Persistent currents and magnetization in two-dimensional magnetic quantum systems

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the “classical” relationship between current and magnetization is shown to hold for systems invariant both by translation and rotation. Applications are given, including the point vortex superposed onto an homogeneous magnetic field, the quantum Hall geometry (an electric field and an homogeneous magnetic field) and the random magnetic impurity problem (a random distribution of point vortices).     

Rabi type oscillations in damped two-dimensional single electron quantum dots

We present a quantized model of a harmonically confined dot atom with inherent damping in the presence of a transverse magnetic field. The model leads to a non-Hermitian Hamiltonian in coordinate space. We have analytically studied the effects of damping on Rabi type oscillations of the system. The model explains the decoherence of Rabi oscillations in a Josephson Junction.     

Magnetic susceptibility of a two-dimensional electron gas in the quantum strong magnetic field limit

It is shown that the peak values of the magnetic susceptibility of a two-dimensional electron gas in the quantum strong magnetic field limit are integral multiples of $\text{μ}{}^2{}_{\mathrm{B}}\text{2π}$.     

Magnetic quantum oscillations in nanowires

Analytical expressions for the magnetization and the longitudinal conductivity of nanowires are derived in a magnetic field, B. We show that the interplay between size and magnetic field energy-level quantizations manifests itself through novel magnetic quantum oscillations in metallic nanowires. There are three characteristic frequencies of de Haas-van Alphen (dHvA) and Shubnikov-de Haas (SdH) oscillations, F = F(0)/(1 + gamma)(3/2), and F(+/-) = 2F(0)/|1 + gamma +/- (1 + gamma)(1/2)|, in contrast with a single frequency F(0) = S(F)plankc/(2pie) in simple bulk metals. The amplitude of oscillations is strongly enhanced in some magic magnetic fields. The wire cross-section area S can be measured using the oscillations as S = 4pi(2)S(F)plank(2)c(2)/(gammae(2)B(2)) along with the Fermi-surface cross-section area, S(F).     

Submillimeter wave induced resistance oscillations in ultra-high mobility two-dimensional electron systems

Submillimeter wave induced resistance oscillations in two ultra-high mobility GaAs/Al_0.24Ga_0.76As quantum well samples have been investigated by means of a backward wave oscillator and far-infrared laser at ³He temperatures. Subnikov–de Haas oscillation, submillimeter wave induced resistance oscillation, and magnetoplasmon resonance occur simultaneously in this frequency regime. The primary radiation induced resistance minimum shifts toward cyclotron resonance with increasing radiation frequency. The positions of these minima agree well with those of the magnetoplasmon resonance. The higher-order harmonics of the resistance oscillation remain around the multiples of the cyclotron resonance frequency. An in situ transmission measurement exhibits an asymmetric broadening of the cyclotron resonance, appearing as a combination of the cyclotron resonance and the magnetoplasmon resonance, but no features directly linked to the microwave induced resistance oscillation can be seen.     

高迁移率二维电子系统中微波辐射引起的磁阻振荡和零电阻

一年以前 ,人们惊奇地发现 :在相当弱的磁场中 ,并不太强的微波辐照就可以使二维半导体的磁阻产生强烈的振荡 ,振幅的最大值可超过无辐照磁阻值的十几倍 ,最小值可以一直降到零 .全世界众多的凝聚态物理学家争相聚焦到这个领域 ,进行了许多实验和理论研究 ,企图弄清这一意外发现的机理 .经过一年多的努力 ,人们已经掌握了这个现象更多的细节 ,对其物理机制也有了初步了解 .但深入的实验和理论探索可能还要继续相当一段时间 .文章将对这个物理现象及相关的理论模型 ,尤其是目前得到较多赞同的光子辅助磁输运模型 ,作一简单的介绍 .     

Oscillatory magnetization of two-dimensional electron gas

Diamagnetic moment of the two-dimensional electron gas is calculated for finite temperature using a simple energy band model and assuming no collisional broadening of Landau levels. Numerical results are presented for GaAs band parameters. The diamagnetic moment oscillates around zero value as a function of magnetic field strength and tends to zero at low fields. It is concluded that both the diamagnetic and the paramagnetic susceptibilities of the 2D electron gas vanish in the low field limit.     

Exchange interaction and oscillations of the magnetization of the electron gas in a quantum cylinder

The exchange energy of the electron gas on a cylindrical surface in a constant magnetic field has been calculated. Analytical formulas describing the contribution of the exchange interaction into oscillations of the magnetization of the electron gas in a quantum cylinder have been obtained. It is shown that the magnetic response of the system exhibits Aharonov-Bohm oscillations for both degenerate and Boltzmann electron gases.     

Experimental researches on quantum transport in semiconductor two-dimensional electron systems

The author reviews contribution of Gakushuin University group to the progress of the quantum transport in semiconductor two-dimensional electron systems (2DES) for forty years from the birth of the 2DES in middle of the 1960s till the finding of temperature dependent collapse of the quantized Hall resistance in the beginning of this century.     

Temperature dependent weak field Hall resistance in two-dimensional carrier systems

Using the Drude-Boltzmann semiclassical transport theory, we calculate the weak-field Hall resistance of a two-dimensional system at low densities and temperatures, assuming carrier scattering by screened random charged impurity centers. The temperature-dependent 2D Hall coefficient shows striking nonmonotonicity in strongly screened systems, and, in particular, we qualitatively explain the recent puzzling experimental observation of a decreasing Hall resistance with increasing temperature in a dilute 2D hole system. We predict that the impurity scattering limited Hall coefficient will eventually increase with temperature at higher temperatures.     

Fractional features in radiation-induced oscillations of the magnetoresistance of two-dimensional electron systems

The magnetoresistance of two-dimensional electron systems irradiated by microwave radiation is calculated. It exhibits oscillatory features at fractional values of the ratio ω/ω_c of the circular frequency of microwave radiation to the cyclotron frequency. The calculation explains existing experimental data by nonequilibrium population of electron states that appears due to one-photon processes and predicts ω/ω_c values near which the basic features in magnetoresistance are expected. In the framework of the mechanism under consideration, the fractional features can be observed only in the crossover from strongly overlapping to separate Landau levels and only at radiation frequencies below the threshold frequencies depending on a fractional value.     

Magnetic quantum oscillations in a monolayer graphene under a perpendicular magnetic field

The de Haas-van Alphen(dHvA) oscillations of electronic magnetization in a monolayer graphene with structureinduced spin-orbit interaction(SOI) are studied.The results show that the dHvA oscillating centre in this system deviates from the well known(zero) value in a conventional two-dimensional electron gas.The inclusion of SOI will change the well-defined sawtooth pattern of magnetic quantum oscillations and result in a beating pattern.In addition,the SOI effects on Hall conductance and magnetic susceptibility are also discussed.     

Sound propagation in two-dimensional electron systems in strong magnetic field

Under the dHvA condition, the sound velocity in two-dimensional electron systems is expected to oscillate strongly as a function of 1/γ₀ which is the ratio of the ideal Fermi energy to the field energy.     

Magnetic field effects on low dimensional electron systems: Luttinger liquid behaviour in a quantum wire

We discuss the effects of a strong magnetic field in quantum wires. We show how the presence of a magnetic field modifies the role played by electron electron interaction producing a strong reduction of the backward scattering corresponding to the Coulomb repulsion. We discuss the consequences of this and other effects of magnetic field on the Tomonaga-Luttinger liquids and especially on their power-law behaviour in all correlation functions. The focal point is the rescaling of all the repulsive terms of the interaction between electrons with opposite momenta, due to the edge localization of the electrons and to the reduction of the length scale. Because of the same two reasons there are some interesting effects of the magnetic field concerning the backward scattering due to the presence of one impurity and the corresponding conductance. As an effect of the magnetic field we find also a spin polarization induced by a combination of electrostatic forces and the Pauli principle, quite similar to the one observed in large Quntum Dots.     

Tunneling between two-dimensional electron systems in a strong magnetic field

We calculate the tunnel current between two parallel two-dimensional electron systems in a strong perpendicular magnetic field. We model the strongly correlated electron systems by Wigner crystals, and describe their low-energy dynamics in terms of magnetophonons. The effects of the magnetophonons on the tunneling processes can be described by an exactly solvable independent-boson model. A tunneling electron shakes up magnetophonons, which results in a conductance peak that is displaced away from zero voltage and broadened compared with the case of no magnetic field. At low temperatures and low enough voltages the tunneling conductance is strongly suppressed, and the I–V characteristics exhibit a power-law behavior. The zero-voltage conductance is thermally activated with an activation temperature 10 K. The results are in very good agreement with experiment.     

Plasma oscillations in two-dimensional electron systems with a superstructure under Stark quantization conditions

The effect of quantizing electric field on plasma oscillations of two-dimensional electron gas in a system with a periodic potential has been theoretically investigated. The coupled-plasmon spectrum ω(q) is calculated for high temperatures (Δ ? T, where Δ is the conduction miniband width and T is temperature in energy units). The calculations are based on the quantum theory of plasma oscillations in the random-phase approximation, with allowance for the umklapp processes.     

Resistance oscillations in two-dimensional electron systems induced by both ac and dc fields

We report on magnetotransport measurements in a high-mobility two-dimensional electron system subject simultaneously to ac (microwave) and dc (Hall) fields. We find that dc excitation affects microwave photoresistance in a nontrivial way. Photoresistance maxima (minima) evolve into minima (maxima) and back, reflecting strong coupling and interplay of ac- and dc-induced effects. Most of our observations can be explained in terms of indirect electron transitions using a new, combined resonant condition. Observed quenching of microwave-induced zero resistance by a dc field cannot be unambiguously linked to a domain model, at least before a systematic theory treating both excitation types within a single framework is developed.     

Nonhomogeneous electrostatic oscillations in two-dimensional systems

A new type of excitations — electrostatic oscillations (ESO) — are shown to exist in the finite superlattices (SL). The ESO are the limiting case of the surface magnetoplasmons when the scale length of the spatial variations in the fields and currents is comparable with the sample dimensions. The formal similarity is found between the ESO and the magnetization vibrations in ferromagnetic materials (Walker's modes [1,2]). The main feature of the ESO is the independence of their frequencis on the absolute dimensions of a sample.