Nonequilibrium Green's Function Approach to Resonant Magnetotunneling Through a Quantum Dot

Keldysh's nonequilibrium Green's function is applied to studying resonant magnetotunneling through a quantum dot. We propose a microscopic Anderson-impurity-like Hamiltonian in which two kinds of the on-site Coulomb interactions are introduced:the interaction of two electrons at the same Landau level with different spins, U₁ and the interaction for the electrons between different Landau levels, U₁. I-V curves are obtained under different magnetic fields in asymmetrical structures which can display both the energy quantization and singleelectron charging effect. The theoretical results are in good agreement with the experiments qualitatively. The linear-response conductance is also discussed.     

石墨烯基磁量子环的低态能谱对磁场的依赖关系

我们采用狄拉克-韦尔 (Dirac-Weyl) 模型, 计算出二维石墨烯基磁量子环和磁量子点分别在垂直非均匀磁场下的低态能谱, 并讨论包括两组旋量分量的低态能谱跟磁场的依赖关系。从直接对角计算法所获得的数值结果表明, 在非均匀磁场下, 磁量子点和磁量子环的能谱中的最低朗道能级(N-=0)皆为高度简并, 且数值恒等为零。在其邻近较高的朗道能级, 磁量子环出现了由磁场诱导的轨道角动量间的跃迁, 而磁量子点则没有。最后本文指出, 除了最低朗道能级(N-=0)外, 两组旋量分量的能谱完全一样, 只是其朗道能级所标记的两组量子数不同而已。     

点缺陷扶手型石墨烯量子点的电子性质研究

基于有限差分方法, 数值求解了Dirac方程, 研究了垂直磁场下的点缺陷扶手型 石墨烯 量子点的能谱结构, 分析了尺寸大小对带隙的影响. 与无磁场时具有一定带隙 (带隙的大小与半径成反比) 的量子点相比, 在外加有限磁场下, 能谱中出现朗道能级, 最低朗道能级能量为零并与磁场强度无关, 并且朗道能级的简并度随着磁场的增加而增加. 进一步的计算表明, 最低朗道能级的简并度与磁场成线性关系, 与半径的平方成线性关系. 本文工作对基于石墨烯量子点的器件设计具有一定的指导意义.     

Magneto-coulomb oscillations in GaAs-AlGaAs quantum dot structures

We report on experiments of the magnetotransport properties of GaAs-AlGaAs lateral quantum dots. At high magnetic fields for a 1 μm square dot structure, current flow occurred via edge states and, with the point contacts adjusted to allow transmission of one or more edge states, a strong backscattering resonance followed by short period oscillations were observed in the magnetoresistance, as B increased. At higher fields for a 2 μm dot, we observe a rapid rise in the magnetoresistance associated with the depopulation of the point contacts and the isolation of the dot from the leads. At still higher fields there occur periodic oscillations whose period was two orders of magnitude larger than would result from interference, or Aharonov-Bohm type effects.We analyze these phenomena using self-consistent electronic structure calculations for our devices. In particular, we show that the evolution of the terrace like structure of the potential profile profoundly affects the single particle spectrum within the dot when several Landau levels are occupied. For the large dot device, we expect that in the high field regime with the dot isolated from the leads, only a single Landau level is occupied in both the dot and the 2DEG region. In this regime, tunneling into and out of the dot is regulated by charging effects. We have introduced a "magneto-Coulomb oscillations" explanation of the periodic resonances that are observed.     

Semiconductor quantum dots in high magnetic fields

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called Λ levels).     

外场调控下硼磷烯量子点的电子结构和光学性质研究

采用紧束缚近似方法对锯齿状六边形硼磷烯量子点在平面电场和垂直磁场调控下的电子结构和光学性质进行了研究. 研究表明,硼磷烯量子点作为直接带隙半导体,在无外加电场和磁场作用时,能隙不随尺寸的改变而变化. 在平面电场调控下,能隙随电场强度的增加逐渐减小直至消失,平面电场方向几乎不会对硼磷烯量子点体系产生影响, 且随量子点尺寸的增大,能隙消失所需电场强度逐渐减小. 在垂直磁场调控下,表现为体态的能级在磁场作用下形成朗道能级,而能隙边缘处的朗道能级近似为一个平带,不随磁通量的改变而变化,态密度主要分布于朗道能级处. 另外,垂直磁场作用下的光吸收主要是由朗道能级之间的跃迁引起的.     

Bound states of Dirac electrons in a graphene-based magnetic quantum dot

We investigate the magnetically confined states of the massless Dirac fermions in a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the dot. The calculated energy spectrum exhibits quite different features with and without the magnetic field inside the dot. It is found that the degeneracy of the relativistic Landau level with negative angular momenta can be lifted, and this degeneracy breaking can be modulated by the magnetic field inside the dot. Moreover, such a system can form the strongly localized states within the dot and along its boundary, especially with the magnetic field inside the dot.     

Magnetotunneling into Fock–Darwin‐like quantum dot states: Lateral matrix elements and the role of selection rules

We study theoretically the magnetotunneling transport through quantum dots formed by thermal diffusion of charged manganese interstitials in the vicinity of a GaAs quantum well [Phys. Rev. Lett. 101 , 226807 (2008)]. In particular, we examine the lateral matrix elements between Landau subbands in the contact and Fock–Darwin‐like states of an individual dot at high magnetic fields. We explicitly demonstrate the effect of spatial deformation of the dot on the wave function's overlap. The comparison with measured data suggests a selection rule similar to angular momentum conservation for tunneling into perfect Fock–Darwin states. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Excitonic energy shell structure of self-assembled InGaAs/GaAs quantum dots

Performing optical spectroscopy of highly homogeneous quantum dot arrays in ultrahigh magnetic fields, an unprecedently well resolved Fock-Darwin spectrum is observed. The existence of up to four degenerate electronic shells is demonstrated where the magnetic field lifts the initial degeneracies, which reappear when levels with different angular momenta come into resonance. The resulting level shifting and crossing pattern also show evidence of many-body effects such as the mixing of configurations and exciton condensation at the resonances.     

Quantum galvanomagnetic properties of n-type inversion layers on Si(100) MOSFET

Transverse magnetoconductivity σ_xx and Hall effect in n-type inversion layers of Si(100) MOSFET are measured for various source-drain fields between 0.08 and 40 V/cm under magnetic fields up to 150 kOe at 1.4 K. Conductivity peaks in low Landau levels are in good agreement with theory. Effect of the source-drain field in the magnetoconductivity is found to be very important in higher Landau levels as well as in the appearance of the lowest Landau level peak. Immobile electrons are clearly observed in conductivity bottoms. Electrode geometry effect for Hall effect measurement under strong magnetic fields is discussed.     

Nonuniform energy level broadening in open quantum dots: the influence of the closed dot eigenstates on transport

We present simulations of a realistically modeled quantum dot with soft boundaries and open leads supporting several modes. The wavefunctions of this open dot can be decomposed in terms of the eigenstates of a corresponding closed dot my means of projection. At particular resonances, this decomposition reveals that transport in the open dot can be mediated through a single eigenstate. Thus, the quantization of closed-dot energy levels can be preserved even as the dot is opened, but we find that there is a selection of particular eigenstates that depends strongly on the positions and nature of the contacts.     

Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels

We have studied a quantum dot with Rashba spin-orbit interaction in noncommutative phase space. The energy eigenvalues are analogous to Landau energy levels. It is shown that this system is related with a physically realizable model of a quantum dot with Rashba spin-orbit interaction in a magnetic field whereby a relation is derived among the noncommutative parameters, spin-orbit coupling strength and magnetic field.     

Resonant tunneling transport through GaAs/AlGaAs superlattices in strong tilted magnetic field

An analysis is presented of the transverse resonant tunneling transport through GaAs/AlGaAs superlattices due to tunneling between Landau levels in quantum wells in a strong tilted magnetic field. A high tunneling rate is demonstrated between Landau levels with Δn ≠ 0 in a magnetic field with a nonzero in-plane component. This leads to substantial broadening and shift of the tunneling resonance and significant changes in the current-voltage characteristics of superlattices. The predicted behavior of the current-voltage characteristics of superlattices in tilted magnetic fields is demonstrated experimentally.     

Quantum-Hall activation gaps in graphene

We have measured the quantum-Hall activation gaps in graphene at filling factors nu=2 and nu=6 for magnetic fields up to 32 T and temperatures from 4 to 300 K. The nu=6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at nu=2 is strongly temperature and field dependent and approaches the expected value for sharp Landau levels for fields B>20 T and temperatures T>100 K. We explain this surprising behavior by a narrowing of the lowest Landau level.     

Higher Landau levels contribution to the energy of interacting electrons in a quantum dot

Properly regularized second-order degenerate perturbation theory is applied to compute the contribution of higher Landau levels to the low-energy spectrum of interacting electrons in a disk-shaped quantum dot. At “filling factor” near , this contribution proves to be larger than energy differences between states with different spin polarizations. After checking convergence of the method in small systems, we show results for a 12-electron quantum dot, a system which is hardly tractable by means of exact diagonalization techniques.     

Giant backscattering resonances in the magneto-resistance of GaAs/AlGaAs quantum dots

We discuss the observation of large resonant features, superimposed upon the quantum Hall plateaux of gated GaAs/AlGaAs quantum dots. The resonances correspond to a magnetically induced increase in the edge state backscattering, and under certain conditions can imply a complete reflection of the applied current. We demonstrate that the resonances are correlated to the depopulation of bulk Landau levels, and suggest they result from an increase in backscatterlng via confined Landau levels, as the latter depopulate in a magnetic field. The resonances are therefore analogous to the Shubnikov-de Haas oscillations, observed in two dimensional electron gas systems, and their temperature dependence is found to take the same functional form. We argue that the resonances are an intrinsic feature of edge state transport in quantum dots, since they result from scattering via Landau levels, controllably confined within the dot, and discuss our results in relation to recent theoretical and experimental studies, of edge state transport in small wires and dots.     

Direct measurement of the Fermi energy in graphene using a double-layer heterostructure

We describe a technique which allows a direct measurement of the relative Fermi energy in an electron system by employing a double-layer heterostructure. We illustrate this method by using a graphene double layer to probe the Fermi energy as a function of carrier density in monolayer graphene, at zero and in high magnetic fields. This technique allows us to determine the Fermi velocity, Landau level spacing, and Landau level broadening. We find that the N=0 Landau level broadening is larger by comparison to the broadening of upper and lower Landau levels.     

Localization and the integer-quantized Hall effect: Diffusion constant for high Landau levels and white noise potential

The diffusion constant and the diagonal conductivity for non-interacting electrons in a two-dimensional, disordered system are studied. A homogeneous magnetic field perpendicular to the electron system is assumed. For weak short-range random potentials and high fields the Landau quantum numbern can be used as expansion parameter. In the limit of high Landau levels the system shows metallic behaviour. Corrections for finiten decrease the conductivity and indicate localized states in the whole energy band. A breakdown of the expansion and stronger localization are observed only for the lowest Landau levels if the typical experimental length scale of the quantized Hall effect is used.     

Quantum dots with disorder and interactions: a solvable large-g limit

We analyze the problem of interacting electrons on a ballistic quantum dot with chaotic boundary conditions, where the effective interactions at low energies are characterized by Landau parameters. When the dimensionless conductance g of the dot is large, the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as g --> infinity (as in a large-N theory), leading to a phase transition in each Landau interaction channel. In the weak-coupling phase constant charging and exchange interactions dominate the low-energy physics, while the strong-coupling phase displays a spontaneous distortion of the Fermi surface, smeared out by disorder.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.