Scanning tunneling miscoscopy is one of the most powerful spectroscopic tools for single-electron excitations. We show that the conductance fluctuations, or noise in the conductance, of a tunneling current into an interacting electron system is dominated by density-density and spin-spin correlations. This allows one to probe two-particle properties (susceptibilities) and collective excitations by standard experimental tunneling methods. We demonstrate this theoretically, using a novel many-body calculation for the multi-center Kondo problem, including both direct and indirect exchange between magnetic atoms. An example of the two-particle correlations around a single magnetic adatom in the Kondo regime, as would be viewed by a scanning tunneling microscope, is given. The spatial dependance of the charge and spin correlations, including the formation of the Kondo cloud in the spin sector, are shown.
A longstanding mystery in understanding cuprate superconductors is the inconsistency between the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we reconcile the two experimental techniques by generalising a theory which was previously applied to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic superconductors. We show that the s…
We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall state at the filling factor $ν=5/2$. The edge current in a single point-contact is considered. We focus on nonlinear behavior of two-terminal conductance with the increase in negative split-gate voltage. Expecting the appearance of the intermediate conductance plateau we calculate the value of its conductance by using the renormalization group (RG) analysis. Further, we show that non-perturbative quasi-particle tunneling is effectively described as perturbative electron tunneling by the instanton method. The two-termina…
Electronic transport in multiwall carbon nanotubes and semiconductor nanowires was compared. In both cases, the non ohmic behavior of the conductance, the so-called zero bias anomaly, shows a temperature dependence that scales with the voltage dependence. This robust scaling law describes the conductance $G(V,T)$ by a single coefficient $α$. A universal behavior as a function of $α$ is found for all samples. Magnetoconductance measurements furthermore show that the conduction regime is weak localization. The observed behavior can be understood in terms of the coulomb blockade theory, providing…
We calculate the current and differential conductance for the junction between a superconducting (SC) STM tip and a Luttinger liquid (LL). For an infinite single-channel LL, the SC coherence peaks are preserved in the tunneling conductance for interactions weaker than a critical value, while for strong interactions (g <0.38), they disappear and are replaced by cusp-like features. For a finite-size wire in contact with non-interacting leads, we find however that the peaks are restored even for extremely strong interactions. In the presence of a source-drain voltage the peaks/cusps split, and th…
We study point contact tunneling between two leads of a Tomonaga-Luttinger liquid through two degenerate resonant levels in parallel. This is one of the simplest cases of a quantum junction problem where the Fermi statistics of the electrons plays a non-trivial role through the Klein factors appearing in bosonization. Using a mapping to a `generalized Coulomb model' studied in the context of the dissipative Hofstadter model, we find that any asymmetry in the tunneling amplitudes from the two leads grows at low temperatures, so that ultimately there is no conductance across the system. For the …
Bilayer quantum Hall system at total filling factor $ν=1$ shows a rich variety of broken symmetry ground states because of the competition between the interlayer and intralayer Coulomb interactions. When the layers are sufficiently close, a bilayer system develops spontaneous interlayer phase-coherence that manifests itself through a spectacular enhancement of the zero-bias interlayer tunneling conductance. We present a theory of this tunneling conductance anomaly, and show that the zero-bias conductance is proportional to the square of the {\it quasiparticle} tunneling amplitude.
We present a large-N theory for the differential conductance, dI/dV, in Kondo systems measured via scanning tunneling spectroscopy. We demonstrate that quantum interference between tunneling processes into the conduction band and into the magnetic f-electron states is crucial in determining the experimental Fano lineshape of dI/dV. This allows one to uniquely extract the Kondo coupling and the ratio of the tunneling amplitudes from the experimental dI/dV curve. Finally, we show that dI/dV directly reflects the strength of the antiferromagnetic interaction in Kondo lattice systems.
The linear conductance of the a small metallic tunnel junction embedded in an electromagnetic environment of arbitrary impedance is determined in the semiclassical limit. Electron tunneling is treated beyond the orthodox theory of Coulomb blockade phenomena by means of a nonperturbative path integral approach. The frequency dependent conductance is obtained from Kubo's formula. The theoretical predictions are valid for high temperatures and/or for large tunneling conductance and are found to explain recent experimental data.
Inelastic tunneling through magnetically anisotropic molecules is studied theoretically in the presence of a strong magnetic field. Since the molecular orientation is not well controlled in tunneling experiments, we consider arbitrary angles between easy axis and field. This destroys all conservation laws except that of charge, leading to a rich fine structure in the differential conductance. Besides single molecules we also study monolayers of molecules with either aligned or random easy axes. We show that detailed information on the molecular transitions and orientations can be obtained from…
We study the complete tunneling spectroscopy of a normal metal/$p$-wave superconductor junction ($N-pS$) and normal metal/heterostructure superconductor junction ($N-hS$) by Blonder-Tinkham-Klapwijk (BTK) method. We find that, for $p$-wave superconductor with non-trivial topology, there exists a quantized zero-bias conductance peak stably, for heterostructure superconductor with non-trivial topology, the emerging zero-bias conductance peak is non-quantized and usually has a considerable gap to the quantized value. Furthermore, it is sensitive to parameters, especially to spin-orbit coupling an…
We consider tunneling from the spin-polarized tip into the Luttinger liquid edge state of quantum spin Hall system. This problem arose in context of the spin and charge fractionalization of an injected electron. Renormalization of the dc conductances of the system is calculated in the fermionic approach and scattering states formalism. In lowest order of tunneling amplitude we confirm previous results for the scaling dependence of conductances. Going beyond the lowest order we show that interaction affects not only the total tunneling rate, but also the asymmetry of the injected current. The h…
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 pseudopsin symmetry of the Dirac quasipart…
We present an explanation for the anomalous behavior in tunneling conductance and noise through a point contact between edge states in the Jain series $ν=p/(2np+1)$, for extremely weak-backscattering and low temperatures [Y.C. Chung, M. Heiblum, and V. Umansky, Phys. Rev. Lett. {\bf{91}}, 216804 (2003)]. We consider edge states with neutral modes propagating at finite velocity, and we show that the activation of their dynamics causes the unexpected change in the temperature power-law of the conductance. Even more importantly, we demonstrate that multiple-quasiparticles tunneling at low energie…
We theoretically investigate the tunneling spectroscopy of a system of two parallel one-dimensional helical conductors in the interacting, Luttinger liquid regime. We calculate the non-linear differential conductance as a function of the voltage bias between the conductors and the orbital momentum shift induced on tunneling electrons by an orthogonal magnetic field. We show that the conductance map exhibits an interference pattern which is characteristic to the interacting helical liquid. This can be contrasted with the different interference pattern from tunneling between regular Luttinger li…
Intergranular conduction in half metallic CrO2 is known to occur through a combination of spin dependent tunneling (driven by Coulomb Blockade (CB) effects) together with certain spin independent (SI) hopping processes. We present evidence that in polycrystalline CrO2 with enhanced grain size, both these process (CB effect and SI Hopping) are suppressed and the functional form of conductance is best described by Fluctuation Induced Tunneling (FIT) in a wide temperature range. Similar features are observed when grain boundary density is increased by Cr2O3 or Cr2O5.The spin dependent tunneling d…
Physical effects of bilayer coupling on the tunneling spectroscopy of high T$_{c}$ cuprates are investigated. The bilayer coupling separates the bonding and antibonding bands and leads to a splitting of the coherence peaks in the tunneling differential conductance. However, the coherence peak of the bonding band is strongly suppressed and broadened by the particle-hole asymmetry in the density of states and finite quasiparticle life-time, and is difficult to resolve by experiments. This gives a qualitative account why the bilayer splitting of the coherence peaks was not clearly observed in tun…
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynam…
We calculate the SIN and SIS tunneling conductances for the spin-fermion model. We argue that at strong spin-fermion coupling, relevant to cuprates, both conductances have dip features near the threshold frequencies when a tunneling electron begin emitting propagating spin excitation. We argue that the resonance spin frequency measured in neutron scattering can be inferred from the tunneling data by analyzing the derivatives of SIN and SIS conductances.
The effects of a non-magnetic Zn impurity substituting an in-plane Cu are studied by solving the Bogoliubov-de Gennes equation self-consistently which is derived from the \ttju Hamiltonian with all the allowed order parameters included. The Zn impurity, modeled in terms of a potential scatterer in unitary limit, induces local staggered magnetic moments around itself, and the calculated NMR shifts from the induced moments are in agreement with the experimental Cu NMR spectra. We also note that the experimentally observed negative slope of the tunneling conductance can result from the next-neare…
We studied the tunneling density of states in YBCO films under strong currents flowing along node directions. The currents were induced by fields of up to 32.4T parallel to the film surface and perpendicular to the $CuO_{2}$ planes. We observed a remarkable change in the tunneling conductance at high fields where the gap-like feature shifts discontinuously from 15meV to a lower bias of 11meV, becoming more pronounced as the field increases. The effect takes place in increasing fields around 9T and the transition back to the initial state occurs around 5T in decreasing fields. We argue that thi…
A generalized method of image, incorporated with the non-equilibrium Keldysh-Green's function formalism, is employed to investigate the tunneling spectroscopy of hybrid systems in the configuration of planar junction. In particular, tunneling spectroscopies of several hybrid systems that exhibit zero-bias conductance peaks (ZBCP) are examined. The well-known metal--d-wave superconductor (ND) junction is first examined in detail. Both the evolution of the ZBCP versus doping and the splitting of the ZBCP in magnetic fields are computed in the framework of the slave-boson mean field theory. Furth…
We consider the low-temperature differential tunneling conductance $G$ for interfaces between a planar insulating material in the Mott-class and a metal. For values of the the applied potential difference $V$ that are not very small, there is a experimentally observed universal regime in which $G \sim V^m$, where $m$ is a universal exponent. We consider the theoretical prediction of the values of $m$ by using the method of Effective Field Theory ($EFT$), which is appropriate for discussing universal phenomena. We describe the Mott material by the $EFT$ pertaining the long-distance behavior of …
We present a theory for the differential shot noise, $dS/dV$, as measured via shot-noise scanning tunneling spectroscopy, and the differential conductance, $dI/dV$, for tunneling into Majorana zero modes (MZMs) in the putative topological superconductor FeSe$_{0.45}$Te$_{0.55}$. We demonstrate that for tunneling into chiral Majorana edge modes near domain walls, as well as MZMs localized in vortex cores and at the end of defect lines, $dS/dV$ vanishes whenever $dI/dV$ reaches a quantized value proportional to the quantum of conductance. These results are independent of the particular orbital t…
Landau Fermi liquid theory predicts that the differential conductivity between metallic point and metal is a symmetric function of voltage bias V. This symmetry holds if the particle-hole symmetry is preserved. We show that the situation can be different when one of the two metals is a strongly correlated one whose electronic system can be represented by a heavy fermion liquid. When the heavy fermion liquid undergoes fermion condensation quantum phase transition, the particle-hole symmetry is violated making both the differential tunneling conductivity and dynamic conductance asymmetric as a f…
We describe scanning tunneling spectroscopic signatures of Majorana zero modes (MZMs) in Kitaev spin liquids. The tunnel conductance is determined by the dynamical spin correlations of the spin liquid, which we compute exactly, and by spin-anisotropic cotunneling form factors. Near a $\mathbb{Z}_2$ vortex, the tunnel conductance has a staircase voltage dependence, where conductance steps arise from MZMs and (at higher voltages) from additional vortex configurations. By scanning the probe tip position, one can detect the vortex locations. Our analysis suggests that topological magnon bound stat…
Measurements of conductance spectra in a superconductor - topological insulator - normal metal thin film junctions of NbN-$\rm Bi_2Se_3$-Au are reported. Junctions with ex-situ and in-situ prepared $\rm NbN-Bi_2Se_3$ interfaces were studied. At low temperatures, all the ex-situ junctions showed coherence peaks in their conductance spectra, but imbedded robust zero bias conductance peaks were observed only in junctions with a metallic or a metal to insulator transition below $\rm T_c$ of the NbN electrode. The in-situ junctions which had about two orders of magnitude lower resistance at low tem…
In mean-field descriptions of nodal d-wave superconductors, generic edges exhibit dispersionless Majorana fermion bands at zero-energy. These states give rise to an extensive ground-state degeneracy, and are protected by time-reversal (TR) symmetry. We argue that the infinite density of states of these flat-bands make them inherently unstable to interactions, and show that repulsive interactions lead to edge FM which splits the flat bands. This edge FM offers an explanation for the observation of splitting of zero-bias peaks in edge tunneling in High-Tc cuprate superconductors. We argue that t…
Using the zero mode method we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent $α(\leq 1)$. We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, the conductance as a function of temperature is $G \sim \frac{e^2}{h} (T/T_F)^{2(α-2)}$, whereas for off-resonance conditions the conductance is $G \sim \frac{e^2}{h} (T/T_F)^{2(α-1)}$. By applying a gate voltage and/or a magnetic field, one of the spin components can be in resonance…
Using a large-N theory in combination with the Keldysh non-equilibrium Greens function formalism, we investigate the current, differential conductance, zero-frequency shot-noise and Fano factor as measured by scanning tunneling shot noise spectroscopy (STSNS) using a scanning tunneling microscope (STM) near single Kondo impurities and in Kondo lattices. We show that the Fano factor $F$ exhibits a characteristic bias dependence arising from Kondo screening that is similar to the Kondo resonance observed in the differential conductance. Moreover, the lineshape of $F$ is strongly dependent on the…
We investigate the role of quantum coherence in tunneling conductance, where quantum criticality turns out to suppress Fano resonance. Based on the nonequilibrium noncrossing approximation, we show that the linear tunneling conductance exhibits weak Fano line-shape with sharp cusp at zero energy in the multichannel Kondo effect, resulting from incoherence associated with quantum criticality of impurity dynamics. In particular, shift of the peak position in the Fano resonance is predicted not to occur for the multichannel Kondo effect, distinguished from the Fermi liquid theory in the single ch…
The problem of resonant tunneling through a quantum dot weakly coupled to spinless Tomonaga-Luttinger liquids has been studied. We compute the linear conductance due to sequential tunneling processes upon employing a master equation approach. Besides the previously used lowest-order golden rule rates describing uncorrelated sequential tunneling (UST) processes, we systematically include higher-order correlated sequential tunneling (CST) diagrams within the standard Weisskopf-Wigner approximation. We provide estimates for the parameter regions where CST effects can be important. Focusing mainly…
We present a formula for tunneling conductance in ballistic ferromagnet/ferromagnetic insulator/superconductor junctions where the superconducting state has opposite spin pairing symmetry. The formula can involve correctly a ferromagnetism has been induced by effective mass difference between up- and down-spin electrons. Then, this effective mass mismatch ferromagnet and standard Stoner ferromagnet have been employed in this paper. As an application of the formulation, we have studied the tunneling effect for junctions including spin-triplet p-wave superconductor. The conductace spectra show a…
We theoretically investigate the effect of various symmetries of the superconducting order parameter Delta(omega) on the normalized tunneling conductance of SIN junctions by directly solving the real-axis Eliashberg equations (EEs) for a half-filled infinite band, with the simplifying assumption mu*=0. We analyze six different symmetries of the order parameter: s, d, s+id, s+d, extended s and anisotropic s, by assuming that the spectral function alpha^{2}F(Omega) contains an isotropic part alpha^{2}F(Omega)_{is} and an anisotropic one, alpha^{2}F(Omega)_{an}, such that alpha^{2}F(Omega)_{an} =…
