Quantum Corrals Research Articles

Correlations, quantum entanglement and interference in nanoscopic systems

Several of the most interesting quantum effects can or could be observed in nanoscopicsystems. For example, the effect of strong correlations between electrons and of quantuminterference can be measured in transport experiments through quantum dots, wires,individual molecules and rings formed by large molecules or arrays of quantum dots. Inaddition, quantum coherence and entanglement can be clearly observed in quantum corrals.In this paper we present calculations of transport properties through Aharonov–Bohmstrongly correlated rings where the characteristic phenomenon of charge–spin separation isclearly observed. Additionally quantum interference effects show up in transport throughπ-conjugated annulene molecules producing important effects on the conductance fordifferent source–drain configurations, leading to the possibility of an interesting switchingeffect.Finally, elliptic quantum corrals offer an ideal system to study quantum entanglementdue to their focalizing properties. Because of an enhanced interaction betweenimpurities localized at the foci, these systems also show interesting quantumdynamical behaviour and offer a challenging scenario for quantum informationexperiments.

Quantum Corral Resonance Widths: Lossy Scattering as Acoustics

We present an approach to predicting extrinsic electron resonance widths within quantum corral nanostructures based on analogies with acoustics. Established quantum mechanical methods for calculating resonance widths, such as multiple scattering theory, build up the scattering atom by atom, ignoring the structure formed by the atoms, such as walls or enclosures. Conversely, particle-in-a-box models, assuming continuous walls, have long been successful in predicting quantum corral energy levels, but not resonance widths. In acoustics, partial reflection from walls and various enclosures has long been incorporated for determining reverberation times. Pursuing an exact analogy between the local density of states of a quantum corral and the acoustic impedance of a concert hall, we show electron lifetimes in nanoscopic structures of arbitrary convex shape are well accounted for by the Sabine formula for acoustic reverberation times. This provides a particularly compact and intuitive prescription for extrinsic finite lifetimes in a particle-in-a-box with leaky walls, including quantum corral atomic walls, given single particle scattering properties.

Detection and Cloaking of Molecular Objects in Coherent Nanostructures Using Inelastic Electron Tunneling Spectroscopy

We address quantum invisibility in the context of electronics in nanoscale quantum structures. We make use of the freedom of design that quantum corrals provide and show that quantum mechanical objects can be hidden inside the corral, with respect to inelastic electron scattering spectroscopy in combination with scanning tunneling microscopy, and we propose a design strategy. A simple illustration of the invisibility is given in terms of an elliptic quantum corral containing a molecule, with a local vibrational mode, at one of the foci. Our work has implications to quantum information technology and presents new tools for nonlocal quantum detection and distinguishing between different molecules.

Bulk state confinement and band folding in nanostructured surfaces

In the recent years, many studies showed that the surface states of noble metals can be confined in natural or artificial nanostructures on surfaces. Moreover, they can also be sensitive to periodic nanostructuration of the surfaces and can form bands with this superperiodicity. In this paper, we show by scanning tunneling spectroscopy that similar behaviors can be observed on bulk states. We present evidences of lateral confinement and ``band folding'' of the bulk state in Cl-based quantum corrals on Au(111) and vicinal Au(23 23 21) surfaces.

Phonon Contribution to the Lifetime of Surface State Quasiparticles Confined in Nanopyramids

We present a scanning tunneling microscopy investigation of the dynamics of hot electrons and holes in Ag pyramidal nanostructures. The geometry of the nanostructure leads to a strong reduction of the decay mechanism into the bulk states and then to a large reflection coefficient of the surface electronic waves. Therefore, in contrast to quantum corrals and adatom islands which show a dominant lossy scattering contribution to the linewidth, the narrow observed structures in the differential conductivity spectra reveal the expected linewidth minimum at the Fermi energy. The electron-phonon contribution to the lifetime is shown to be dominant, in agreement with previous photoemission measurements.

Spatiotemporal dynamics in Rayleigh band of photonic quantum ring laser

Spatiotemporal dynamic simulations are carried out for the carrier-field interactions of photonic quantum ring lasers of three dimensional (3D) whispering cave modes (WCMs). We observe quantum wires-like carrier re-distributions naturally formed in the Rayleigh band region of the active quantum well plane. Apart from the regular two dimensional (2D) whispering gallery mode (WGM), the 3D WCM’s major polarization state favors a strong carrier-photon coupling for the carriers in the Rayleigh band, such that the powerful transient coupling generates photonic quantum rings (PQRs), or concentric quantum rings with a half-wavelength pitch of imminently recombinant carriers, i.e., a photonic quantum corral effect. This feature is responsible for the low threshold currents and thermally stable spectra, which opens the way for easy optical mega-pixel (‘Omega’) chip fabrications.

Dichotomous Array of Chiral Quantum Corrals by a Self-Assembled Nanoporous Kagomé Network

The confinement of surface-state electrons by a complex supramolecular network is studied with low-temperature scanning tunneling microscopy and rationalized by electronic structure calculations using a boundary element method. We focus on the self-assembly of dicarbonitrile-sexiphenyl molecules on Ag(111) creating an open kagomé topology tessellating the surface into pores with different size and symmetry. This superlattice imposes a distinct surface electronic structure modulation, as observed by tunneling spectroscopy and thus acts as a dichotomous array of quantum corrals. The inhomogenous lateral electronic density distribution in the chiral cavities is reproduced by an effective pseudopotential model. Our results demonstrate the engineering of ensembles of elaborate quantum resonance states by molecular self-assembly at surfaces.

Quantum entanglement in elliptical quantum corrals

Abstract Quantum corrals present interesting properties due to the combination of confinement and, in the case of elliptical corrals, to their focalizing properties. We study the case when two magnetic impurities are added to the non-interacting corral, where they interact via a superexchange AF interaction J with the surface electrons in the ellipse. Previous results showed that, when both impurities are located at the foci of the system, they experience an enhanced magnetic interaction, as compared to the one they would have in an open surface. For small J and even filling, they are locked in a singlet state, which weakens for larger values of this parameter. When J is much larger than the hopping parameter of the electrons in the ellipse, both spins decorrelate while forming a local singlet with the electrons of the ellipse, thus presenting a confined RKKY–Kondo transition. We interpret this behaviour by means of the von Neumann entropy between the localized impurities and the itinerant electrons of the ellipse: for small J the entropy is nearly zero while for large J it is maximum. In addition, the local density of states provides us with a concrete experimental tool for detecting the Kondo regime.

Scanning tunneling spectrum of electrons confined in a rectangular quantumcorral

We obtained the scanning tunneling spectrum (STS) of an electron confined in arectangular quantum corral by considering the electron to be in a quasi-stationary state.Because of non-hermiticity of the Hamiltonian, the electron has a complex eigenenergy. Theimaginary part gives the peak width coming mainly from the electron tunneling through acorral barrier. Our STS is consistent with the experimental spectrum that had beenmeasured for electrons confined in a rectangular quantum corral. We obtained peak widthsagainst energy levels and components of the STS which are constructed withquasi-stationary eigenstates. It is shown that normalization of a wavefunction byconsidering its time evolution is decisive in obtaining the proper STS. Moreover, wespecified the position dependence of STS in relation to the image of the surface localdensity of states.

Mapping of the electron transmission through the wall of a quantum corral

We report on a theoretical study of the escape of confined surface states electrons from quantum corrals made of Cu adatoms on a Cu(1 1 1) surface. This study maps electron transmission through the corral wall and provides an extension of our earlier work focused on confinement in Cu corrals [S. Díaz-Tendero, F.E. Olsson, A.G. Borisov, J.P. Gauyacq, Phys. Rev. B 77 (2008) 205403]. The existence of two decay modes for the confined surface state is stressed: (i) non-resonant tunnelling through the corral wall concentrated on the Cu adatoms and (ii) a resonant-induced decay involving the transient formation of a resonant state localized on top of the corral wall. The present mapping of the electron transmission reveals how the interference between the two decay modes works: there exist regions where the electron leaves the corral, balanced by regions where it enters the corral, though the global behaviour of the quasi-stationary states is electron escape from the corral.

The Ring: A Leitmotif in Plasmonics

An interesting paper in this issue describes an experiment that is an optical analogue of the "quantum corral" on metal surfaces constructed and observed using scanning tunneling microscopy more than a decade ago. In this Perspective, the mechanism underlying the confinement and manipulation of light in metallic nanorings and related structures are discussed, with an emphasis on recent results.

Photonic quantum ring laser of 3D whispering cave mode

A new whispering cave mode (WCM), a three-dimensional (3D) case of Lord Rayleigh's 2D whispering gallery modes, based upon 3D total internal reflection is presented, where GaAs quantum well (QW) near-vertical microdisk resonators exhibit a strong carrier–photon coupling for the QW carriers located in the Rayleigh band, generating 2D-to-1D carrier phase transitions of photonic quantum ring (PQR). It is a ‘photonic’ quantum corral effect (PQCE), whose simulation work produces a tangled web pattern of imminent recombinant carriers in picoseconds timescale. The PQCE is responsible for the ultralow threshold currents below 300nA for a single mode GaAs PQR laser, and a prototype GaN PQR laser with a threshold near and below 1μA.

Electron wrangling in quantum corrals

Unprecedented control over the superposition of electronic states in a 'quantum corral', exerted by changing the position of a single atom within it, provides a powerful tool for studying the quantum behaviour of matter.

Single-atom gating of quantum-state superpositions

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space - or Hilbert space - is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral1 can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real-space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.

Impurities in elliptical quantum corrals

Elliptical quantum corrals present interesting properties due to the combination of confinement and focalizing properties. We show here that two magnetic impurities located at the foci of the systems experience an enhanced interaction, as compared to the one they would have in an open surface. These impurities interact via a superexchange AF interaction J with the surface electrons in the ellipse. For small J they are locked in a singlet state, which weakens for larger values of this parameter. When J is much larger than the hopping parameter of the electrons in the ellipse, both spins decorrelate and form a singlet with the nearest electron, thus presenting a confined RKKY–Kondo transition. We can also interpret this behavior via the entanglement or von Neumann entropy between the localized impurities and the itinerant electrons of the ellipse: for small J the entropy is nearly zero while for large J it is maximum.

Quantum drums beat as one

First there was 'IBM' written with 35 xenon atoms, followed by the quantum corral, the quantum mirage and, now, the quantum drum

Analysis of Scanning Tunneling Microscopy Images and Scanning Tunneling Spectrum of Electrons Confined in Equilateral Triangular Quantum Corrals

We determined the stationary states of an electron confined in an equilateral triangular quantum corral by the superposition of electron waves undergoing successive reflections at three barrier walls. By using wave functions and eigenenergies, we analyzed scanning tunneling microscopy (STM) images and scanning tunneling spectra for the quantum corral. Our results are consistent with experimental STM images observed in the differential conductance mode (d I /d V ) and scanning tunneling spectra. It is pointed out that the d I /d V image is not simply proportional to the surface local density of states but is greatly dependent on a filtering function.

Spin−Orbit Coupling Induced Interference in Quantum Corrals

Lack of inversion symmetry at a metallic surface can lead to an observable spin-orbit interaction. For certain metal surfaces, such as the Au(111) surface, the experimentally observed spin-orbit coupling results in spin rotation lengths on the order of tens of nanometers, which is the typical length scale associated with quantum corral structures formed on metal surfaces. In this work, multiple scattering theory is used to calculate the local density of states (LDOS) of quantum corral structures composed of nonmagnetic adatoms in the presence of spin-orbit coupling. Contrary to previous theoretical predictions, spin-orbit coupling induced modulations are observed in the theoretical LDOS, which should be observable using scanning tunneling microscopy.

Effect of quantum confinement of surface electrons on adatom–adatom interactions

The quantum confinement of surface-state electrons in atomic-scale nanostructures is studied by means of the Korringa–Kohn–Rostoker (KKR) Green's function method. We demonstrate that the surface-state mediated interaction between adatoms can be significantly modified by the quantum confinement of surface electrons. We show that quantum corrals and quantum mirrors constructed on metal surfaces can be used to tailor the exchange interaction between magnetic adatoms at large distances. We discuss the self-organization of adatoms on metal surfaces caused by quantum confinement.

Static and dynamical properties of elliptical quantum corrals

Due to their focalizing properties, elliptic quantum corrals present very interesting physical behaviors. In this work, we analyze static and dynamical properties of these systems. Results are presented for realistic values of the parameters, which might be useful for comparison with experiments. We study noninteracting corrals and their response to several kinds of external perturbations, observing that, for realistic values of the Fermi level, the dynamics involves only a few number of excited states, making the system quite robust with respect to possible sources of decoherence. We also study the system in the presence of two S=1/2 impurities located at its foci, which interact with the electrons of the ellipse via a superexchange interaction J. This system is diagonalized numerically and properties such as the spin gap and spin-spin static and dynamical correlations are studied. We find that, for small J, both spins are locked in a singlet or triplet state, for even or odd filling, respectively, and its spin dynamics consists mainly of a single peak above the spin gap. In this limit, we can define an effective Heisenberg Hamiltonian to describe the low-energy properties. For larger J, more states are involved and the localized spins decorrelate in a manner similar to the Ruderman-Kittel-Kasuya-Yosida-Kondo transition for the two-impurity problem.