The emergence of local moments in graphene zigzag edges, grain boundaries, vacancies and sp3 defects has been widely studied theoretically. However, conclusive experimental evidence is scarce. Recent progress in on-surface synthesis has made it possible to create nanographenes, such as triangulenes, with local moments in their ground states, and to probe them using scanning tunnelling microscope (STM) spectroscopy. Here we review the application of the theory of sequential and cotunneling transport to relate the dI/dV spectra with the spin properties of nanographenes probed by STM. This approach permits us to connect the dI/dV with the many-body energies and wavefunctions of the graphene nanostructures. We apply this method describing the electronic states of the nanographenes by means of exact diagonalization of the Hubbard model within a restricted Active Space. This permits us to provide a proper quantum description of the emergence of local moments in graphene and its interplay with transport. We discuss the results of this theory in the case of diradical nanographenes, such as triangulene, rectangular ribbons and the Clar goblet, that have been recently studied experimentally by means of STM spectroscopy. This approach permits us to calculate both the dI/dV spectra, that yields excitation energies, as well as the atomically resolved conductivity maps, that provide information on the wavefunctions of the collective spin modes.
Single layer graphene islands with a typical diameter of several nanometers were grown on a Pt (111) substrate. Scanning tunneling microscopy (STM) analysis showed most of islands are hexagonally shaped and the zigzag-type edge predominates over the armchair-type edge. The apparent height at the atoms on the zigzag edge is enhanced with respect to the inside atoms for a small sample bias voltage, while such an enhancement was not observed at the atoms on the armchair edge. This result provides an experimental evidence of spatially (at the zigzag edge) and energetically (at the Fermi level) loc…
Nanographenes with zigzag edges are predicted to manifest non-trivial pi-magnetism resulting from the interplay of hybridization of localized frontier states and Coulomb repulsion between valence electrons. This provides a chemically tunable platform to explore quantum magnetism at the nanoscale and opens avenues toward organic spintronics. The magnetic stability in nanographenes is thus far limited by the weak magnetic exchange coupling which remains below the room temperature thermal energy. Here, we report the synthesis of large rhombus-shaped nanographenes with zigzag periphery on gold and…
Tailoring magnetism of nanographenes via tip-controlled dehydrogenation
Empa—Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技研究院）；Technical University of Dresden（德累斯顿工业大学）；University of Zurich（苏黎世大学）；University of Bern（伯尔尼大学）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微观结构物理研究所）
Learning Inhomogeneous Heisenberg Hamiltonians in Nanographene Spin Chains
Aalto University（阿尔托大学）；Empa—Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科技与检测局）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Max Planck Institute of Microstructure Physics（马克斯·普朗克微结构物理研究所）；Technische Universität Dresden（德累斯顿工业大学）
Exchange interactions and intermolecular hybridization in a spin-1/2 nanographene dimer
Department of Chemistry, University of Zurich（苏黎世大学化学系）；Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Universidad del País Vasco UPV/EHU（巴斯克国立大学先进聚合物与材料系：物理、化学与技术）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）；Integrated Systems Laboratory, ETH Zürich（苏黎世联邦理工学院集成系统实验室）；International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学化学、生物化学与药学系）
The two apparently disparate phenomena, viz. the Klein tunneling and the electric field driven topological phase transition(TPT), exhibited by the silicene converge on the issue of the no change in the pseudo-spin. An ensuing possibility is that the former, in the case of a normal/magnetic/normal silicene junction, may be considered theoretically as a probe to ascertain the onset of the latter. In this communication, we explore this option and calculate the total transmission probability(TTP). We find that TPT is characterized by a cusp in a plot of TTP as a function of the electric field.
Using low-temperature scanning tunneling spectroscopy applied to the Cs-induced two-dimensional electron system (2DES) on p-type InSb(110), we probe electron-electron interaction effects in the quantum Hall regime. The 2DES is decoupled from p-doped bulk states and exhibits spreading resistance within the insulating quantum Hall phases. In quantitative agreement with calculations we find an exchange enhancement of the spin splitting. Moreover, we observe that both the spatially averaged as well as the local density of states feature a characteristic Coulomb gap at the Fermi level. These result…
Spectroscopic measurements with low-temperature scanning tunneling microscopes have been used very successfully for studying not only individual atomic or molecular spins on surfaces but also complexly designed coupled systems. The symmetry breaking of the supporting surface induces magnetic anisotropy which lead to characteristic fingerprints in the spectrum of the differential conductance and can be well understood with simple model Hamiltonians. Furthermore, correlated many-particle states can emerge due to the interaction with itinerant electrons of the electrodes, making these systems ide…
Scanning tunneling spectroscopy (STS) has yielded significant insight on the electronic structure of graphene and other two-dimensional (2D) materials. STS directly measures a fundamental and directly calculable quantity: the single particle density of states (SPDOS). Due to experimental setup limitations, however, STS has been unable to explore 2D materials in ultra-high magnetic fields where electron-electron interactions can drastically change the SPDOS. Recent developments in the assembly of heterostructures composed of graphene and hexagonal boron nitride have enabled a device-based alter…
Probing two-dimensional single-layer quantum magnets remains a significant challenge. In this letter, we propose exploiting tunneling spectroscopy in the presence of magnetic impurities to obtain information about the magnon dispersion relations in analogy to quasiparticle interference in non-magnetic materials. We show this technique can be used to establish the dispersion relations even for frustrated magnets, where the presence of an impurity generally leads to a nontrivial spin texture. Finally, we consider the problem of establishing Chern magnon bands in 2D magnets showing how tuneable i…
Expert attention is attracted to the obvious contradiction of the assumption on macroscopic quantum tunnelling and on superposition of two macroscopically distinct quantum states of superconducting loop, considered as flux qubit, with the law of angular momentum conservation and the universally recognized quantum formalism.
A recently demonstrated quantum electron pump is discussed within the framework of photon-assisted tunneling. Due to lack of time-reversal symmetry, different results are obtained for the pump current depending on whether or not final-state Pauli blocking factors are used when describing the tunneling process. Whilst in both cases the current depends quadratically on the driving amplitude for moderate pumping, a marked difference is predicted for the temperature dependence. With blocking factors the pump current decreases roughly linearly with temperature until k_B T ~ \hbarωis reached, wherea…
Scanning tunneling spectroscopy requires the application of a potential difference between the sample and a tip. In metal-vacuum-metal junctions, one can safely assume that the potential is constant along the metallic substrate. Here, we show that the inhomogeneous shape of the electric potential has to be taken into account when probing spatially extended molecules on a decoupling layer. To this end, oligothiophene-based molecules were deposited on a monolayer of molybdenum disulfide (MoS$_2$) on a Au(111) surface. By probing the delocalized molecular orbital along the thiophene-backbone, we …
Tunneling across superconducting junctions proceeds by a rich variety of processes, which transfer single electrons, Cooper pairs, or even larger numbers of electrons by multiple Andreev reflections. Photon-assisted tunneling combined with the venerable Tien-Gordon model has long been a powerful tool to identify tunneling processes between superconductors. Here, we probe superconducting tunnel junctions including an impurity-induced Yu-Shiba-Rusinov (YSR) state by exposing a scanning tunneling microscope with a superconducting tip to microwave radiation. We find that a simple Tien-Gordon descr…
Unambiguous identification of Majorana physics presents an outstanding problem whose solution could render topological quantum computing feasible. We develop a numerical approach to treat finite-size superconducting chains supporting Majorana fermions, which is based on iterative application of a two-site Bogoliubov transformation. We demonstrate the applicability of the method by studying a resonant level attached to the superconductor subject to external perturbations. In the topological phase, we show that the spectrum of a single resonant level allows to distinguish peak coming from Majora…
This review covers recent experimental progress in probing the electronic properties of graphene and how they are influenced by various substrates, by the presence of a magnetic field and by the proximity to a superconductor. The focus is on results obtained using scanning tunneling microscopy, spectroscopy, transport and magneto-transport techniques.
Probing topological Floquet states in graphene with ultrafast terahertz scanning tunneling microscopy
University of Bremen（不来梅大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Paul Scherrer Institute（保罗谢尔研究所）；University of Fribourg（弗里堡大学）；The Flatiron Institute（_flatiron研究所）；Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）
Defects in hexagonal boron nitride (h-BN) layer can facilitate tunneling current through thick h-BN tunneling barriers. We have investigated such current-mediating defects as local probes for materials in two dimensional heterostructure stacks. Besides $IV$ characteristics and negative differential conductance, we have characterized the electrical properties of h-BN defects in vertical graphene-h-BN-Cr/Au tunnel junctions in terms of low frequency current noise. Our results indicate a charge sensitivity of 1.5$\times$$ 10^-5$e/$\sqrt Hz$ at 10 $Hz$, which is equal to good metallic single elect…
Recently, the rhombohedral trilayer graphene (r-TLG) has attracted much attention because of its low-energy flat bands, which are predicted to result in many strongly correlated phenomena. Here, we demonstrate that it is possible to probe the stacking order and electronic spectrum of the r-TLG directly with a scanning tunneling microscopy around a monoatomic step edge of the top graphene layer. The tunneling spectra of the r-TLG exhibit four adjacent peaks, which are generated by the low-energy flat bands, flanking the charge neutrality point. Based on these spectra, the true energy gap and th…
We study the effect of volumetric constraints on the structure and electronic transport properties of distilled water in a nanopore with embedded electrodes. Combining classical molecular dynamics simulations with quantum scattering theory, we show that the structural motifs water assumes inside the pore can be probed directly by tunneling. In particular, we show that the current does not follow a simple exponential curve at a critical pore diameter of about 8 Å, rather it is larger than the one expected from simple tunneling through a barrier. This is due to a structural transition from bulk-…
Andreev bound states (ABSs) are localized quantum states that contain both electron and hole components. They ubiquitously reside in inhomogeneous superconducting systems. Following theoretical analysis, we propose to probe the electron-hole weights of an ABS via a local tunneling measurement that detects the transient current under a steplike pulse bias. With our protocol, the ABS energy level can also be obtained from peaks of the Fourier spectrum of the transient current. Our protocol can be applied to detect robust zero-energy Majorana bound states (MBSs), which have equal electron-hole we…
The photon-assisted tunneling (PAT) through a single wall carbon nanotube quantum well (QW) under influence an external electromagnetic field for probing of the Tomonaga Luttinger liquid (TLL) state is suggested. The elementary TLL excitations inside the quantum well are density ($ρ_{\pm}$) and spin ($σ_{\pm} $) bosons. The bosons populate the quantized energy levels $ε^{ρ+}_n =Δn/ g$ and $ε^{ρ-(σ\pm)}_n = Δn$ where $Δ= h v_F /L $ is the interlevel spacing, $n$ is an integer number, $L$ is the tube length, $g$ is the TLL parameter. Since the electromagnetic field acts on the $ρ_{+}$ bosons onl…
The tunneling current and shot noise of the current between two Fractional Quantum Hall (FQH) edges in the $ ν=12/5 $ FQH state in electronic Mach-Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of $k=3 $ parafermion statistics in the $ ν=12/5 $ FQH state. More specifically, the dependence of the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric under the change of the sign of the applied voltage. This property is absent in the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 el…
In noncentrosymmetric superconductors (NCSs), the conversion of a charge current into spin magnetization - the so called magnetoelectric effect - is the direct indicator of the unconventional, mixed-parity order parameter. This paper proposes a scheme to detect the magnetoelectric effect by anomalous, equal-spin Andreev tunneling in NCS/ferromagnet contacts. The proposal relies on the ability to generate spin-polarized triplet pairing by passing an electric current through an NCS. Such an induced triplet pairing bears a similarity to the paradigmatic nonunitary pairing in triplet superfluids w…
Recently, a single atom transistor was deterministically fabricated using phosphorus in Si by H-desorption lithography with a scanning tunneling microscope (STM). This milestone in precision, achieved by operating the STM in the conventional tunneling mode, typically utilizes very slow ($\sim\!10^2~\mathrm{nm^2/s}$) patterning speeds. By contrast, using the STM in a high voltage ($>10~\mathrm{V}$) field emission mode, patterning speeds can be increased by orders of magnitude to $\gtrsim\!10^4~\mathrm{nm^2/s}$. We show that the rapid patterning negligibly affects the functionality of relatively…
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…
Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi$_2$Se$_3$ ultrathin films. At two-dimensional limit, bulk electrons becomes quantized and the quantization can be controlled by film thickness at single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of phase relaxation length $l_ϕ$ and inelastic scattering lifetime $τ$ of topological surface-state electrons. We …
We theoretically analyze a state-of-the-art experimental method based on a combination of electron spin resonance and scanning tunneling microscopy (ESR-STM), to directly probe the spin fluctuations in the Kondo effect. The Kondo impurity is exchange coupled to the probe spin, and the ESR-STM setup detects the small level shifts in the probe spin induced by the spin fluctuations of the Kondo impurity. We use the open quantum system approach by regarding the probe spin as the "system" and the Kondo impurity spin as the fluctuating "bath" to evaluate the resonance line shifts in terms of the dyn…
Macroscopic resonant tunneling between the two lowest lying states of a bistable RF-SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian shaped profile that is not peaked at the resonance point, but is shifted to a bias at which the initial well is higher than the target well. The r.m.s. amplitude of the noise, which is proportional to the decoherence rate 1/T_2^*, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low frequency (…
The nature of the fractional quantum Hall state with filling factor $ν=2/3$ and its edge modes continues to remain an open problem in low-dimensional condensed matter physics. Here, we suggest an experimental setting to probe the $ν=2/3$ edge by tunnel-coupling it to a $ν=1$ integer quantum Hall edge in another layer of a two-dimensional electron gas (2DEG). In this double-layer geometry, the momentum of tunneling electrons may be boosted by an auxiliary magnetic field parallel to the two planes of 2DEGs. We evaluate the current as a function of bias voltage and the boosting magnetic field. It…
We present an extension of the tunneling theory for scanning tunneling microcopy (STM) to include different types of vibrational-electronic couplings responsible for inelastic contributions to the tunnel current in the strong-coupling limit. It allows for a better understanding of more complex scanning tunneling spectra of molecules on a metallic substrate in separating elastic and inelastic contributions. The starting point is the exact solution of the spectral functions for the electronic active local orbitals in the absence of the STM tip. This includes electron-phonon coupling in the coupl…
Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises ultrathin insulating multiferroics, spin liquids, and ferromagnets, but new characterization methods are required to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI3 as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and inter-layer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95%,…
We demonstrate a new method for locally probing the edge states in the quantum Hall regime utilizing a side coupled quantum dot positioned at an edge of a Hall bar. By measuring the tunneling of electrons from the edge states into the dot, we acquire information on the local electrochemical potential and electron temperature of the edge states. Furthermore, this method allows us to observe the spatial modulation of the electrostatic potential at the edge state due to many-body screening effect.
Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-sized quantum corrals, depend on careful positioning of adatoms at clean surfaces. Here we demonstrate an entirely different approach, inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphene's unique properties, namely gate-tunable light-like carriers, we create Whispering Gallery Mode (WGM) resonators defined by circular pn-junctions, induced by a scanning tunneling probe. We …
The bias dependence of spin injection in graphene lateral spin valves is systematically studied to determine the factors affecting the tunneling spin injection efficiency. Three types of junctions are investigated, including MgO and hexagonal boron nitride (hBN) tunnel barriers and direct contacts. A DC bias current applied to the injector electrode induces a strong nonlinear bias dependence of the nonlocal spin signal for both MgO and hBN tunnel barriers. Furthermore, this signal reverses its sign at a negative DC bias for both kinds of tunnel barriers. The analysis of the bias dependence for…
Temperature is a fundamental parameter in the study of physical phenomena. At the nanoscale, local temperature differences can be harnessed to design novel thermal nanoelectronic devices or test quantum thermodynamical concepts. Determining temperature locally is hence of particular relevance. Here, we present a primary electron thermometer that allows probing the local temperature of a single electron reservoir in single-electron devices. The thermometer is based on cyclic electron tunneling between a system with discrete energy levels and a single electron reservoir. When driven at a finite …
Interactions in one-dimensional (1D) electron systems are expected to cause a dynamical separation of electronic spin and charge degrees of freedom. A promising system for experimental observation of this non-Fermi-liquid effect consists of two quantum wires coupled via tunneling through an extended uniform barrier. Here we consider the minimal model of an interacting 1D electron system exhibiting spin-charge separation and calculate the differential tunneling conductance as well as the density-density response function. Both quantities exhibit distinct strong features arising from spin-charge…
Two dimensional electronic systems under strong magnetic field form quantum Hall (QH) edge states, which propagate along the boundary of a sample with a dissipationless current. Engineering the pathway of these propagating one-dimensional chiral modes enables the investigation of quantum tunneling between adjacent QH states. Here, we report tunneling transport in spatially controlled networks of QH edge states in bilayer graphene. We observe resonant tunneling between co-propagating QH edges across barriers formed by electrically defining incompressible strips. Employing spectroscopic tunnelin…
We derive the local density of states from itinerant and boundary states around transport barriers and edges in graphene and show that the itinerant states lead to mesoscale undulations that could be used to probe their scattering properties in equilibrium without the need for lateral transport measurements. This finding will facilitate vetting of extended structural defects such as grain boundaries or line defects as transport barriers for switchable graphene resonant tunneling transistors. We also show that barriers could exhibit double minima and that the charge density away from highly ref…
We study single electron transport across a single Bi dopant in a Silicon Nanotransistor to assess how the strong hyperfine coupling with the Bi nuclear spin $I=9/2$ affects the transport characteristics of the device. In the sequential tunneling regime we find that at, temperatures in the range of $100 mK$, $dI/dV$ curves reflect the zero field hyperfine splitting as well as its evolution under an applied magnetic field. Our non-equilibrium quantum simulations show that nuclear spins can be partially polarized parallel or antiparallel to the electronic spin just tuning the applied bias.
The interplay between spin and charge in solids is currently among the most discussed topics in condensed matter physics. Such interplay gives rise to magneto-electric coupling, which in the case of solids was named magneto-electric effect, as predicted by Curie on the basis of symmetry considerations. This effect enables the manipulation of magnetization using electrical field or, conversely, the manipulation of electrical polarization by magnetic field. The latter is known as the magnetocapacitance effect. Here, we show that non-equilibrium spin accumulation can induce tunnel magnetocapacita…
Recently, it was shown both theoretically and experimentally that certain three-dimensional (3D) materials have Dirac points in the Brillouin zone, thus being 3D analogs of graphene. Moreover, it was suggested that under specific conditions a pair of localized impurities placed inside a three-dimensional Dirac semimetal may lead to the formation of an unusual antibonding state. In the meantime, the effect of vibrational degrees of freedom which are present in any realistic system has avoided attention. In this work, we address the influence of phonons on characteristic features of (anti)bondin…
We study the electronic structure of a single self-assembled InAs quantum dot by probing elastic single-electron tunneling through a single pair of weakly coupled dots. In the region below pinch-off voltage, the non-linear threshold voltage behavior provides electronic addition energies exactly as the linear, Coulomb blockade oscillation does. By analyzing it, we identify the s and p shell addition spectrum for up to six electrons in the single InAs dot, i.e. one of the coupled dots. The evolution of shell addition spectrum with magnetic field provides Fock-Darwin spectra of s and p shell.
Probing up-conversion electroluminescence of decoupled porphyrin molecules in a plasmonic nanocavity
Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Institut de Physique, École Polytechnique Fédéral Lausanne（洛桑联邦理工学院物理研究所）；Gleb Wataghin Institute of Physics - University of Campinas - UNICAMP（坎皮纳斯大学格莱布·瓦塔金物理研究所）；Nanjing University（南京大学）
We consider a quantum dot coupled to a topological superconductor and two normal leads and study transport properties of the system. Using Keldysh path-integral approach, we study current fluctuations (shot noise) within the low-energy effective theory. We argue that the combination of the tunneling conductance and the shot noise through a quantum dot allows one to distinguish between the topological (Majorana) and non-topological (e.g., Kondo) origin of the zero-bias conduction peak. Specifically, we show that, while the tunneling conductance might exhibit zero-bias anomaly due to Majorana or…
Electron transfer processes at molecule-semiconductor interfaces involve a complex mixture of thermionic, tunneling and hopping events. Traditionally these processes have been modeled in a piece-meal fashion, relying on phenomenological treatments such as Simmons and Richardson equations that are not vetted in atomistic systems and do not flow seamlessly into each other. We present a unified modeling approach, based on the Non-equilibrium Greens function (NEGF) formalism that allows us to integrate diverse transport regimes and establish a comprehensive quantitative theory. By comparing our si…
Graphene quantum dots are considered as promising alternatives to quantum dots in III-V semiconductors, e.g., for the use as spin qubits due to their consistency made of light atoms including spin-free nuclei which both imply relatively long spin decoherene times. However, this potential has not been realized in experiments so far, most likely, due to a missing control of the edge configurations of the quantum dots. Thus, a more fundamental investigation of Graphene quantum dots appears to be necessary including a full control of the wave function properties most favorably during transport spe…
The tunneling Hamiltonian describes a particle transfer from one region to the other. While there is no particle storage in the tunneling region itself, it has associated certain amount of energy. We name the corresponding flux energy reactance since, like an electrical reactance, it manifests itself in time-dependent transport only. Noticeably, this quantity is crucial to reproduce the universal charge relaxation resistance for a single-channel quantum capacitor at low temperatures. We show that a conceptually simple experiment is capable of demonstrating the existence of the energy reactance…
