Single electron charging effects in semiconductor quantum dots

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas (2 DEG) of a GaAs/AlGaAs heterostructure. The gate structure allows an independent control of the conductances of the two tunnel barriers separating the quantum dot from the two 2 DEG leads, and enables us to vary the number of electrons that are localized in the dot. We have measured Coulomb oscillations in the conductance and the Coulomb staircase in current-voltage characteristics and studied their dependence on the conductances of the tunnel barriers. We show experimentally that at zero magnetic field charging effects start to affect the transport properties when both barrier conductances are smaller than the first quantized conductance value of a point contact at 2e ²/h. The experiments are described by a simple model in terms of electrochemical potentials, which includes both the discreteness of the electron charge and the quantum energy states due to confinement.     

Detection of Magnetic Gap in Topological Surface States of MnBi_2Te_4

Recently, intrinsic antiferromagnetic topological insulator MnBi_2Te_4 has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi_2Te_4.However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 me V, which vanishes as the sample becomes paramagnetic with increasing temperature.The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy.Combining these results, the magnetism-induced gap in topological surface states of MnBi_2Te_4 is revealed.     

Multipeak Kondo effect in one- and two-electron quantum dots

We have fabricated a few-electron quantum dot that can be tuned down to zero electrons while maintaining strong coupling to the leads. Using a nearby quantum point contact as a charge sensor, we can determine the absolute number of electrons in the quantum dot. We find several sharp peaks in the differential conductance, occurring at both zero and finite source-drain bias, for the one- and two-electron quantum dot. We attribute the peaks at finite bias to a Kondo effect through excited states of the quantum dot and investigate the magnetic field dependence of these Kondo resonances.     

Bulk-edge correspondence in graphene with/without magnetic field: Chiral symmetry,Dirac fermions and edge states

There are two types of edge states in graphene with/without magnetic field. One is a quantum Hall edge state, which is topologically protected against small perturbation. The other is a chiral zero mode that is localized near the boundary with/without magnetic field. The latter is also topological but is guaranteed to be at zero energy by the chiral symmetry, which is also responsible for massless Dirac-like dispersion. Conceptual roles of the edge states are stressed and reviewed from the point of view of the bulk-edge correspondence and topological order.     

Effect of Quantum Point Contact Measurement on Electron Spin State in Quantum Dots

We study the time evolution of two electron spin states in a double quantum-dot system, which includes a nearby quantum point contact （QPC） as a measurement device. We find that the QPC measurement induced decoherence is in the microsecond timescale. We also find that the enhanced QPC measurement will trap the system in its initial spin states, which is consistent with the quantum Zeno effect.     

Long-lived resonances supported by a contact interaction in crossed magnetic and electric fields

The lifetime of the resonance states of an electron interacting with a zero-range potential in the presence of crossed magnetic and electric fields is studied for the case where the electron is confined in the direction of the magnetic field by a parabolic quantum well. It is shown that long-lived electric field-induced resonances exist in this system even when the zero-range potential does not support any field-free bound state. The relationship of these resonances with the Landau states localized near the point interaction is discussed.     

Disordered quantum walks in two-dimensional lattices

The properties of the two-dimensional quantum walk with point,line,and circle disorders in phase are reported.Localization is observed in the two-dimensional quantum walk with certain phase disorder and specific initial coin states.We give an explanation of the localization behavior via the localized stationary states of the unitary operator of the walker+coin system and the overlap between the initial state of the whole system and the localized stationary states.     

Kondo quantum criticality of magnetic adatoms in graphene

We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as TK∝|J-Jc|1/3 near the critical coupling Jc, and the local spin is effectively screened by a super-Ohmic bath. For this class, the RKKY interaction decays spatially with a fast power law ～1/R7. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.     

The renormalization group and quantum edge states

The role of edge states in phenomena like the quantum Hall effect is well known, and the basic physics has a wide field-theoretic interest. In this paper we introduce a new model exhibiting quantum Hall-like features. We show how the choice of boundary conditions for a one-particle Schrödinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic field. In each case, edge states arise from a non-trivial scaling limit involving the boundary condition, and chirality of the boundary condition plays an essential role. Second quantization of these quantum mechanical systems leads to a multi-particle ground state carrying a persistent current at the edge. We show that the theory quantized with this vacuum displays an “anomaly” at the edge which is the mark of a quantized Hall conductivity in the presence of an external magnetic field. These models therefore possess characteristics which make them indistinguishable from the quantum Hall effect at macroscopic distances. We also offer interpretations for the physics of such boundary conditions which may have a bearing on the nature of the excitations in these models.     

Detection of hidden localized states by the quantum Hall effect in graphene

We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device.     

STM/STS measurements of two-dimensional electronic states trapped around surface defects in magnetic fields

The local density of states (LDOS) near point defects on a surface of highly oriented pyrolytic graphite (HOPG) was studied at very low temperatures in magnetic fields up to 6 T. We observed localized electronic states over a distance of the magnetic length around the defects in differential tunnel conductance images at the valley energies of the Landau levels (LLs) as well as relatively extended states at the peak ones of LLs. These states appear mainly at energies above the Fermi energy corresponding to the electron LL bands. The data suggest that the quantum Hall state is realized in the quasi two dimensional electron system in HOPG. At the peak energy associated with the n=0 (electron) and -1 (hole) LLs characteristic of the graphite structure, a reduced LDOS around the defects is observed. The spatial distribution is almost field independent, which indicates that it represents the potential shape produced by the defects.     

Quantum tunneling between paramagnetic and superconducting states of a nanometer-scale superconducting grain placed in a magnetic field

We consider the process of quantum tunneling between the superconducting and paramagnetic states of a nanometer-scale superconducting grain placed in a magnetic field. The grain is supposed to be weakly coupled to a normal metallic contact that plays the role of the spin reservoir. Using the instanton method, we find the probability of the quantum tunneling process and express it in terms of the applied magnetic field, order parameter of the superconducting grain, and conductance of the tunneling junction between the grain and metallic contact.     

Fractal characteristics of critical and localized states in incommensurate quantum systems

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.     

Cumulative quantum work-deficit versus entanglement in the dynamics of an infinite spin chain

We find that the dynamical phase transition (DPT) in nearest-neighbor bipartite entanglement of time-evolved states of the anisotropic infinite quantum XY spin chain, in a transverse time-dependent magnetic field, can be quantitatively characterized by the dynamics of an information-theoretic quantum correlation measure, namely, quantum work-deficit (QWD). We show that only those nonequilibrium states exhibit entanglement resurrection after death, on changing the field parameter during the DPT, for which the cumulative bipartite QWD is above a threshold. The results point to an interesting inter-relation between two quantum correlation measures that are conceptualized from different perspectives.     

量子点接触对单电子量子态的量子测量

研究了用介观量子点接触(QPC)对单电子两态和多态系统的量子测量问题.发现,在任意测量电压下,该测量问题不能用标准的Lindblad量子主方程描述.考虑了测量仪器和被测系统之间的能量交换对细致平衡关系的影响,对该问题提供了一个恰当的理论描述,并对未来的固态量子测量和量子反馈控制可能产生一定影响. 关键词： 量子测量 量子比特 细致平衡 退局域化     

Arithmetic of the Integer Quantum Hall Effect

The integer quantum Hall effect (IQHE) is analysed, considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted, and their variation is studied as a function of magnetic field. The number of current-carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis addresses certain basic questions in the IQHE, particularly the one about floatation of extended states as the magnetic field tends to zero.     

Metastable and spin-polarized states in electron systems with localized electron–electron interaction

We study the formation of spontaneous spin polarization in inhomogeneous electron systems with pair interaction localized in a small region that is not separated by a barrier from surrounding gas of non-interacting electrons. Such a system is interesting as a minimal model of a quantum point contact in which the electron–electron interaction is strong in a small constriction coupled to electron reservoirs without barriers. Based on the analysis of the grand potential within the self-consistent field approximation, we find that the formation of the polarized state strongly differs from the Bloch or Stoner transition in homogeneous interacting systems. The main difference is that a metastable state appears in the critical point in addition to the globally stable state, so that when the interaction parameter exceeds a critical value, two states coexist. One state has spin polarization and the other is unpolarized. Another feature is that the spin polarization increases continuously with the interaction parameter and has a square-root singularity in the critical point. We study the critical conditions and the grand potentials of the polarized and unpolarized states for one-dimensional and two-dimensional models in the case of extremely small size of the interaction region.     

The quantum lifetime of the Davydov soliton

Considering an infinite spine in the Alpha-helix, stationary states should be eigenstates of a translational operator. These states should be nonlocalized in contradiction to a localized soliton. The difference in energy between localized and nonlocalized (Bloch) states is due to zero point motion and gives information about the quantum stability of the Davydov soliton. We develop a theory of statinary states and show that only for the limiting case of a classical lattice the product ansatz by Davydov is exact. Finally, we calculate the width of the soliton band to get information on the lifetime of the localized soliton.     

Tunable conductance of magnetic nanowires with structured domain walls

We show that in a magnetic nanowire with double magnetic domain walls, quantum interference results in spin-split quasistationary states localized mainly between the domain walls. Spin-flip-assisted transmission through the domain structure increases strongly when these size-quantized states are tuned on resonance with the Fermi energy, e.g., upon varying the distance between the domain walls which results in resonance-type peaks of the wire conductance. This novel phenomenon is shown to be utilizable to manipulate the spin density in the domain vicinity. The domain wall parameters are readily controllable, and the predicted effect is hence exploitable in spintronic devices.     

Quasiparticle states and quantum interference induced by magnetic impurities on a two-dimensional topological superconductor

We theoretically study the effect of localized magnetic impurities on two-dimensional topological superconductor (TSC). We show that the local density of states (LDOS) can be tuned by the effective exchange field m, the chemical potential μ of TSC, and the distance Δr as well as the relative spin angle α between two impurities. The changes in Δr between two impurities alter the interference and result in significant modifications to the bonding and antibonding states. Furthermore, the bound-state spin LDOS induced by single and double magnetic impurity scattering, the quantum corrals and the quantum mirages are also discussed. Finally, we briefly compare the impurities in TSC with those in topological insulators.