Scanning Tunneling Microscopy Spectra Research Articles

Electronic theory for scanning tunneling microscopy spectra in infinite-layer nickelate superconductors

Recent scanning tunneling microscopy (STM) observation of U-shaped and V-shaped spectra (and their mixture) in superconducting Nd$_{1-x}$Sr$_x$NiO$_2$ thin films has been interpreted as presence of two distinct gap symmetries in this nickelate superconductor [Gu et al., Nat. Comm. 11, 6027 (2020)]. Here, using a two-band model of nickelates capturing dominant contributions from Ni-$3d_{x^2-y^2}$ and rare-earth (R)-$5d_{3z^2 - r^2}$ orbitals, we show that the experimental observation can be simply explained within a pairing scenario characterized by a conventional $d_{x^2-y^2}$-wave gap structure with lowest harmonic on the Ni-band and a $d_{x^2-y^2}$-wave gap with higher-harmonics on the R-band. We perform realistic simulations of STM spectra employing first-principles Wannier functions to properly account for the tunneling processes and obtain V, U, and mixed spectral line-shapes depending on the position of the STM tip within the unit cell. The V- and U-shaped spectra are contributed from Ni and R-bands, respectively, and Wannier functions, in essence, provide position-dependent weighing factors, determining the spectral line-shape at a given intra-unit cell position. We propose a phase-sensitive experiment to distinguish between the proposed $d$-wave gap structure and time-reversal symmetry breaking $d+is$ gap which yields very similar intra-unit cell spectra.

Unveiling Odd-Frequency Pairing around a Magnetic Impurity in a Superconductor.

We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Because of the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity, which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of magnetic impurities immersed in a Pb/Si(111) monolayer, we show experimental evidence of the occurrence of the odd-frequency pairing in these systems and explicitly extract its superconducting function from the data.

On the mystery of the absence of a spin-orbit gap in scanning tunneling microscopy spectra of germanene

Germanene, the germanium analogue of graphene, shares many properties with its carbon counterpart. Both materials are two-dimensional materials that host Dirac fermions. There are, however, also a few important differences between these two materials: (1) graphene has a planar honeycomb lattice, whereas germanene’s honeycomb lattice is buckled and (2) the spin-orbit gap in germanene is predicted to be about three orders of magnitude larger than the spin-orbit gap in graphene (24 meV for germanene versus 20 μeV for graphene). Surprisingly, scanning tunneling spectra recorded on germanene layers synthesized on different substrates do not show any sign of the presence of a spin-orbit gap. To date the exact origin of the absence of this spin-orbit gap in the scanning tunneling spectra of germanene has remained a mystery. In this work we show that the absence of the spin-orbit gap can be explained by germanene’s exceptionally low work function of only 3.8 eV. The difference in work function between germanene and the scanning tunneling microscopy tip (the work functions of most commonly used STM tips are in the range of 4.5 to 5.5 eV) gives rise to an electric field in the tunnel junction. This electric field results in a strong suppression of the size of the spin-orbit gap.

Consistency between ARPES and STM measurements on SmB6

Strongly correlated topological surface states are promising platforms for next-generation quantum applications, but they remain elusive in real materials. The correlated Kondo insulator SmB$_6$ is one of the most promising candidates, with theoretically predicted heavy Dirac surface states supported by transport and scanning tunneling microscopy (STM) experiments. However, a puzzling discrepancy appears between STM and angle-resolved photoemission (ARPES) experiments on SmB$_6$. Although ARPES detects spin-textured surface states, their velocity is an order of magnitude higher than expected, while the Dirac point -- the hallmark of any topological system -- can only be inferred deep within the bulk valence band. A significant challenge is that SmB$_6$ lacks a natural cleavage plane, resulting in ordered surface domains limited to 10s of nanometers. Here we use STM to show that surface band bending can shift energy features by 10s of meV between domains. Starting from our STM spectra, we simulate the full spectral function as an average over multiple domains with different surface potentials. Our simulation shows excellent agreement with ARPES data, and thus resolves the apparent discrepancy between large-area measurements that average over multiple band-shifted domains and atomically-resolved measurements within a single domain.

Simulation of inelastic spin flip excitations and Kondo effect in STM spectroscopy of magnetic molecules on metal substrates

Single-ion magnetic anisotropy in molecular magnets leads to spin flip excitations that can be measured by inelastic scanning tunneling microscope (STM) spectroscopy. Here I present a semi ab initio scheme to compute the spectral features associated with inelastic spin flip excitations and Kondo effect of single molecular magnets. To this end density functional theory calculations of the molecule on the substrate are combined with more sophisticated many-body techniques for solving the Anderson impurity problem of the spin-carrying orbitals of the magnetic molecule coupled to the rest of the system, containing a phenomenological magnetic anisotropy term. For calculating the STM spectra an exact expression for the in the ideal STM limit, when the coupling to the STM tip becomes negligibly small, is derived. In this limit the is simply related to the spectral function of the molecule–substrate system. For the case of an Fe porphyrin molecule on the Au(1 1 1) substrate, the calculated STM spectra are in good agreement with recently measured STM spectra, showing the typical step features at finite bias associated with spin flip excitation of a spin-1 quantum magnet. For the case of Kondo effect in Mn porphyrin on Au(1 1 1), the agreement with the experimental spectra is not as good due to the neglect of quantum interference in the tunneling.

Strong correlation effects in theoretical STM studies of magnetic adatoms

We present a theoretical study for the scanning tunneling microscopy (STM) spectra of surface-supported magnetic nanostructures, incorporating strong correlation effects. As concrete examples, we study Co and Mn adatoms on the Cu(111) surface, which are expected to represent the opposite limits of the Kondo physics and local moment behavior, using a combination of density functional theory and both quantum Monte Carlo and exact diagonalization impurity solvers. We examine in detail the effects of temperature $T$, correlation strength $U$, and the impurity $d$ electron occupancy $N_d$ on the local density of states. We also study the effective coherence energy scale, i.e., the Kondo temperature $T_K$, which can be extracted from the STM spectra. Theoretical STM spectra are computed as a function of the STM tip position relative to each adatom. Because of the multi-orbital nature of the adatoms, the STM spectra are shown to consist of a complicated superposition of orbital contributions, with different orbital symmetries, self-energies and Kondo temperatures. For the Mn adatom, which is close to half-filling, the STM spectra are featureless near the Fermi level. On the other hand, the quasiparticle peak for Co adatom gives rise to strongly position-dependent Fano line-shapes.

Bases for time-resolved probing of transient carrier dynamics by optical pump–probe scanning tunneling microscopy

The tangled mechanism that produces optical pump-probe scanning tunneling microscopy spectra from semiconductors was analyzed by comparing model simulation data with experimental data. The nonlinearities reflected in the spectra, namely, the excitations generated by paired laser pulses with a delay time, the logarithmic relationship between carrier density and surface photovoltage (SPV), and the effect of the change in tunneling barrier height depending on SPV, were examined along with the delay-time-dependent integration process used in measurement. The optimum conditions required to realize reliable measurement, as well as the validity of the microscopy technique, were demonstrated for the first time.

Dynamics of Electronic Inhomogeneities in Cuprates

A phenomenological model is constructed which can reconcile the simultaneous existence of low-energy Bogoljubov quasiparticles and high-energy electronic order as observed by scanning tunneling microscopy (STM) experiments in cuprates. The theory can account for the high-energy contrast reversal in the STM spectra between positive and negative bias as characteristic for charge-density wave scattering. On the other hand the low-energy Fourier-transform of the local density of states is an even function of bias which provides an alternative to the formation of pair-density waves.

Unconventional scanning tunneling conductance spectra for graphene

We compute the tunneling conductance of graphene as measured by a scanning tunneling microscope (STM) with a normal/superconducting tip. We demonstrate that for undoped graphene with zero Fermi energy, the first derivative of the tunneling conductance with respect to the applied voltage is proportional to the density of states of the STM tip. We also show that the shape of the STM spectra for graphene doped with impurities depends qualitatively on the position of the impurity atom in the graphene matrix and relate this unconventional phenomenon to the pseudospin symmetry of the Dirac quasiparticles in graphene. We suggest experiments to test our theory.

Model of Quasiparticles Coupled to a Frequency-Dependent Charge-Density-Wave Order Parameter in Cuprate Superconductors

We investigate a model where superconducting electrons are coupled to a frequency dependent charge-density wave order parameter Delta_{r}(omega). Our approach can reconcile the simultaneous existence of low-energy Bogoljubov quasiparticles and high energy electronic order as observed in scanning tunneling microscopy (STM) experiments. The theory accounts for the contrast reversal in the STM spectra between positive and negative bias observed above the pairing gap. An intrinsic relation between scattering rate and inhomogeneities follows naturally.

Effect of quasiparticle spectral weight and consistency of energy gaps obtained from STM and ARPES spectra for underdoped superconductor Bi 2Sr 2CaCu 2O 8 + δ

By comparing the recently obtained superconducting energy gaps from the scanning tunneling microscopy (STM) and the angle-resolved photoemission spectroscopy (ARPES) for underdoped superconductor Bi 2Sr 2CaCu 2O 8 + δ , significant distinctions were observed. By properly taking the effect of quasiparticle spectral weight in the STM spectra into account, good consistency between both energy gaps obtained by STM and ARPES is unveiled.

Temperature annealing of tracks induced by ion irradiation of graphite

Highly oriented pyrolytic graphite (HOPG) samples were irradiated by Xe ions of initial kinetic energy of 3MeV/u. The irradiations were performed at temperatures of 500 and 800K. Scanning tunneling microscopy (STM) images show that the tracks occasionally have elongated structures under high-temperature irradiation. The track creation yield at 800K is by three orders of magnitude smaller compared to that obtained during room-temperature irradiation. STM and Raman spectra show that amorphization occurs in graphite samples irradiated at 500K to higher fluences, but not at 800K. The obtained experimental results clearly reveal that the irradiation under high temperature causes track annealing.

Modulation of the local density of states within thed-density wave theory of the underdoped cuprates

The low temperature scanning tunneling microscopy spectra in the underdoped regime are analyzed from the perspective of coexisting $d$-density wave and $d$-wave superconducting states. The calculations are carried out in the presence of a low concentration of unitary impurities and within the framework of the fully self-consistent Bogoliubov--de Gennes theory, which allows local modulations of the magnitude of the order parameters in response to the impurities. Our theory captures the essential aspects of the experiments in the underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (BSCCO) at very low temperatures.

Localization of the Cu(111) Surface State by Single Cu Adatoms

The Cu adatom-induced localization of the two-dimensional Shockley surface state at the Cu(111) surface was identified from experimental and simulated scanning tunneling microscopy spectra. The localization gives rise to a resonance located just below the surface state band edge. The adatom-induced surface state localization is discussed in terms of the existence theorem for bound states in any attractive two-dimensional potential. We also identify adatom-induced resonance states deriving from atomic orbitals in both experimental and simulated spectra.

Defect and anisotropic gap-induced quasi-one-dimensional modulation of the local density of states ofYBa2Cu3O7−δ

Motivated by recent angle-resolved photoemission spectroscopy (ARPES) measurement that superconducting ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) is consistent with a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+s$-symmetry gap, we show possible defect-induced quasi-one-dimensional modulations of the local density of states in YBCO. These stripelike structures are more conspicuous at higher measuring biases of the scanning tunneling microscopy (STM). Observation of these STM spectra would provide a unified picture of anisotropic gap on YBCO among STM, ARPES, and inelastic neutron scattering measurements.

Spin collective mode and quasiparticle contributions to STM spectra of d-wave superconductors with pinning

We present additional details of the scanning tunneling microscopy spectra predicted by the model of pinning of dynamic spin collective modes in d-wave superconductor proposed by Polkovnikov et al. [Phys. Rev. B 65 (2002) 220509]. Along with modulations at the twice the wavevector of the spin collective mode, the local density of states (LDOS) displays features linked to the spectrum of the Bogoliubov quasiparticles. The former is expected to depend more strongly on an applied magnetic field or the doping concentration. The spin collective mode and the quasiparticles are distinct, co-existing, low energy excitations of the d-wave superconductor (strongly coupled only in some sectors of the Brillouin zone), and should not be viewed as mutually exclusive sources of LDOS modulation.

Kondo effect and STM spectra through ferromagnetic nanoclusters

Motivated by recent scanning tunneling microscope (STM) experiments on cobalt clusters adsorbed on single wall metallic nanotubes [Odom {\em et al.}, Science {\bf 290}, 1549 (2000)], we study theoretically the size dependence of STM spectra and spin-flip scattering of electrons from finite size ferromagnetic clusters adsorbed on metallic surfaces. We study two models of nanometer size ferromagnets: (i) An itinerant model with delocalized s, p and d electrons and (ii) a local moment model with both localized d-level spins and delocalized cluster electrons. The effective exchange coupling between the spin of the cluster and the conduction electrons of the metallic substrate depends on the specific details of the single particle density of states on the cluster. The calculated Kondo coupling is inversely proportional to the total spin of the ferromagnetic cluster in both models and thus the Kondo temperature is rapidly suppressed as the size of the cluster increases. Mesoscopic fluctuations in the charging energies and magnetization of nanoclusters can lead to large fluctuations in the Kondo temperatures and a very asymmetric voltage dependence of the STM spectra. We compare our results to the experiments.

Voltage-dependent scanning-tunneling microscopy of a crystal surface: Graphite.

We discuss the possible application of the scanning tunneling microscope (STM) to surface electronic spectroscopy, with an explicit calculation of the voltage-dependent tunneling current for an ideal STM experiment performed on graphite. We study how surface and bulk electronic states are reflected in the tunneling J-V spectra, and show that empty surface states of graphite may be well discriminated against bulklike structures by considering STM spectra at different tip-surface separations.