Electron System In Magnetic Field Research Articles

Ballistic-to-hydrodynamic transition and collective modes for two-dimensional electron systems in magnetic field

The recent demonstrations of viscous hydrodynamic electron flow in two-dimensional electron systems poses serious questions to the validity of existing transport theories, including the ballistic model, the collision-induced and collisionless hydrodynamics. While the theories of transport at hydrodynamic-to-ballistic crossover for free 2d electrons are well established, the same is not true for electrons in magnetic fields. In this work, we develop an analytically solvable model describing the transition from ballistic to hydrodynamic transport with changing the strength of electron-electron collisions in magnetic fields. Within this model, we find an expression for the high-frequency non-local conductivity tensor of 2d electrons. It is valid at arbitrary relation between frequency of external field $\omega$, the cyclotron frequency $\omega_c$, and the frequency of e-e collisions $\tau^{-1}_{ee}$. We use the obtained expression to study the transformation of 2d magnetoplasmon modes at hydrodynamic-to-ballistic crossover. In the true hydrodynamic regime, $\omega\tau_{ee} \ll 1$, the 2DES supports a single magnetoplasmon mode that is not split at cyclotron harmonics. In the ballistic regime, $\omega\tau_{ee} \gg 1$, the plasmon dispersion develops splittings at cyclotron harmonics, forming the Bernstein modes. A formal long-wavelength expansion of kinetic equations ("collisionless hydrodynamics") predicts the first splitting of plasmon dispersion at $\omega\approx 2\omega_c$. Still, such expansion fails to predict the zero and negative group velocity sections of true magnetoplasmon dispersion, for which the full kinetic model is required.

Bernstein modes and giant microwave response of a two-dimensional electron system

We report on a new contribution to the microwave response of a two-dimensional electron system in magnetic field which originates from excitation of virtual Bernstein modes. These collective modes emerge as a result of interaction between usual magnetoplasmon mode and cyclotron resonance harmonics. The electrons are found to experience a strongly enhanced radiation field when its frequency falls in a gap of the Bernstein modes spectrum. This field can give rise to nonlinear effects, one of which, the parametric cyclotron resonance, is discussed. We argue that this resonance leads to a plasma instability in the ultraclean system. The instability-induced heating is responsible for the giant photoresistivity spike recently observed in the vicinity of the 2nd cyclotron resonance harmonic.

Local-gauge finite-element method for electron waves in magnetic fields

The finite-element method (FEM) has already been extended to analyze transport properties of electron waves of two-dimensional electron systems in magnetic fields. Although many researchers have created new formulations or improvements to this method, few have analyzed how this method is applied to realistic systems. The present paper suggests that conventional formulations of the FEM do not give accurate results for large systems or for strong magnetic fields; in addition, it suggests that the selected gauge significantly influences the numerical results. Furthermore, this paper proposes a conceptually different formulation of the FEM that solves the poor convergence problem. This formulation is simple: matrix elements are multiplied by the Peierls phase in the absence of a magnetic field. To show the advantages of this formulation, numerical examples are presented.

Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law

We consider two-dimensional randomly deformed circular quantum dots with two attached waveguides (an emitter and a collector) in magnetic fields as an electronic analogy of the blackbody radiation. Transport properties through them are numerically investigated. The fraction of the current carried by each propagating mode in the collector is computed for transmission currents when each propagating mode is incident. By taking the statistical average in shape, it is shown that a universal frequency distribution is obtained for a sufficiently deformed system even though magnetic fields are so strong that electron waves form edge states. Then, the transmission currents are randomly distributed over all propagating modes. On average, each propagating mode carries the same current as in the absence of a magnetic field. It is also confirmed that a finite size dot cannot be a model of a reservoir even if it is chaotic.

Optical mapping of properties of two-dimensional electron system in magnetic fields

Real-space mappings of a Hall photovoltage are performed by local laser excitation using optical microscope setup with a spatial resolution of about 2 μ m . The obtained images of broad and narrow strips presumably reflect the diffusion of the optically created electrons in the bulk and the edge states. The image near a current contact is considered to reflect the potential gradient near the contact.

Renormalization of impurity scattering in one-dimensional interacting electron systems in magnetic field

We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On the contrary, we show that in a strong magnetic field the interaction may suppress the backscattering of majority-spin electrons by the impurity potential in the vicinity of the weak-potential fixed point. This implies that in a certain temperature range the impurity becomes almost transparent for the majority-spin electrons while it is impenetrable for the minority-spin ones. The impurity potential can thus have a strong spin-filtering effect.

Charge-density response function of two-dimensional electron systems in a magnetic field

We examine charge density excitations in two-dimensional electron systems in a strong perpendicular magnetic field. Our theoretical framework is the extended random-phase approximation (extended RPA, ERPA), which takes into account all the second-order self-energies of particle-hole propagators. Our results are different from the RPA response functions qualitatively, and are consistent with recent empirical findings. We explain our results in detail in connection with two-particle-two-hole degrees of freedom and the Kohn theorem.

Photoconductivity of 2D electron systems in magnetic field

According to recent photoconductivity measurements in 2D electron semiconductor systems in magnetic fields normal to the 2D plane, the photoconductivity as a function of magnetic field exhibits oscillations in the region of fields much weaker than those necessary for the observation of the Shubnikov-de Haas effect. In this paper, the aforementioned oscillations are interpreted as a two-dimensional analogue of magnetophoton (phonon) oscillations studied in detail by different authors on 3D samples.

Fermi-edge singularities in a one-dimensional electron system in magnetic field

Fermi-edge singularities (FESs) have been found in the photoluminescence (PL) spectra of n-type doped GaAs quantum wires produced by strain-confinement. This is in contrast to the PL from the original heterojunction where no such features were observed. The FES dominates the spectrum of the quantum wires at low magnetic field. On increasing the magnetic field, the intensity of the FES falls sharply as the Fermi energy drops to the lowest one-dimensional subband. This behaviour of the FESs is in qualitative agreement with theory [Phys. Rev. B 49 (1994) 16781].

Modification of the intersubband excitation spectrum in a two-dimensional electron system under a perpendicular magnetic field.

Under an external magnetic field, new branches of spin- and charge-density waves have been studied in a quasi-two-dimensional electron system whose ground state has more than one Landau level occupied by electrons. These collective excitations can be treated as manifestations of the multicomponent nature of the electron system in magnetic field, whereas the occupied Landau levels should be associated with degrees of freedom.

Critical Level Statistics in Two-Dimensional Disordered Electron Systems

The level statistics in the two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The level spacing distribution functions $P(s)$'s are found to be independent of the system size or of the type of the potential distribution, suggesting the universality. They behave as $s^2$ in the small $s$ region in the former case, while $s^4$ rise is seen in the latter.

Localisation in the quantum hall regime

The present status of the study of localisation in two-dimensional disordered electron systems in magnetic fields in the quantum Hall regime is reviewed. The critical behaviour of localisation characteristics of quantum Hall system is elucidated by numerical results and its relevance to low-temperature transport properties is studied. The perturbational approach and the σ xx − σ xy diagram are also reviewed. The relation to the weak-magnetic-field localisation, variable-range hopping conduction and quantum fluctuations in the quantum Hall regime are also discussed.

Two-dimensional electron systems in magnetic field: high H as a classical limit

The authors study the thermodynamics of a 2D electron system in perpendicular magnetic field H. It is shown that, for a wide class of interaction and external potentials (including irregular ones), the grand partition function takes the form of a classical partition function as H to infinity . Some consequences of this theorem are also discussed.