework of gauge invariant variables to describe fractional quantum Hall (FQH) states, and prove that the wavefunction can always be represented by a unique holomorphic multi-variable complex function. As a special case, within the lowest Landau level, this function reduces to the well-known holomorphic coordinate representation of wavefunctions in the symmetric gauge. Using this framework, we derive an analytic guiding center Schr\"odinger's equation governing FQH states; it has a novel structure. We show how the electronic interaction is parametrized by generalized pseudopotentials, which depend on the Landau level occupancy pattern; they reduce to the Haldane pseudopotentials when only one Landau level is considered. Our formulation is apt for incorporating a new combination of techniques, from symmetric functions, Galois theory and complex analysis, to accurately predict the physics of FQH states using first principles.

Broken Symmetries and Kohn’s Theorem in Graphene Cyclotron Resonance

The magnetoplasmon spectrum of Landau level transitions in hexagonal boron nitride-encapsulated graphene is explored via infrared transmission magnetospectroscopy, as a function of the filling factor at fixed magnetic field. As the lowest Landau level occupancy is increased from half-filling, a non-monotonic progression of multiple cyclotron resonance peaks is observed, with a single peak evolving into four peaks and back to two, all with linewidths of order 0.5 meV. This provides a novel window on the interplay of electron interactions with broken spin and valley symmetries in the quantum Hall regime. Analysis of the peak energies shows an indirect enhancement of spin gaps below the Fermi energy, a Dirac mass at half-filling that is nearly 50\% larger than when the lowest Landau level is completely full, and a small but clear particle-hole asymmetry. We suggest a key role is played by the boron nitride in enabling interaction-enhanced broken symmetries to be observed in graphene cyclotron resonance.

Theoretical Models of Highly Magnetic White Dwarf Stars with Non-Polytropic Equation of State

Super-massive white dwarf (WD) stars in the mass range 2.4 - 2.8 solar masses are believed to be the progenitors of “super-luminous” Type Ia supernovae according to a hypothesis proposed by some researchers. They theorize such a higher mass of the WD due to the presence of a very strong magnetic field inside it. We revisit their first work on magnetic WDs (MWDs) and present our theoretical results that are very different from theirs. The main reason for this difference is in the use of the equation of state (EoS) to make stellar models of MWDs. An electron gas in a magnetic field is Landau quantized and hence, the resulting EoS becomes non-polytropic. By constructing models of MWDs using such an EoS, we highlight that a strong magnetic field inside a WD would make the star super-massive. We have found that our stellar models do indeed fall in the mass range given above. Moreover, we are also able to address an observational finding that the mean mass of MWDs are almost double that of non-magnetic WDs. Magnetic field changes the momentum-space of the electrons which in turn changes their density of states (DOS), and that in turn changes the EoS of matter inside the star. By correlating the magnetic DOS with the non-polytropic EoS, we were also able to find a physical reason behind our theoretical result of super-massive WDs with strong magnetic fields. In order to construct these models, we have considered different equations of state with at most three Landau levels occupied and have plotted our results as mass-radius relations for a particular chosen value of maximum Fermi energy. Our results also show that a multiple Landau-level system of electrons leads to such an EoS that gives multiple branches in the mass-radius relations, and that the super-massive MWDs are obtained when the Landau-level occupancy is limited to just one level. Finally, our theoretical results can be explained solely on the basis of quantum and statistical mechanics that warrant no assumptions regarding stars.

Interaction-Induced Shubnikov-de Haas Oscillations in Optical Conductivity of Monolayer MoSe_{2}.

We report polarization-resolved resonant reflection spectroscopy of a charge-tunable atomically thin valley semiconductor hosting tightly bound excitons coupled to a dilute system of fully spin- and valley-polarized holes in the presence of a strong magnetic field. We find that exciton-hole interactions manifest themselves in hole-density dependent, Shubnikov-de Haas-like oscillations in the energy and line broadening of the excitonic resonances. These oscillations are evidenced to be precisely correlated with the occupation of Landau levels, thus demonstrating that strong interactions between the excitons and Landau-quantized itinerant carriers enable optical investigation of quantum-Hall physics in transition metal dichalcogenides.

Phase slips and parity jumps in quantum oscillations of inverted InAs/GaSb quantum wells

We present magnetotransport measurements of a strongly hybridized inverted InAs/GaSb double quantum well. We find that the spin-orbit interaction leads to an appreciable spin-splitting of hole-like states, which form distinct Landau levels in a perpendicular magnetic field. The resulting quantum Hall state is governed by a periodic even and odd total filling arising due to the simultaneous occupation of electron-like and hole-like Landau levels of differing degeneracy. Furthermore, oscillatory charge transfer between all involved subbands leads to discrete phase slips in the usual sequential filling of Landau levels, and coincidentally the phase slips are close to $\pi$. These results shed new insights on the Landau level structure in composite systems and have consequences for interpreting intercepts obtained from index plots, which are routinely employed to investigate the presence of Berry's phase.

Characterization of individual layers in a bilayer electron system produced in a wide quantum well

Here, we report on a transparent method to characterize individual layers in a double-layer electron system, which forms in a wide quantum well, and to determine their electron densities. The technique relies on the simultaneous measurement of the capacitances between the electron system and gates located on either side of the well. Modifications to the electron wave function due to the population of the second subband and the appearance of an additional electron layer can be detected. The magnetic field dependence of these capacitances is dominated by quantum corrections caused by the occupation of Landau levels in the nearest electron layer. The technique should be equally applicable to other implementations of a double layer electron system.

Heterostructure symmetry and the orientation of the quantum Hall nematic phases

Clean two-dimensional electron systems in GaAs/AlGaAs heterostructures exhibit anisotropic collective phases, the quantum Hall nematics, at high Landau level occupancy and low temperatures. An as yet unknown native symmetry-breaking potential consistently orients these phases relative to the crystalline axes of the host material. Here we report an extensive set of measurements examining the role of the structural symmetries of the heterostructure in determining the orientation of the nematics. In single quantum well samples we find that neither the local symmetry of the confinement potential nor the distance between the electron system and the sample surface dictates the orientation of the nematic. In remarkable contrast, for two-dimensional electrons confined at a single heterointerface between GaAs and AlGaAs, the nematic orientation depends on the depth of the two-dimensional electron system beneath the sample surface.

Charge Tuning of Nonresonant Magnetoexciton Phonon Interactions in Graphene

Far from resonance, the coupling of the G-band phonon to magnetoexcitons in single layer graphene displays kinks and splittings versus filling factor that are well described by Pauli blocking and unblocking of inter- and intra-Landau level transitions. We explore the nonresonant electron-phonon coupling by high-magnetic field Raman scattering while electrostatic tuning of the carrier density controls the filling factor. We show qualitative and quantitative agreement between spectra and a linearized model of electron-phonon interactions in magnetic fields. The splitting is caused by dichroism of left- and right-handed circular polarized light due to lifting of the G-band phonon degeneracy, and the piecewise linear slopes are caused by the linear occupancy of sequential Landau levels versus ν.

Rarita–Schwinger particles under the influence of strong magnetic fields

In this work, we calculate the solutions of the Rarita–Schwinger equation with the inclusion of the electromagnetic interaction. Our gauge and coupling prescription choices lead to Dirac-type solutions. One of the consequences of our results is that all inconsistencies related to noncovariance and noncausality are avoided, and the Landau level occupation of particles turns out to be quite different from the usual spin 1/2 particle system occupation numbers. Our results do not indicate that the well known results obtained by Velo and Zwanzinger in 1969 are false or incorrect; they rather indicate that there exists an alternative way to deal with this problem that should be further explored, since this is a matter of interest in recent results related to heavy ion collisions and nuclear astrophysics.

The theory of bypassed-isotope formation in the universe

A Fermi-gas model for the atomic nucleus in the presence of a quantizing magnetic field is considered. The energy of the magnetized neutrons is determined taking into account the Pauli paramagnetism, and the energy of the magnetized protons taking into account Landau diamagnetism and Pauli paramagnetism. To determine the characteristics of the proton-gas energy in a quantizing magnetic field, we use a model for the proton motion in which the initial energy of the proton and the magnetic field strength enable estimation of the maximum Landau quantum number. The latter characterizes the proton motion perpendicular to the direction of the magnetic field. Due to the occupation of Landau levels by protons, it is possible to estimate the kinetic energy for continuous motion along the magnetic field from zero to a certain finite value. As a result, the magnetic field of a certain strength facilitates neutron evaporation from the nucleus and increases the stability of the protons in the nucleus.

Influence of strong magnetic fields and instantons on the phase structure of the two-flavor Nambu–Jona-Lasinio model

Both in heavy-ion collisions as in magnetars very strong magnetic fields are produced, which has its influence on the phases of matter involved. In this paper we investigate the effect of strong magnetic fields (B = 5 m_pi^2 /e = 1.7 x 10^19 G) on the chiral symmetry restoring phase transition using the Nambu-Jona-Lasinio model. It is observed that the pattern of phase transitions depends on the relative magnitude of the magnetic field and the instanton interaction strength. We study two specific regimes in the phase diagram, high chemical potential and zero temperature and vice versa, which are of relevance for neutron stars and heavy-ion collisions respectively. In order to shed light on the behavior of the phase transitions we study the dependence of the minima of the effective potential on the occupation of Landau levels. We observe a near-degeneracy of multiple minima with differing occupation numbers, of which some become the global minimum upon changing the magnetic field or the chemical potential. These minima differ considerably in the amount of chiral symmetry breaking and in some cases also of isospin breaking.

Enhancement of valley splitting in (100) Si MOSFETs at high magnetic fields

We report the density and magnetic field dependence of the valley splitting of two-dimensional electrons in (100) Si metal–oxide–semiconductor field-effect transistors, as determined via activation measurements in the quantum Hall regime. We find that the valley activation gap can be greatly enhanced at high magnetic fields as compared to the bare valley splitting. The observation of strong dependence of the valley activation gap on orbital Landau level occupancy and similar behavior of nearby spin gaps suggest that electron–electron interactions play a large role in the observed enhancement.

Vanishing Hall Coefficient in the Extreme Quantum Limit in Photocarrier-DopedSrTiO3

We explore the extreme quantum limit of photogenerated electrons in quantum paraelectric SrTiO3. This regime is distinct from conventional semiconductors, due to the large electron effective mass and large dielectric constant. At low temperature, the magnetoresistance and Hall resistivity saturate at a high magnetic field, deviating from conventional behavior. As a result, the Hall coefficient vanishes on the scale of the ratio of the Landau level splitting to the thermal energy, indicating the essential role of lowest Landau level occupancy, as limited by thermal broadening.

Electron tunneling spectroscopy of a quantum antidot in the integer quantum Hall regime

Quantum antidot, a small potential hill introduced into a two-dimensional electron system, presents an attractive tool to study quantum mechanics of interacting electrons. Here, we present experiments on electron resonant tunneling via a quantum antidot on the integer $i=1$, 2, 3, 4, 5, and 6 quantum Hall plateaus. Several features are reported. First, as a function of magnetic field, we observe up to six quasiperiodic resonant tunneling peaks within the fundamental flux period: When flux $h∕e$ is added to the area of the antidot, there are $i$ peaks on the $i\text{th}$ integer plateau when $i$ spin-polarized Landau levels are occupied. Corresponding backgate voltage data show one peak per added charge $e$ on all integer plateaus. Second, we observe tunneling dips in four-terminal resistance (``forward scattering'') on the even $i=2$, 4, and 6 plateaus when the populations of both spins are nearly equal. We also report an internal structure observed within the $h∕e$ period: On the $i=3$ spin-split plateau, two of the three resonant tunneling peaks are higher and/or closer than the third. Puzzlingly, in this regime, when the backgate voltage is swept, the tunneling peaks are grouped in pairs. These results are attributed to the dominance of the electron-electron Coulomb interaction, effectively mixing the Landau level occupation, and to the self-consistent electrostatics of the antidot.

Quantum transport in electron Fabry-Perot interferometers

We report experiments on Fabry-Perot electron interferometers in the integer quantum Hall regime. The $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure devices consist of two constrictions defined by etch trenches in two-dimensional electron layer, enclosing an approximately circular island. The interferometer is formed by counterpropagating chiral edge channels coupled by tunneling in the two constrictions. Interference fringes are observed as conductance oscillations, similar to the Aharonov-Bohm effect. Front gates deposited in etch trenches allow us to fine tune the device and to change the constriction filling $f$ relative to the bulk filling. Quantum-coherent conductance oscillations are observed on the $f=1--4$ plateaus. On plateau $f$, we observe $f$ conductance oscillations per fundamental flux period $h∕e$. This is attributed to the dominance of the electron-electron Coulomb interaction, effectively mixing Landau level occupation. On the other hand, the back-gate charge period is the same (one electron) on all plateaus, independent of filling. This is attributed to the self-consistent electrostatics in the large electron island. We also report dependence of the oscillation period on front-gate voltage for $f=1$, 2, and 4 for three devices. We find a linear dependence, with the slope inversely proportional to $f$ for $f=1$ and 2.

Two-dimensional superconductor in a tilted magnetic field: States with finite Cooper-pair momentum

Varying the angle $\ensuremath{\theta}$ between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers $0<n<\ensuremath{\infty}.$ The stable order-parameter structure and magnetic-field distribution for these states is found by minimizing the quasiclassical free energy near ${H}_{c2}$ including nonlinear terms. One finds states with coexisting linelike and pointlike order-parameter zeros and states with coexisting vortices and antivortices. The magnetic response may be diamagnetic or paramagnetic depending on the position within the unit cell. The structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at $\ensuremath{\theta}=0$ is reconsidered. The transition $\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}$ of the paramagnetic vortex states to the FFLO limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.

Theory of the quantum Hall effect atν=12in a wide quantum well

In a monolayer system a composite (c) fermion with two flux quanta (fluxons) is known to be generated at the Landau level occupation number (filling factor) $\ensuremath{\nu}=\frac{1}{2}.$ In a bilayer system two c fermions are bound via the phonon exchange to form a pair (p) c boson with parallel electron spins and the system of condensed pc bosons generates a quantum Hall effect (QHE) state at $\ensuremath{\nu}=\frac{1}{2}.$ Similar pc bosons are formed more efficiently at $\ensuremath{\nu}=1,$ and the QHE state developed is stronger. These QHE states become weaker at a tilted magnetic field since the pc boson has a p-wave-type charge distribution with the preferred axis along [001].

DISTRIBUTION OF EQUILIBRIUM EDGE CURRENTS

The distribution of equilibrium edge current density in 2D system subjected to a strong (quantizing) magnetic field has been studied. The case of half plane in normal magnetic field has been considered. The transition from classical strong magnetic field to ultra-quantum limit has been investigated. We have shown that the edge current density oscillates and decays with distance from the edge. The oscillations have been attributed to the Fermi wavelength of electrons. The additional component of the current smoothly depending on the distance but sensitive to the occupation of Landau levels has been found. The temperature suppression of oscillations has been studied.