Pseudomagnetic fields and Landau levels for out-of-plane elastic waves in gradient snowflake-shaped crystals

The study of pseudomagnetic fields (PMF) in classical waves draws a growing attention due to the strength of PMF far higher than real magnetic fields. Here, we show that a giant PMF for out-of-plane elastic waves can be created in the snowflake-shaped crystals by introducing a gradient angle modulation along one direction. In particular, we demonstrate that the Landau energy levels for out-of-plane elastic waves can be formed near the Dirac cone region, as a hallmark of high-field physics induced by PMF. Moreover, the sublattice polarized bulk states similar to the behavior of graphene electron in magnetic fields are achieved in our elastic systems. Furthermore, the magnetic-induced edge state propagation along bend pathway is also demonstrated. Our study provides a new paradigm for manipulating the elastic waves in aspects of information processing and energy transport.     

Effect of a nonuniform magnetic field on the Landau states in a biased AA-stacked graphene bilayer

We study the Landau states in the biased AA-stacked graphene bilayer under an exponentially decaying magnetic field along one spatial dimension. The results show that the energy eigenvalues of the system are strongly dependent on the inhomogeneity of the magnetic field and the bias voltage between the graphene layers, and in particular the reordering and mixing of finite Landau states could occur. Moreover, we also demonstrate that the current carrying states induced by the decaying magnetic field propagate vertically to the magnetic-field gradient within the graphene sample and can be further modulated by the bias voltage between the layers.     

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.     

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.     

Spin edge states in two-dimensional electron systems in the presence of Zeeman effect

We study the spin edge states, induced by the combined effect of Bychkov-Rashba spinorbit and Zeeman interactions or of Dresselhaus spin-orbit and Zeeman interactions in a twodimensional electron system, exposed to a perpendicular quantizing magnetic field and restricted by a hard-wall confining potential. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum versus the momentum and the magnetic field. We calculate the average spin components and the average transverse position of electron. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. Depending on the type of spin-orbit coupling and the principal quantum number, the Zeeman term in the combination with spin-orbit interaction increases or decreases essentially the splitting of bulk Landau levels while it has a weak influence on the spin edge states.     

磁场中的拓扑绝缘体边缘态性质

用数值方法研究了拓扑绝缘体薄膜体系在外加垂直磁场 作用下其边缘态的性质. 磁场的加入通过耦合k+eA, 即Peierls势替换关系和 该作用导致的Zeeman交换场体现在哈密顿量中. 考虑窄条圆环状结构的二维InAs/GaSb/AlSb薄膜量子阱材料, 当其处于拓扑非平庸状态, 即量子自旋霍尔态时, 会出现受时间反演对称性保护的两支简并边缘态, 而在垂直磁场的作用下, 时间反演对称性被破坏, 这时能带将形成一条条的朗道能级, 原来简并的两支边缘态也会分开到朗道能级谱线的两侧, 从电子态密度的空间分布情况则可以看到边缘态分别局域在材料的两个边界. 随着磁场的增大, 位于同一边界上的不同 自旋极化的边缘态将出现分离: 一支仍然局域在边缘, 另一支则随外加磁场的增加而有逐渐演化到材料内部的趋势. 文中还计算了同一边界上的两支边缘态之间的散射, 结果表明由于两个边缘态在空间发生分离, 相互之间的散射被很大的压制, 得到了其散射随磁场增加没有明显变化的结论, 所以磁场并不会增强散射过程, 也没有破坏体拓扑材料的性质, 说明了量子自旋霍尔态在没有时间反演对称的情况下也可以有较强的稳定性.     

Spontaneously gapped ground state in suspended bilayer graphene

Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.     

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。     

Novel optical probe for quantum Hall system

Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.     

Modification of Landau Levels in a 2D Ring Due to Rotation Effects and Edge States

The properties of a 2D quantum ring under rotating and external magnetic field effects are investigated. The Landau levels and their inertial effects on them are initially analyzed. Among the results obtained, it is emphasized that the rotation lifted the degeneracy of Landau levels. The second part deals with the electronic confinement in a 2D ring modeled by a hard wall potential. The eigenstates are described by Landau states as long as they are not too close to the ring edges. On the other hand, near the ring edges, the energies increase monotonically. These states are known as edge states. Edge states have a significant role in the physical properties of the ring. Thus, the Fermi energy and magnetization are analyzed. In the specific case of magnetization, two approaches are considered. In the first approach, an analytical result for magnetization is obtained but without considering rotation. Numerical results show the de Haas-Van Alphen (dHvA) oscillations. In the second approach, rotating effects are considered. In addition to the dHvA oscillations, the Aharonov–Bohm-type (AB) oscillations are verified, which are associated with the presence of edge states. The effects of rotation on the results are discussed and it is found that rotation is responsible for inducing AB oscillations.     

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime.We show that analytical solutions to the Dirac equation can be obtained,where the spectrum of energy corresponds to the relativistic Landau levels.We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.     

A full numerical calculation of the Franz--Keldysh effect on magnetoexcitons in a bulk semiconductor

We have performed a full numerical calculation of the Franz--Keldysh (FK) effect on magnetoexcitons in a bulk GaAs semiconductor. By employing an initial value method in combination with the application of a perfect matched layer, the numerical effort and storage size are dramatically reduced due to a significant reduction in both computed domain and number of base functions. In the absence of an electric field, the higher magnetoexcitonic peaks show distinct Fano lineshape due to the degeneracy with continuum states of the lower Landau levels. The magnetoexcitons that belong to the zeroth Landau level remain in bound states and lead to Lorentzian lineshape, because they are not degenerated with continuum states. In the presence of an electric field, the FK effect on each magnetoexcitonic resonance can be identified for high magnetic fields. However, for low magnetic fields, the FK oscillations dominate the spectrum structure in the vicinity of the bandgap edge and the magnetoexcitonic resonances dominate the spectrum structure of higher energies. In the moderate electric fields, the interplay of FK effect and magnetoexcitonic resonance leads to a complex and rich structure in the absorption spectrum.     

On atomic analogue of Landau quantization

We have studied the physics of atoms with permanent electric dipole moment and nonvanishing magnetic moment interacting with an electric field and inhomogeneous magnetic field. This system can be demonstrated as the atomic analogue of Landau quantization of charged particles in a uniform magnetic field. This Landau-like atomic problem is also studied with space-space noncommutative coordinates.     

Electronic states on the surface of graphite

Graphite consists of graphene layers in an AB (Bernal) stacking arrangement. The introduction of defects can reduce the coupling between the top graphene layers and the bulk crystal producing new electronic states that reflect the degree of coupling. We employ low temperature high magnetic field scanning tunneling microscopy (STM) and spectroscopy (STS) to access these states and study their evolution with the degree of coupling. STS in magnetic field directly probes the dimensionality of electronic states. Thus two-dimensional states produce a discrete series of Landau levels while three-dimensional states form Landau bands providing a clear distinction between completely decoupled top layers and ones that are coupled to the substrate. We show that the completely decoupled layers are characterized by a single sequence of Landau levels with square-root dependence on field and level index indicative of massless Dirac fermions. In contrast weakly coupled bilayers produce special sequences reflecting the degree of coupling, and multilayers produce sequences reflecting the coexistence of massless and massive Dirac fermions. In addition we show that the graphite surface is soft and that an STM tip can be quite invasive when brought too close to the surface and that there is a characteristic tip-sample distance beyond which the effect of sample-tip interaction is negligible.     

Lifshitz Tails in Constant Magnetic Fields

We consider the 2D Landau Hamiltonian H perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of H. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained by the first author and T. Wolff in [25] for the case of a vanishing magnetic field.     

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.     

Quantum mechanical Hamiltonians with large ground-state degeneracy

Nonrelativistic Hamiltonians with large, even infinite, ground-state degeneracy are studied by connecting the degeneracy to the property of a Dirac operator. We then identify a special class of Hamiltonians, for which the full space of degenerate ground states in any spatial dimension can be exhibited explicitly. The two-dimensional version of the latter coincides with the Pauli Hamiltonian, and recently-discussed models leading to higher-dimensional Landau levels are obtained as special cases of the higher-dimensional version of this Hamiltonian. But, in our framework, it is only the asymptotic behavior of the background ‘potential’ that matters for the ground-state degeneracy. We work out in detail the ground states of the three-dimensional model in the presence of a uniform magnetic field and such potential. In the latter case one can see degenerate stacking of all 2d Landau levels along the magnetic field axis.     

Effect of interactions, disorder and magnetic field in the Hubbard model in two dimensions

The effects of both interactions and Zeeman magnetic field in disordered electronic systems are explored in the Hubbard model on a square lattice. We investigate the thermodynamic (density, magnetization, density of states) and transport (conductivity) properties using determinantal quantum Monte Carlo and inhomogeneous Hartree Fock techniques. We find that at half filling there is a novel metallic phase at intermediate disorder that is sandwiched between a Mott insulator and an Anderson insulator. The metallic phase is highly inhomogeneous and coexists with antiferromagnetic long-range order. At quarter filling also the combined effects of disorder and interactions produce a conducting state which can be destroyed by applying a Zeeman field, resulting in a magnetic field-driven transition. We discuss the implication of our results for experiments.     

Spatial fluctuations of the density of states in magnetic fields observed with scanning tunneling spectroscopy

Scanning tunneling spectroscopy images on n-InAs(110) exhibit a strong magnetic field dependent contrast on the 50 nm length scale, indicating fluctuations in the density of states of the sample. The contrast is correlated to previously observed Landau oscillations in dI/dV curves. Its origin is a spatial fluctuation of the Landau level energy of 3-4 meV caused by the inhomogeneous distribution of dopant atoms. Besides inducing large-scale fluctuations in the density of states, dopants preserve their ability to scatter electron waves. The resulting wave pattern is found to depend on the magnetic field. It is suggested that the dependence is guided by the condensation of the electronic states on Landau tubes.     

Band structure and transport property of graphene/h-BN heterostructure under local potentials

We investigate band structure and transport property of lattice-matched graphene/hexagonal boron nitride (h-BN) heterostructure using the tight-binding approach. It shows that local potentials can significantly modify the band structure and the transport property. A method to individually manipulate the edge states by local potentials is proposed, including shifts and other deformations of edge bands. The two-terminal conductance of each layer is quantized but the interlayer conductance is non-quantized due to band mixing. In addition, we explore the Landau level spectrum in graphene/h-BN nanoribbons under both magnetic field and local potentials. The plateaus-like behavior of the interlayer conductance is observed.