Topological response theory of doped topological insulators

We generalize the topological response theory of three-dimensional topological insulators (TI) to metallic systems-specifically, doped TI with finite bulk carrier density and a time-reversal symmetry breaking field near the surface. We show that there is an inhomogeneity-induced Berry phase contribution to the surface Hall conductivity that is completely determined by the occupied states and is independent of other details such as band dispersion and impurities. In the limit of zero bulk carrier density, this intrinsic surface Hall conductivity reduces to the half-integer quantized surface Hall conductivity of TI. Based on our theory we predict the behavior of the surface Hall conductivity for a doped topological insulator with a top gate, which can be directly compared with experiments.     

Superconducting quantum interference devices made of Sb-doped Bi2Se3 topological insulator nanoribbons

We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) made of Sb-doped Bi₂Se₃ topological insulator (TI) nanoribbon (NR) contacted with PbIn superconducting electrodes. When an external magnetic field was applied along the NR axis, the TI NR exhibited periodic magneto-conductance oscillations, the so-called Aharonov-Bohm oscillations, owing to one-dimensional subbands. Below the superconducting transition temperature of PbIn electrodes, we observed supercurrent flow through TI NR-based SQUID. The critical current periodically modulates with a magnetic field perpendicular to the SQUID loop, revealing that the periodicity corresponds to the superconducting flux quantum. Our experimental observations can be useful to explore Majorana bound states (MBS) in TI NR, promising for developing topological quantum information devices.     

Optical absorption and magnetotransport in quantum wires in a perpendicular magnetic field

A periodic array of δ function potentials are used to simulate the potential barriers between quantum wires in the presence or absence of lattice site dislocation. The exact eigenenergies and eigenfunctions are found by employing a numerical diagonalization procedure. Based on these results, a self-consistent field theory is derived for the mid-infrared absorption coefficient of the system. The crossover from a cyclotron mode to two tunneling coupled modes and finally to edge and 1D lattice magnetoplasmon modes with increasing modulation strength is investigated. The magnetic field enhanced and suppressed electron tunneling, associated with the evolution to cyclotron modes at strong magnetic fields passing through the formation of tunneling coupled modes, is observed. The edge mode excitation energy oscillates as a function of the electron density. These oscillations correspond to a soft or hard potential wall for which the electron states are extended or localized, respectively. The displacement of the 1D lattice magnetoplasmon modes under strong modulation is found to be periodic and corresponds to the evolution from a complex unit cell which is composed of one narrow and one wide quantum wire to a simple unit cell containing only one quantum wire. The magnetoresistivities and the associated conductivities are also calculated for the lateral surface superlattice. At strong potential modulation there is a giant peak in the Hall conductivity and many peaks in its resistivity in the quantum regime. With strong modulation, the suppression of the transverse conductivity along with oscillations in its resistivity are obtained.     

Aharonov–Bohm oscillations caused by non-topological surface states in Dirac nanowires

One intriguing fingerprint of surface states in topological insulators is the Aharonov–Bohm effect in magnetoconductivity of nanowires. We show that surface states in nanowires of Dirac materials (bismuth, bismuth antimony, and lead tin chalcogenides) being in non-topological phase, exhibit the same effect as amendment to magnetoconductivity of the bulk states. We consider a simple model of a cylindrical nanowire, which is described by the 3D Dirac equation with a general T-invariant boundary condition. The boundary condition is determined by a single phenomenological parameter whose sign defines topological-like and non-topological surface states. The non-topological surface states emerge outside the gap. In a longitudinal magnetic field B, they lead to Aharonov–Bohm amendment for the density of states and correspondingly for the conductivity of the nanowire. The phase of these magnetic oscillations increases with B from π to 2π.     

Helical quantum states in HgTe quantum dots with inverted band structures

We investigate theoretically the electron states in HgTe quantum dots (QDs) with inverted band structures. In sharp contrast to conventional semiconductor quantum dots, the quantum states in the gap of the HgTe QD are fully spin-polarized and show ringlike density distributions near the boundary of the QD and spin-angular momentum locking. The persistent charge currents and magnetic moments, i.e., the Aharonov-Bohm effect, can be observed in such a QD structure. This feature offers us a practical way to detect these exotic ringlike edge states by using the SQUID technique.     

Effect of atomic impurities on the helical surface states of the topological insulator Bi2Te3

The effect of atomic impurities including N, O, Na, Ti and Co on the surface states of the topological insulator (TI) Bi(2)Te(3) is studied using pseudopotential first principles methods. The robustness of the TI surface states is particularly investigated against magnetic and non-magnetic atomic adsorption by calculating the electronic band structure, charge transfer, and magnetic moments. Interestingly, it is found that a non-magnetic nitrogen atom has produced a residual magnetic moment and opens a gap in the surface states whereas Na and O atoms preserve the Dirac-like dispersion. The charge transfer from the adatoms produces an electric dipole field that causes Rashba splitting in the surface bands. For atomic impurities with 3d orbitals (Ti and Co), the TI surface states are destroyed and two spin-resolved resonance peaks are developed near the Fermi level in the DOS.     

Tunneling conductivity oscillations in a magnetic field in metal-insulator-narrow-gap-HgCdTe structures: The energy spectrum and spin-orbit splitting of 2D states

We study tunneling conductivity oscillations in a magnetic field in narrow-gap p-HgCdTe-oxide-metal (Yb, Al) structures. In tunnel structures with Yb we detect two types of tunneling conductivity oscillations. The first is related to the crossing of the Landau levels of two-dimensional (2D) states localized in the surface quantum well of the semiconductor, and has an energy E _F+eV, where E _F is the Fermi energy of the semiconductor and V is the bias voltage; the second has an energy E _F. We find that in such structures with an asymmetric quantum well there is strong spin-orbit splitting in the spectrum of the 2D states. In p-HgCdTe-oxide-Al tunnel structures the surface potential is much weaker and only oscillations of the first type are observed. We find that in such structures there is only one spin state of the 2D carriers, while the second is pushed into the continuous spectrum because of strong spin-orbit coupling. To analyze the experimental results we calculate the spectrum of 2D states localized in the surface quantum well in a semiconductor with a Kane dispersion law. We find that all the experimental results are in good agreement with the results of calculations. Finally, we discuss the features of “kinematically coupled” states in an asymmetric quantum well. Zh. éksp. Teor. Fiz. 112, 537–550 (August 1997)     

Engineering near-surface electron states in three-dimensional topological insulators

Using the continual model of a semi-infinite three dimensional (3D) topological insulator (TI) we study the effect of the surface potential (SP) on the formation of helical topological states near the surface. The results reveal that spatial profile and spectrum of these states strongly depend on the SP type and strength. We pay special attention to the 3D TI substrate/non-magnetic insulating overlayer system to illustrate the principles of the topological near-surface states engineering.     

Electronic properties of a Weyl semimetal in crossed magnetic and electric fields

The study of Weyl semimetals is one of the most challenging problems of condensed matter physics. These materials exhibit interesting properties in a magnetic field. In this work, we investigate the Landau bands and the density of states (DOS) oscillations in a Weyl semimetal in crossed magnetic and electric fields. An expression is obtained for the energy spectrum of the system using the following three different methods: an algebraic approach, a Lorentz shift-based approach, and a quasi-classical approach. It is interesting that the energy spectrum calculated in terms of the quasi-classical approach coincides with the spectrum obtained using the microscopic approaches. An electric field is shown to change the Landau bands radically. In addition, the classical motion of a three-dimensional Dirac fermion in crossed fields is studied. In the case of a Dirac spectrum, the longitudinal (with respect to magnetic field) component of momentum (p _z ∥ H) is shown to be an oscillating function of the magnetic field. When the electric field is v⊥H/c, the Landau levels collapse and the motion becomes fully linear in an unusual manner. In this case, the wavefunction of bulk states vanishes and only states with p _z = 0 are retained. An electric field affects the character of DOS oscillations. An analytical expression is obtained for the quantum capacitance in crossed fields in the cases of strong and weak electric fields. Thus, an electric field is an additional parameter for adjusting the diamagnetic properties of Weyl semimetals.     

Shubnikov-de Haas oscillations in n-channel silicon 〈100〉 MOSFETS in magnetic fields up to 35 T

Shubnikov-de Haas oscillations have been studied in n-channel silicon 〈100〉 MOSFETS in magnetic fields up to 35 T. At high magnetic fields the shape of the conductivity peaks becomes asymmetric and the conductivity from whole regions of the Landau level spectrum is suppressed by the magnetic field. The asymmetry is thought to arise from the low effective density of scatterers which occurs for high magnetic fields, as predicted by Ando. These effects may also be related to the presence of phenomena such as Wigner crystallisation or Anderson localisation.     

Quantum Hall effect from the topological surface states of strained bulk HgTe

We report transport studies on a three-dimensional, 70-nm-thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semimetallic HgTe, which thus becomes a three-dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states.     

石墨烯量子磁输运性质的电场效应

最近研究发现石墨烯在一维周期性电学或磁学调制势下,其扩散电导率会出现Weiss振荡.本文进一步探索了面外加垂直磁场和面内加横向电场以及一维周期性弱调制电学势的多场耦合作用下,石墨烯的量子磁输运性质,结果表明:Weiss振荡振幅和电导率数值都随着静电场的增加而增加.有趣的是,当电场与磁场的比值达到某一临界值,即β_1=E/(ν_F·B)=1时,输运电导率的Weiss振荡突然消失.这一奇特现象在传统的二维电子气体中是不存在的,因此可以归因于石墨烯载流子外加电磁场的反常相对论性能谱.     

Eccentricity effects on the quantum confinement in double quantum rings

This work presents a theoretical study of the energy spectrum of GaAs/AlGaAs concentric double quantum rings, under an applied magnetic field directed perpendicular to the ring plane. The Schrödinger equation for this system is solved in a realistic model consisting of rings with finite barrier potentials. Numerical results show that increasing the magnetic field intensity leads to oscillations in the ground state energy which, in contrast to the usual Aharonov-Bohm oscillations, do not have a well defined period, due to the coupling between inner and outer ring states. However, when one considers an elliptical geometry for the rings, the energy spectra of the inner and outer ring states are decoupled and the periodicity of the oscillations is recovered.     

Temperature effects on the magnetoplasmon spectrum of a weakly modulated graphene monolayer

In this work, we determine the effects of temperature on the magnetoplasmon spectrum of an electrically modulated graphene monolayer as well as a two-dimensional electron gas (2DEG). The intra-Landau band magnetoplasmon spectrum within the self-consistent field approach is investigated for both the aforementioned systems. Results obtained not only exhibit Shubnikov-de Haas (SdH) oscillations but also commensurability oscillations (Weiss oscillations). These oscillations are periodic as a function of inverse magnetic field. We find that both the magnetic oscillations, SdH and Weiss, have a greater amplitude and are more robust against temperature in graphene compared to a conventional 2DEG. Furthermore, there is a π phase shift between the magnetoplasmon oscillations in the two systems which can be attributed to Dirac electrons in graphene acquiring a Berry's phase as they traverse a closed path in a magnetic field.     

Photoconductivity of a two-dimensional electron system with spin-orbit coupling in AC magnetic field

The response of an electron system to a dc probe field is analyzed in the case when an initial deviation of conduction-electron spin degrees of freedom from equilibrium in a microwave magnetic field induces combined resonance transitions in the electron system. It is shown that a perturbation of spin degrees of freedom is converted into kinetic energy and modifies transport coefficients, leading to oscillations of diagonal components of the conductivity tensor.     

Magnetoquantum de Haas-van Alphen oscillations in spin-split two-dimensional Fermi liquid

Theory of magnetoquantum oscillations with spin-split structure in strongly anisotropic (two-dimensional (2D)) metal is developed in the formalism of level approach. Parametric method for exact calculation of oscillations wave forms and amplitudes, developed earlier for spin degenerate levels is generalized on a 2D electron system with spin-split levels. General results are proved: 1) proportionality relation between magnetization and chemical potential oscillations accounting for spin-split energy levels and magnetic field unperturbed levels (states of reservoir), 2) basic equation for chemical potential oscillations invariant to various models of 2D and 1D energy bands (intersecting or overlapping) and localized states. Equilibrium transfer of carriers between overlapping 2D and 1D bands, characterizing the band structure of organic quasi 2D metals, is considered. Transfer parameter, calculated in this model to be of the order of unity, confirms the fact that the wave form of oscillations in organic metals should be quasisymmetric up to ultralow temperature. Presented theory accounts for spin-split magnetization oscillations at magnetic field directions tilted relative to the anisotropic axis of a metal. Theoretical results are compared with available experimental data on organic quasi-2D metal α-(BEDT-TTF)₂KHg(SNC)₄ explaining the appearance of clear split structure under the kink magnetic field and absence above by the corresponding change in the electron g-factor rather than cyclotron mass. Received 20 December 2000 and Received in final form 13 July 2001     

耦合电磁场对石墨烯量子磁振荡的影响

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应.我们发现,石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱,且当电场与磁场比值超过某一临界值时,量子磁振荡会突然消失,这与非相对论二维电子气的情况显著不同.这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释.此外,我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减.我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用,进而探测自旋轨道耦合引起的能隙.     

Strain imaging of a perpendicular recording head in a Hard Disk Drive

Imaging of magnetic-field-induced strains using scanning probe microscopy enables us to observe magnetic domain structures and magnetic force distributions. This method has an ability of observing magnetic structures in deep portions along with surface structures. We observed an air-bearing surface of a perpendicular recording head in a hard disk drive in large areas including the whole yokes, and investigated characteristics of the magnetic poles and layers subjected to magnetic fields produced by writing coil currents. Attractive forces independent of the field directions acted between the upper and lower yokes made by soft material, which generated surface displacements in the ABS. The signals were second-harmonic oscillations for alternating currents without a dc bias, and the amplitude images represented the field distribution. Meanwhile, fixed magnetic charges in both ends of the read sensor, which were produced by the hard-bias film, were subjected to the fields. The fixed charges, which hardly changed by the fields, lead to strains depending on the field directions, and generated specific contrasts of one pair of bright-dark spots in the strain images. In the absence of surface underlayer, the fields by the writing coil broke into the read sensor sandwiched by the shield layers.     

Transport studies of localized and extended states of a two-dimensional electron gas in low magnetic fields

We have observed the quantum Hall effect in a high mobility two-dimensional electron gas to filling factors up to 80 at 0.3 K. This demonstrates the presence of both localized and extended states at low field, and explains the failure of the standard semi-classical analysis of Shubnikov–de Haas (SdH) oscillations in this regime. We go on to derive a general expression for the conductivity due to rectangular bands of extended states, and show that the observed temperature dependence of the SdH oscillations is consistent with this picture. An analysis of the oscillations using this expression reveals the predicted levitation of the extended states as the magnetic field is reduced.