Direct observation of geometrical phase transitions in mesoscopic superconductors by scanning tunneling microscopy

Using scanning tunneling microscopy, we mapped the distribution of the local density of states in a single crystal superconductor heterostructure with an array of submicron normal metal islands. We observe the coexistence of strongly interacting multiquanta vortex lattice with interstitial Abrikosov vortices. The newly formed composite magnetic flux structure undergoes a series of phase transitions between different topological configuration states. The vortex configuration states are strongly dependent on the number of flux quanta and the nanoscale confinement architecture of the mesoscopic superconductor. Here, we present images of vortex phase transitions due to confinement effects when the number of magnetic flux quanta in the system changes. The vortex dynamics in these systems could serve as a model for behavior of confined many-body systems when the number of particles changes.     

Vortex lattices in planar Bose-Einstein condensates with dipolar interactions

In this Letter, we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with quantum tunneling processes, which affects the relative displacement of two neighboring vortex lattices and leads to the loss of phase coherence between different condensates.     

一维双组分玻色-爱因斯坦凝聚体系的量子隧穿特性

利用双模近似方法研究了一维双组分玻色-爱因斯坦凝聚体(Bose-Einstein condensates,BECs)的量子隧穿特性.从描述三维双组分BECs系统的Gross-Pitaevskii方程(GPE)出发,得到了描述一维体系的GP方程.把体系波函数写成原子数和相位指数的乘积,得到描述体系隧穿特性的费曼方程.数值求解费曼方程,研究了原子之间相互作用(双组分BECs体系原子之间的相互作用包括组分内部原子之间的相互作用和不同组分原子之间的相互作用)对隧穿特性的影响.结果显示,当原子之间的相互作用较弱时,体系发生量子隧穿现象,表现为原子数在平衡位置附近作周期振荡;随着原子之间相互作用增强,体系经历一个临界状态,进入自俘获状态,即由于原子之间相互作用的存在,在对称双势阱中演化的BECs可以呈现出原子数高度的不对称分布,好像绝大数原子被其中一个势阱俘获.从隧穿到自俘获原子之间的相互作用存在一个临界值,从而体系的能量也对应一个临界值,根据体系的哈密顿函数,就能求出相互作用临界值的表达式.     

Recent progresses of quantum confinement in graphene quantum dots

Graphene quantum dots (GQDs) not only have potential applications on spin qubit, but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron–electron (e–e) interaction. The tip-induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimensional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes.     

Effect of quantum fluctuations on bose-einstein condensation of bilayer atomic gases in rapid rotation

We investigate vortex states and quantum fluctuations of bilayer atomic gases in rapid rotation. Among mean-field solutions of the Gross-Pitaevskii equation, we consider two types of vortex configurations: the vortex core positions of the layers are coincident or staggered. It is found that the coincident type is energetically preferred in the practical parameter regime. We also calculate the dispersion relations of collective modes and the filling factor for bosons outside the condensates. In the double layer system, quantum depletion is found to be suppressed due to interlayer tunneling. This means that Bose-Einstein condensation is stabilized compared to the single layer case.     

Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.     

Tunable quantum dot arrays formed from self-assembled metal-organic networks

The confinement of Ag(111) surface-state electrons by self-assembled, nanoporous metal-organic networks is studied using low-temperature scanning tunneling microscopy and spectroscopy as well as electronic structure calculations. The honeycomb networks of Co metal centers and dicarbonitrile-oligophenyl linkers induce surface resonance states confined in the cavities with a tunable energy level alignment. We find that electron scattering is repulsive on the molecules and weakly attractive on Co. The tailored networks represent periodic arrays of uniform and coupled quantum dots.     

Doping of monatomic Cu chains with single Co atoms

Close-packed Co-Cu chains of various length and composition were assembled from single Co and Cu atoms on Cu(111) by atom manipulation in a low-temperature scanning tunneling microscope. Local spectroscopy reveals significant electronic Co-Cu coupling leading to confined quantum states delocalized along the heteroatomic chain. Composite Co-Cu chains provide a model case in which the quantum state of an atomic-scale host structure can be tuned by the controlled incorporation of foreign atoms.     

Confined Shockley surface states on the (111) facets of gold clusters

Combining low-temperature scanning tunneling microscopy and spectroscopy with high-resolution ultraviolet photoemission, we have revealed a confined Shockley surface state on the (111) facets of gold clusters with about N=10(4) atoms grown in nanopits on highly oriented graphite. With tunneling spectroscopy, we observed energy dependent nodal patterns in the dI/dV maps, which are in quantitative agreement with the two-dimensional confinement of the surface state within the hexagonal facet area. The results indicate that the lattice of the ionic cores influences the electronic properties of the clusters significantly.     

Nonlinear tunneling and chaos between two Bose–Einstein condensates trapped in time-dependent potential

In this Letter, we discuss the macroscopic quantum self-trapping (MQST) and coherent atomic tunneling between two weakly coupled Bose–Einstein condensates confined in a time-dependent double-well trap. It is shown that the nonlinear interaction and the time-periodic external field can dramatically affect the MQST, lead to the high-order Bloch harmonics of the population imbalance, and periodic or chaotic behavior. We give out the onset point of chaos by Lyapunov exponent and the phase plots. It is found that the sudden change on the quasi-energy corresponds to the transition from libration to rotation.     

Effects of crystal shape on the energy levels of zero-dimensional PbS quantum dots

Nanometer-size PbS quantum dots have been made by electrodeposition on a Au(111) substrate. The deposited nanocrystals have a flattened cubic shape. We probed the single-electron energy-level spectrum of individual quantum dots by scanning tunneling spectroscopy and found that it deviates strongly from that of spherical PbS quantum dots. The measured energy-level spectrum is successfully explained by considering strong confinement in a flattened cubic box.     

Vortex states of rapidly rotating dilute Bose-Einstein condensates

We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.     

Manipulating the Kondo resonance through quantum size effects

Manipulating the Kondo effect by quantum confinement has been achieved by placing magnetic molecules on silicon-supported nanostructures. The Kondo resonance of individual manganese phthalocyanine (MnPc) molecules adsorbed on the top of Pb islands was studied by scanning tunneling spectroscopy. Oscillating Kondo temperatures as a function of film thickness were observed and attributed to the formation of the thickness-dependent quantum-well states in the host Pb islands. The present approach provides a technologically feasible way for single spin manipulation by precise thickness control of thin films.     

Local spectroscopy of two-dimensional states in Na films on Cu(111)

Alkali overlayers on noble metal surfaces exhibit two-dimensional electronic states. We investigated the electronic structure of Na on Cu(111) at T=5 K with scanning tunneling spectroscopy. In agreement with photoelectron spectroscopy we found two electronic bands close to the Fermi energy which correspond to quantum well states (QWS). In second monolayer islands, confinement of the QWS was observed.     

Spatial imaging of valence band electronic structures in a GaSb/InAs quantum well

We measure local density of states (LDOS) for GaSb/InAs heterostructures with quantum wells in the valence band by scanning tunneling spectroscopy (STS) on the cleaved surface. Clear standingwave patterns of LDOS corresponding to the holes confined in the quantum wells are observed.     

环形势阱中旋转玻色爱因斯坦凝聚体的基态

应用托马斯-费米近似和虚时演化数值方法研究环形势阱中旋转玻色爱因斯坦凝聚体的基态密度分布.当增加其旋转角频率,或者增加环形势阱的宽度及相应的中心高度,凝聚体基态密度分布均从涡旋晶格相转变为巨涡旋相.当旋转角频率为零时,增加环形势阱的宽度及相应的中心高度,凝聚体基态密度分布从一个圆盘变为圆环.解析结果与数值结果相互吻合.     

Wave-function mapping of graphene quantum dots with soft confinement

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moiré potential and a 10% penetration of an Ir surface resonance into the graphene layer.     

Instanton approach to Josephson tunneling between trapped condensates

An instanton method is proposed to investigate the quantum tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. We point out some intrinsic pathologies in the earlier treatments of other authors and make an effort to go beyond these very simple zero order models. The tunneling amplitude may be calculated in the Thomas-Fermi approximation and beyond it; we find it depends on the number of the trapped atoms, through the chemical potential. Some suggestions are given for the observation of the Josephson oscillation and the MQST. Received 29 June 2001 and Received in final form 17 September 2001     

Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor(Li_(0.84)Fe_(0.16))OHFeSe

The Major ana zero mode(MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in(Li_(0.84)Fe_(0.16))OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Major ana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state,and consequently, the conductance at zero bias is quantized as 2e~2/h. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.