Lowest order in inelastic tunneling approximation: Efficient scheme for simulation of inelastic electron tunneling data

Abstract

We have developed an efficient and accurate formalism which allows the simulation at the ab initio level of inelastic electron tunneling spectroscopy data under a scanning tunneling microscope setup. It exploits fully the tunneling regime by carrying out the structural optimization and vibrational mode calculations for surface and tip independently. The most relevant interactions in the inelastic current are identified as the inelastic tunneling terms, which are taken into account up to lowest order, while all other inelastic contributions are neglected. As long as the system is under tunneling regime conditions and there is no physisorbed molecule on the surface or tip apex, this lowest order in inelastic tunneling (LOIT) approach reduces drastically the computational cost compared to related approaches while maintaining a good accuracy. Adopting the wide-band limit for both tip and surface further reduces calculation times significantly, and is shown to give similar results to when the full energy dependence of the Green's functions is taken into account. The LOIT is applied to the Cu(111) + CO system probed by a clean and a CO contaminated tip to find good agreement with previous works. Different parameters involved in the calculations such as basis sets, k sampling, tip-sample distance, or temperature, among others, are discussed in detail.

Influence of atomic tip structure on the intensity of inelastic tunneling spectroscopy data analyzed by combined scanning tunneling spectroscopy, force microscopy, and density functional theory

“…These advantages of STM-IETS have accelerated research in related fields [7][8][9][10][11][12][13][14][15][16]. Owing to recent progress in the theoretical description of IETS [17][18][19][20][21][22], the qualitative understanding has been improved considerably: the symmetry of the wave functions of a tip and a molecule on a substrate and a vibrational mode of the molecule are predicted to influence the efficiency of the inelastic process (γ inel ) for the tunneling current involving the molecule. In order to discuss γ inel on the basis of the intensity of IETS, we have to consider that IETS intensity is described by the multiplication of two factors: (1) the ratio of the tunneling current passing through a molecule to the total tunneling current (I molecule /I total ) and (2) the efficiency of the inelastic process (γ inel ).…”

“…The conclusion that γ inel does not depend on the oppositeelectrode geometry can be rationalized by considering the symmetry of the tip states with respect to the molecular axis [18][19][20]. In the case of the CO molecule, the twofold degenerate π -symmetric molecular states predominantly con- tribute to the inelastic tunneling process [ Fig.…”

“…In order to measure the conductance (dI /dV ) and IET signal (d 2 I/dV 2 ), a modulation voltage (2338.7 Hz, 1 mV rms ) is added to the sample bias and the first and second harmonics in the current are detected by a lock-in amplifier (HF2LI, Zurich Instruments, Zürich, Switzerland). Throughout the whole paper, the IET signal is normalized by the differential conductance, i.e., IETS = (d 2 I/dV 2 )/(dI/dV ) [10,14,18,20]. The tip is formed from an etched tungsten wire, cleaned by field evaporation and repeatedly poked into the Cu substrate to prepare various tip apexes [23,24,30].…”

Nonequilibrium distribution functions for quantum transport: Universality and approximation for the steady state regime

“…When Eq. (D4) is recast in terms of the Fermi distributions f L and f R entering the definition of f NE 0 , one recovers the lowest order expansion results obtained from scattering theory [70][71][72] and from NEGF 45,46,50,73 if the spectral function A C is calculated in the absence of interaction. The important point here is that our results are obtained in a rather straightforward manner by using the concept of NE distribution.…”

“…NE distribution functions have been used in large systems but only for non-interacting cases or for cases where the interactions are treated in a meanfield manner 51 . The effects of NE and MB effects for eph coupled realistic systems have been considered, however only at the level of a lowest order expansion for the coupling, and in conjunction with some form of selfconsistency 45,[48][49][50] . The really important point in the use of NE distributions for complex systems is that both the NE and MB effects are taken into account in the statistics of the finite size open quantum system (the central region C).…”