Fermi Wavelength Research Articles

Optical responses of a metal with sub-nm gaps.

If the size of a metallic structure is reduced to be comparable to or even smaller than the typical quantum-mechanical lengths such as the Fermi wavelength or Thomas-Fermi wavelength, the electronic structure and optical responses are modulated by quantum effects. Here, we calculate the optical responses of a metal with sub-nm gaps using the eigenstates obtained from an effective-mass quantum theory. According to our simulation, the dielectric responses can be significantly modified by tuning the inter-gap distances. Remarkably, sub-nm gaps occupying a 0.3% volumetric fraction can elongate the penetration depth by an order of magnitude in the terahertz regime. We find that the detailed dependences of electron-photon interaction matrix elements on the involved electronic wavefunctions play an important role in the optical responses. The results draw our attention to these recently fabricated systems.

Magnetic field-induced helical mode and topological transitions in a topological insulator nanoribbon.

The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.

Asymptotics of surface-plasmon redshift saturation at subnanometric separations

Many promising nanophotonics endeavours hinge upon the unique plasmonic properties of nanometallic structures with narrow non-metallic gaps, which support super-concentrated bonding modes that singularly redshift with decreasing separations. In this letter, we present a descriptive physical picture, complemented by elementary asymptotic formulae, of a nonlocal mechanism for plasmon-redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalisation of the corresponding local ones. Specifically, the renormalisation furnishes an asymptotic plasmon-frequency lower bound that scales with the $1/4$-power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations.

Highly Conductive Polycrystalline Metallic Ring in a Magnetic Field

Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ∼ I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction. Keywords—Electrical Conduction, Electron Phase Coherence, Polycrystalline Metal, Magnetic Field.

Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films

We develop a theory for the vortex unbinding transition in homogeneously disordered superconducting films. This theory incorporates the effects of quantum, mesoscopic and thermal fluctuations stemming from length scales ranging from the superconducting coherence length down to the Fermi wavelength. In particular, we extend the renormalization group treatment of the diffusive nonlinear sigma model to the superconducting side of the transition. Furthermore, we explore the mesoscopic fluctuations of parameters in the Ginzburg-Landau functional. Using the developed theory, we determine the dependence of essential observables (including the vortex unbinding temperature, the superconducting density, as well as the temperature-dependent resistivity and thermal conductivity) on microscopic characteristics such as the disorder-induced scattering rate and bare interaction couplings.

Ballistic Transport in Graphene Antidot Lattices.

The bulk carrier mobility in graphene was shown to be enhanced in graphene-boron nitride heterostructures. However, nanopatterning graphene can add extra damage and drastically degrade the intrinsic properties by edge disorder. Here we show that graphene embedded into a heterostructure with hexagonal boron nitride (hBN) on both sides is protected during a nanopatterning step. In this way, we can prepare graphene-based antidot lattices where the high mobility is preserved. We report magnetotransport experiments in those antidot lattices with lattice periods down to 50 nm. We observe pronounced commensurability features stemming from ballistic orbits around one or several antidots. Due to the short lattice period in our samples, we can also explore the boundary between the classical and the quantum transport regime, as the Fermi wavelength of the electrons approaches the smallest length scale of the artificial potential.

Universal spatial correlations in the anisotropic Kondo screening cloud: Analytical insights and numerically exact results from a coherent state expansion

We analyze the spatial correlations in the spin density of an electron gas in the vicinity of a Kondo impurity. Our analysis extends to the spin-anisotropic regime, which was not investigated in the literature. We use an original and numerically exact method, based on a systematic coherent-state expansion of the ground state of the underlying spin-boson Hamiltonian, which we apply to the computation of observables that are specific to the fermionic Kondo model. We also present an important technical improvement to the method, that obviates the need to discretize modes of the Fermi sea, and allows one to tackle the problem in the thermodynamic limit. One can thus obtain excellent spatial resolution over arbitrary length scales, for a relatively low computational cost, a feature that gives the method an advantage over popular techniques such as NRG and DMRG. We find that the anisotropic Kondo model shows rich universal scaling behavior in the spatial structure of the entanglement cloud. First, SU(2) spin-symmetry is dynamically restored in a finite domain in parameter space in vicinity of the isotropic line, as expected from poor man's scaling. We are also able to obtain in closed analytical form a set of different, yet universal, scaling curves for strong exchange asymmetry, which are parametrized by the longitudinal exchange coupling. Deep inside the cloud, i.e. for distances smaller than the Kondo length, the correlation between the electron spin density and the impurity spin oscillates between ferromagnetic and antiferromagnetic values at the scale of the Fermi wavelength, an effect that is drastically enhanced at strongly anisotropic couplings. Our results also provide further numerical checks and alternative analytical approximations for the recently computed Kondo overlaps [PRL 114, 080601 (2015)].

Coherent long-range magnetic bound states in a superconductor

The quantum coherent coupling of completely different degrees of freedom is a challenging path towards creating new functionalities for quantum electronics. Usually the antagonistic coupling between spins of magnetic impurities and superconductivity leads to the destruction of the superconducting order. Here we show that a localized classical spin of an iron atom immersed in a superconducting condensate can give rise to new kind of long range coherent magnetic quantum state. In addition to the well-known Shiba bound state present on top of an impurity we reveal the existence of a star shaped pattern which extends as far as 12 nm from the impurity location. This large spatial dispersion turns out to be related, in a non-trivial way, to the superconducting coherence length. Inside star branches we observed short scale interference fringes with a particle-hole asymmetry. Our theoretical approach captures these features and relates them to the electronic band structure and the Fermi wave length of the superconductor. The discovery of a directional long range effect implies that distant magnetic atoms could coherently interact leading to new topological superconducting phases with fascinating properties.

Spin-dependent coherent transport in a double quantum dot system

We study spin-resolved resonant tunneling in a system of two quantum dots sandwiched between doped quantum wells. In the coherent (Dicke) regime, i.e., when quantum dot separation is smaller than the Fermi wavelength in a two-dimensional electron gas in quantum wells, application of an in-plane magnetic field leads to a pronounced spin-resolved structure of the conductance peak lineshape even for very small Zeeman splitting of the quantum dots' resonant levels. In the presence of electron-gas spin-orbit coupling, this spin-resolved structure gets washed out due to Fermi surface deformation in the momentum space. We also show that Aharonov-Bohm flux penetrating the area enclosed by electron tunneling pathways completely destroys conductance spin structure.

Observation of negative refraction of Dirac fermions in graphene

Half a century ago, Veselago proposed left-handed materials with negative permittivity and permeability, in which waves propagate with phase and group velocities in opposite directions. Significant work has been undertaken to attain this left-handed response, such as establishing a negative refractive index in so-called metamaterials, which consist of periodic sub-wavelength structures. However, an electronic counterpart has not been demonstrated owing to difficulties in creating repeated structures smaller than the electronic Fermi wavelength (\lambda_F) of the order ~ 10 nm. Here, without needing to engineer sub-wavelength structures, we demonstrate negative refractive behaviour of Dirac fermions in graphene, exploiting its unique relativistic band structure. Analysis of both electron focusing through a n-p-n flat lens and negative refraction across n-p junctions confirms left-handed behaviour in the electronic system. This new approach to electronic optics is of particular relevance to the on-going efforts to develop novel quantum devices with emerging layered materials.

Real structure influence on the electron–phonon coupling properties of niobium

We performed density functional theory calculations using niobium (Nb) as a model system of a conventional superconductor, to correlate the distortion of twin defects with the electron–phonon coupling properties. Calculations using different settings of the Nb elementary cell (relaxed, distorted, super cell with zig‐zag twin defect) showed that only by including real structure elements into the setting, the Eliashberg spectral function representing the electron–phonon coupling properties was derived convincingly. Based on these density functional theory calculations of the electron–phonon cou‐ pling properties of Nb, we suggest a model for a combined superconducting/charge density wave ground state which uses a lattice distortion induced into the crystal by two‐dimensional defects as modulated background potential of the charge density wave phase. The coexistence of both phases is hereby necessary for a fine‐tuning of the Fermi surface within the small local domain of the defect to match the wavelength of the lattice distortion and the Fermi wavelength by pairing fermions to bosons. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

Multitip scanning gate microscopy for ballistic transport studies in systems with a two-dimensional electron gas

We consider conductance mapping of systems based on the two-dimensional electron gas with scanning gate microscopy using two and more tips of the atomic force microscope. The paper contains results of numerical simulations for a model tip potential with a proposal of a few procedures for extraction and manipulation the ballistic transport properties. In particular, we demonstrate that the multi-tip techniques can be used for readout of the Fermi wavelength, detection of potential defects, filtering specific transverse modes, tuning the system into resonant conditions under which a stable map of a local density of states can be extracted from conductance maps using a third tip.

Rough surface electrical contact resistance considering scale dependent properties and quantum effects

The objective of this work is to evaluate the effect of scale dependent mechanical and electrical properties on electrical contact resistance (ECR) between rough surfaces. This work attempts to build on existing ECR models that neglect potentially important quantum- and size-dependent contact and electrical conduction mechanisms present due to the asperity sizes on typical surfaces. The electrical conductance at small scales can quantize or show a stepping trend as the contact area is varied in the range of the free electron Fermi wavelength squared. This work then evaluates if these effects remain important for the interface between rough surfaces, which may include many small scale contacts of varying sizes. The results suggest that these effects may be significant in some cases, while insignificant for others. It depends on the load and the multiscale structure of the surface roughness.

Metal Nanoclusters: Applications in Environmental Monitoring and Cancer Therapy

Metal nanoclusters (NCs), with dimensions between metal atoms and nanoparticles, have attracted more and more attention due to their unique physical and chemical properties. With their size approaching the Fermi wavelength of electrons, metal NCs possess molecule-like properties and excellent fluorescence emission. Owing to their ultrasmall size, strong fluorescence, and excellent biocompatibility, they have been widely studied in environmental and biological fields concerning their applications. In this review, we will introduce the properties of metal NCs, mainly focusing on the synthesis of metal alloy NCs and the recent progress in their applications in environmental monitoring and cancer therapy.

Fermionic and Majorana bound states in hybrid nanowires with non-uniform spin-orbit interaction

We study intragap bound states in the topological phase of a Rashba nanowire in the presence of a magnetic field and with non-uniform spin orbit interaction (SOI) and proximity-induced superconductivity gap. We show that fermionic bound states (FBS) can emerge inside the proximity gap. They are localized at the junction between two wire sections characterized by different directions of the SOI vectors, and they coexist with Majorana bound states (MBS) localized at the nanowire ends. The energy of the FBS is determined by the angle between the SOI vectors and the lengthscale over which the SOI changes compared to the Fermi wavelength and the localization length. We also consider double-junctions and show that the two emerging FBSs can hybridize and form a double quantum dot-like structure inside the gap. We find explicit analytical solutions of the bound states and their energies for certain parameter regimes such as weak and strong SOI. The analytical results are confirmed and complemented by an independent numerical tight-binding model approach. Such FBS can act as quasiparticle traps and thus can have implications for topological quantum computing schemes based on braiding MBSs.

Integer and fractional quantum anomalous Hall effect in a strip of stripes model

We study the quantum anomalous Hall effect in a strip of stripes model coupled to a magnetic texture with zero total magnetization and in the presence of strong electron-electron interactions. A helical magnetization along the stripes and a spin-selective coupling between the stripes gives rise to a bulk gap and chiral edge modes. Depending on the ratio between the period of the magnetic structure and the Fermi wavelength, the system can exhibit the integer or fractional quantum anomalous Hall effect. In the fractional regime, the quasiparticles have fractional charges and non-trivial Abelian braid statistics.

Position-dependent effect of non-magnetic impurities on superconducting properties of nanowires

Anderson's theorem states that non-magnetic impurities do not change the bulk properties of conventional superconductors. However, as the dimensionality is reduced, the effect of impurities becomes more significant. Here we investigate superconducting nanowires with diameter comparable to the Fermi wavelength (which is less than the superconducting coherence length) by using a microscopic description based on the Bogoliubov-de Gennes method. We find that: 1) impurities strongly affect the superconducting properties, 2) the effect is impurity position dependent, and 3) it exhibits opposite behavior for resonant and off-resonant wire widths. We show that this is due to the interplay between the shape resonances of the order parameter and the subband energy spectrum induced by the lateral quantum confinement. These effects can be used to manipulate the Josephson current, filter electrons by subband and investigate the symmetries of the superconducting subband gaps.

Fluorescent Gold Nanoclusters: Synthesis and Recent Biological Application

Fluorescent gold nanoclusters (AuNCs) have been extensively studied due to their unique construction and distinctive properties, which place them between single metal atoms and larger nanoparticles. The dimension of AuNCs is comparable to the Fermi wavelength of electrons, which lead to size‐dependent fluorescence and other molecule‐like properties. In this review, we summarize various synthesis strategies of fluorescent AuNCs and recent advances of biological applications such as biosensing, biolabeling, and bioimaging. The synthetic methods are considered as two routes: “Atoms to Clusters” and “Nanoparticles to Clusters.” The surface functionalization of AuNCs is described as the precondition for making future bioapplications possible, which can eventually influence their stability, biocompatibility, and other properties. And then we focus on the recent advances of AuNCs‐based applications in biological sensing, biolabeling, and bioimaging and finally discuss the current challenges of AuNCs in controllable synthesis and biological application.

Observation of quantized conductance in neutral matter.

In transport experiments, the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. Observations of quantized steps in electrical conductance have provided important insights into the physics of mesoscopic systems and have allowed the development of quantum electronic devices. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles. In its most fundamental form, it requires a quantum-degenerate Fermi gas, a ballistic and adiabatic transport channel, and a constriction with dimensions comparable to the Fermi wavelength. Here we report the observation of quantized conductance in the transport of neutral atoms driven by a chemical potential bias. The atoms are in an ultraballistic regime, where their mean free path exceeds not only the size of the transport channel, but also the size of the entire system, including the atom reservoirs. We use high-resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi-two-dimensional ballistic channel connecting the reservoirs. By varying either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaux in the atom conductance. The conductance in the first plateau is found to be equal to the universal conductance quantum, 1/h. We use Landauer's formula to model our results and find good agreement for low gate potentials, with all parameters determined a priori. Our experiment lets us investigate quantum conductors with wide control not only over the channel geometry, but also over the reservoir properties, such as interaction strength, size and thermalization rate.

Vortex Street in Homogeneous Dense Dusty Magnetoplasma

For studying the vortex structure in uniform dense dusty astrophysical conditions, a two-dimensional nonlinear equation is derived employing the quantum magnetoplasma hydrodynamic model and considering the strong collisional effect. The coherent vortex solution is obtained by perturbation analysis method. It is shown that the distribution of the electrostatic potential forms spatially a periodic vortex street, and is controlled temporally by the arbitrary function of time that may lead to abundant spacial distributions. It is found that the dust charge number, collision frequency, electron Fermi wavelength and quantum correction all play significant roles to the spatial distribution of vortex street.