Non-local electron transport through normal and topological ladder-like atomic systems

Abstract

We propose a locally protected ladder-like atomic system (nanoconductor) on a substrate that is insensitive to external perturbations. The system corresponds to coupled atomic chains fabricated on different surfaces. Electron transport properties of such conductors are studied theoretically using the model tight-binding Su-Schriffer-Hegger (SSH) Hamiltonian and Green's function formalism. We have found that the conductance of the system is almost insensitive to single adatoms and oscillates as a function of the side chain length with very large periods. Non-local character of the electron transport was observed also for topological SSH chains where nontrivial end states survive in the presence of disturbances as well as for different substrates. We have found that the careful inspection of the density of states or charge waves can provide the information about the atom energy levels and hopping amplitudes. Moreover, the ladder-like geometry allows one to distinguish between normal and topological zero-energy states. It is important that topological chains do not reveal Friedel oscillations which are observed in non-topological chains.

Implementation of the Su–Schrieffer–Heeger Model in the Self-Assembly Si–In Atomic Chains on the Si(553)–Au Surface

“…A similar energy spectrum structure is expected for a trimer 1D lattice; except here, electron bands replace single states, with topological end states potentially manifesting within the energy gap. While in the original SSH chain, the topological modes precisely appear at the midgap energy, boundary topological states can also emerge at nonzero energies in extended SSH models. ,− , Moreover, it is worth noting that even in cases where the inversion symmetry is broken (due to disorders, defects, different on-site energies, asymmetrical couplings, or time-dependent perturbations), the localized nature of topological states can persist in such systems. ,, Additionally, ladder-like atomic systems such as two coupled SSH chains − and other SSH chain geometries ,− , also reveal nontrivial topological end states.…”

“…, where G ii r (E) represents the retarded Green function associated with the ith site of the chain and can be computed using the equation of motion technique. 46,68 , generally relies on the arrangement of surface atoms and electron localization/delocalization in the substrate. In our considered system, resembling a semiconductor-like surface, we approximate the chain-surface coupling within a wide band approximation as energy-independent, such that Γ ij (E) = Γδ ij .…”

“…Electronic properties of the system are analyzed within the framework of Green’s function method. The LDOS for each site is obtained using the relation L D O S i ( E ) = prefix− 1 π .25em I m .25em G i i r ( E ) , where G ii r ( E ) represents the retarded Green function associated with the i th site of the chain and can be computed using the equation of motion technique. , This yields algebraic complex equations for G r , expressed as  · Ĝ r = Î , where Î represents the unit matrix. The elements of the  matrix are defined as A i j = ( E − ε i ) δ i j + i normalΓ i j 2 − t i , j δ false⟨ i , j false⟩ .…”

Topological Atomic Chains on 2D Hybrid Structure

“…Atomic wires as the thinnest possible electrical conductors are especially interesting objects to study mainly from practical point of view. Their electronic properties are the subject of many theoretical and experimental papers as they reveal a great deal of interesting physical phenomena which are often hard to notice in bulk materials, e.g., spincharge separation [6,7], Majorana topological states [8,9], charge-density waves [10][11][12], turnstile effects, photon-assisted tunneling and pumping effects, or coherent destruction of tunneling [13][14][15][16][17][18][19][20]. In low-dimensional structures one can also observe unique solidstate phases such as time crystals [21][22][23], transient crystals [24] or Floquet topological insulators [25,26].…”

“…Topological chains are special materials where energy gaps appear inside the system and the edge states (topological states) are observed at the system boundaries. Such materials have unique electrical properties, i.e., topological states are insensitive to external perturbations, they survive for different substrates, reveal long-range conductance oscillations and can play a role of effective electron pumps [11,20]. Simple topological phases in one-dimensional chains can be obtained within a fermionic Su-Schrieffer-Heeger (SSH) model [29,30].…”