Surface-State-Assisted Tunneling

• Surface-state-assisted tunneling is a transport process where electronic states localized at surfaces or interfaces actively mediate tunneling, enabling resonant, defect-mediated, and interference-driven phenomena.
• The mechanism is demonstrated in diverse systems, from semiconductor–oxide interfaces with trap-assisted and Fowler–Nordheim tunneling to STM studies revealing vibration-assisted resonant tunneling.
• This topic informs advanced material engineering by linking surface reconstructions, adatom-induced states, and field-renormalized resonances to tailored electronic transport in superconducting and topological nanodevices.

Surface-state-assisted tunneling denotes a class of transport processes in which electronic states localized at a surface, interface, or edge materially participate in tunneling. In the current literature, that participation ranges from semiconductor–oxide interface trapping and defect-mediated injection to resonant transport through adatom-induced gap states, tunneling through Shockley or Tamm surface bands, transport through superconducting bound states and Majorana-related surface channels, and barrier reshaping by reconstructed surface-confined metallic layers. The phrase is therefore broader than any single microscopic mechanism, and several papers use more specific terms such as interface states, adatom-induced gap state, Shockley surface state, Tamm-type surface state, Yu–Shiba–Rusinov state, surface Andreev bound state, Fermi arc state, or electronic reconstruction (Ma et al., 11 Jan 2026, Kumar et al., 16 Apr 2025, Li et al., 2021, Schreyer et al., 2020, Ruby et al., 2015, Yamakage et al., 2011, Siu et al., 2016, Wang et al., 2017).

1. Terminology and phenomenological scope

A narrow usage would restrict surface-state-assisted tunneling to transport through canonical intrinsic surface bands such as Shockley or Tamm states. The recent literature does not support that restriction. In strained Ge/SiGe, the relevant assisting states are interface states at the semiconductor–oxide boundary rather than a buried heterointerface state (Ma et al., 11 Jan 2026). In Au/WSe$_2$, the assisting state is an Au-adatom-induced localized in-gap state rather than a native extended surface band (Kumar et al., 16 Apr 2025). In ultrathin oxides, terrace-edge conductance enhancement is attributed to electronic reconstruction and partial metallization of a surface layer rather than to a discrete trap or a conventional surface band (Wang et al., 2017). In CeCoIn$_5$, STM contrast arises from tunneling into a surface-reconstructed, correlation-enhanced $d$-orbital texture rather than into a named Shockley/Tamm state (Kim et al., 2017).

Representative platform	Assisting state	Characteristic transport signature
Strained Ge/SiGe heterostructure	Semiconductor–oxide interface states (Ma et al., 11 Jan 2026)	TAT-to-Fowler–Nordheim crossover
Au adatom on WSe$_2$	Adatom-induced localized in-gap state (Kumar et al., 16 Apr 2025)	Resonant double-barrier tunneling with vibrational sidebands
Au(111)	Shockley surface state (Li et al., 2021)	Additional channel near $E_F$; interference-induced transmission drop
La(0001)	Unoccupied Tamm-type surface state (Schreyer et al., 2020)	Stark shift and linewidth broadening in STM
Pb/Mn/Pb superconducting STM	Yu–Shiba–Rusinov state (Ruby et al., 2015)	Single-electron to Andreev crossover
Na$_3$Bi thin film	Fermi arc surface states (Siu et al., 2016)	Finite transmission inside a bulk gap

A second common simplification is to equate the topic only with conductance enhancement. Several systems instead show suppression or line-shape inversion once a surface-related channel interferes with a background bulk channel. The Au(111) Shockley state can generate a robust transmission drop at the surface-state band edge through coupling between bulk and surface-state transport channels, and the theoretical impurity-on-surface model produces position-dependent peak, dip, and asymmetric Fano-like structures through interference between direct and resonant tunneling paths (Li et al., 2021, Mantsevich et al., 2010).

2. Semiconductor–oxide interfaces and trap-mediated injection

In strained Ge/SiGe quantum devices, the most explicit modern use of the topic is the cryogenic filling of interface states at the semiconductor–oxide boundary in a reverse-graded Hall-bar FET. The carrier path is from a 2D hole gas in a 16 nm strained Ge quantum well, upward through a 32 nm Si$_{0.2}$Ge$_{0.8}$ barrier, to interface states near the top-surface semiconductor–oxide boundary, modeled as charge in the SiO$_x$ region. At $T\approx 4.5\ \mathrm{K}$, each measurement cycle steps the gate to a chosen negative bias and holds it for about $_5$0; the source-drain current then decays over time before stabilizing, consistent with gradual loss of holes from the quantum well and capture into interface states. A one-dimensional self-consistent Schrödinger–Poisson inversion reconstructs the saturated interface charge density $_5$1 by matching simulated and Hall-extracted 2DHG density within 1%, and the cumulative trapped charge increases almost linearly with $_5$2, with a Pearson correlation of $_5$3. The transport analysis is written as

$_5$4

with direct tunneling through the full 32 nm barrier calculated to be negligible, around $_5$5; the dominant mechanism is trap-assisted tunneling (TAT) at small and moderate negative bias, followed by a crossover to Fowler–Nordheim tunneling for $_5$6 once the barrier becomes strongly triangular (Ma et al., 11 Jan 2026).

That result refines a purely Fowler–Nordheim picture. The final trapped charge responsible for drift resides at the semiconductor–oxide interface, but the low-field supply path is attributed to defect states inside the SiGe barrier, likely dislocation-related. The extracted TAT current densities correspond to total leakage currents of roughly 10 pA to tens of nA for a gate area $_5$7, matching the order of the observed current evolution, and the same two-regime picture survives sensitivity analysis of trap density, capture cross section, and trap energy (Ma et al., 11 Jan 2026).

The TFET literature places the same physics in a room-temperature device context. In top-gate, double-gate, and gate-all-around tunnel FETs, traps positioned in the source–channel tunneling region provide an intermediate path that precedes direct band-to-band tunneling. Within a modified Shockley–Read–Hall description, the field-enhancement factor $_5$8 can reach about $_5$9 for typical TFET fields of $d$0, so phonon-assisted interface TAT dominates the leakage before BTBT turns on and obscures the steep turn-on at room temperature for common trap densities. The same study argues that, unless BTBT can be increased separately, the interface trap density $d$1 must be reduced by roughly 40–100 times compared with the state of the art for the steep turn-on of III–V TFETs to become clearly observable at room temperature; it further identifies the combination of the intrinsic Urbach tail and the surface trap density as the determinant of subthreshold swing (Sajjad et al., 2016).

3. Localized resonances in STM and spectroscopic line shapes

A clean realization of localized-state-assisted tunneling is provided by STM on single Au adatoms on double-layer WSe$d$2 grown on epitaxial graphene. The transport geometry is a natural double barrier, tip–vacuum–Au state–WSe$d$3–graphene, and the Au adatom creates a localized in-gap state mainly derived from the unpaired Au $d$4 orbital hybridized with surrounding TMD orbitals. Its energy lies inside the $d$5 band gap near the Fermi level, but varies from adatom to adatom because of disorder potential; a survey over 88 individual adatoms gives a distribution centered at $d$6 with $d$7. The junction is strongly asymmetric, with $d$8 and hence $d$9. Around the resonance $_2$0, the conductance shows equally spaced vibrational sidebands with spacing $_2$1, corresponding to $_2$2 after voltage-division correction, and Poisson-distributed intensities with Huang–Rhys factor $_2$3. The mechanistic picture is therefore not just resonant tunneling through a surface-localized state, but vibration-assisted resonant double-barrier tunneling through an adatom-induced in-gap state (Kumar et al., 16 Apr 2025).

The theoretical impurity-on-semiconductor-surface model clarifies how such localized assisting states alter STM observables even without vibrational structure. It couples a semiconductor continuum to a tip continuum through two simultaneous pathways: a direct channel and a resonant channel via a localized surface/impurity state. The local $_2$4 contains both $_2$5 and $_2$6, weighted by tunneling rates and modulated by $_2$7, so the conductance depends not only on energy but also on lateral position. For shallow impurities, a self-consistent mean-field treatment shifts the effective level to $_2$8; for deep impurities, the Hubbard-I approximation produces an additional feature near $_2$9. The result is a family of peak, dip, and asymmetric line shapes that evolve over distances comparable to the lattice period and are strongly modified by on-site Coulomb interaction (Mantsevich et al., 2010).

These two cases establish a general point. A surface-localized assisting state need not merely add a resonance to the local density of states. It can define the voltage-division physics of a double-barrier junction, produce charging peaks and vibronic sidebands, or act as one arm of an interference problem in which the measured conductance is a coherent superposition of direct and resonant channels (Kumar et al., 16 Apr 2025, Mantsevich et al., 2010).

4. Intrinsic surface bands, interference, and junction-field renormalization

Canonical intrinsic surface bands remain an important limiting case. On La(0001), tunneling spectroscopy resolves an unoccupied Tamm-type surface state of $E_F$0-band origin at $E_F$1 above $E_F$2 in the low-current limit. Varying the tunneling current from 0.1 nA to 8000 nA at 1.7 K changes the local junction field while the current–distance relation remains exponential over 7.3 Å, so the system stays in the tunneling regime. Under these conditions the resonance shifts by 45.9 meV toward lower energy, corresponding to 43.3% of the initial peak position, and its linewidth broadens with a slope $E_F$3. The state therefore acts as a field-renormalized resonant final state: the surface channel remains the same object spectroscopically, but its energy and lifetime are strongly modified by the tip-vacuum-sample field (Schreyer et al., 2020).

On Au(111), the relevant intrinsic state is the Shockley surface state in the projected bulk gap. In a semi-infinite surface calculation its binding energy at $E_F$4 is about $E_F$5 below the Fermi level and it is mainly of $E_F$6-orbital character. When a tip tunnels into a clean Au(111) surface, this state opens an additional transport channel above its band edge; near the Fermi energy it can contribute more than 30\% of the electron transport. Once the junction becomes more strongly coupled, however, the same surface channel can suppress transmission through destructive quantum interference between bulk and surface-state transport paths, producing a significant and robust transmission drop at the surface-state band edge in both metallic and molecular junctions. Capturing this physics requires a real-space self-energy construction that retains surface-propagating asymptotic states; standard supercell NEGF with periodic in-plane boundary conditions misses that contribution (Li et al., 2021).

Taken together, these systems show that intrinsic surface bands are not passive spectroscopic markers. They can act as additional channels, as field-sensitive resonances, or as interference pathways that reshape transmission. The sign of the effect—enhancement or suppression—is therefore not universal (Schreyer et al., 2020, Li et al., 2021).

5. Superconducting and topological boundary channels

In superconductors, surface-state-assisted tunneling appears most clearly through impurity-induced and topological bound states inside the gap. For a Pb-coated superconducting tip tunneling into a Pb(111) substrate with a Mn adatom, the assisting state is a localized Yu–Shiba–Rusinov state at energy $E_F$7. With weak tip coupling, the dominant current is single-electron tunneling into the Shiba state, followed by relaxation between the bound state and the quasiparticle continuum; with stronger coupling, resonant Andreev reflection through the same state dominates. The main thresholds occur at $E_F$8, while thermal peaks appear at $E_F$9. This system demonstrates that a localized surface or near-surface subgap state can mediate both sequential single-particle transport and coherent two-electron transfer, with the crossover determined by the competition between tunnel rates and relaxation rates (Ruby et al., 2015).

Microwave irradiation exposes the same distinction at the level of photon-assisted sidebands. For a superconducting STM junction irradiated at $_3$0, the generalized Tien–Gordon form

$_3$1

describes single-electron tunneling and ordinary $_3$2 processes into the bare substrate, but it breaks down for tunneling via YSR states in the resonant Andreev regime. For a YSR state at $_3$3, low-conductance data follow sequential single-electron sideband splitting, whereas high-conductance data exhibit a Y-shaped microwave map because the electron and hole tunneling components are dressed separately. The dominant sideband spacing remains $_3$4, even though the underlying transport is Andreev-mediated two-electron transfer (Peters et al., 2020).

Topological superconductors provide a more delocalized version of the same idea. In superconducting topological insulators, odd-parity pairing supports surface Andreev bound states realized as helical Majorana fermions. Their dispersion undergoes a structural transition—cone $_3$5 caldera in the full-gap case and ridge $_3$6 valley in the nodal case—controlled by the chemical potential and the effective mass parameter $_3$7. Near these transitions the surface spectral weight accumulates near zero energy, and normal-metal/STI junctions develop robust zero-bias conductance peaks. The low-bias conductance is therefore not set by a generic 3D topological-superconductor surface cone alone, but by a surface-state reconstruction tied to the topological-insulator parent band structure (Yamakage et al., 2011).

A non-superconducting topological analog appears in Na$_3$8Bi thin films. Confinement opens a bulk subband gap of roughly 63–79 meV, but Fermi-arc-derived surface states remain inside that gap. In a gated three-segment thin-film device, those arc states allow finite transmission even when ordinary propagating bulk states are absent in the central segment. The finite in-gap transmission is smaller than bulk-to-bulk transmission because of poor spatial overlap between bulk source states and central surface states, but it is distinctly nonzero and absent from single-Weyl-node models that omit both intervalley scattering and Fermi arcs (Siu et al., 2016).

6. Reconstructed surfaces, terrace edges, and material engineering

Surface-state-assisted tunneling can also emerge from self-consistent reconstruction of the surface electronic structure. In ultrathin BaTiO$_3$9/SrRuO$_{0.2}$0/SrTiO$_{0.2}$1(001) heterostructures, conductive AFM reveals highly conductive stripe-like regions near one-unit-cell terrace edges. For 3 u.c. BTO, the ratio $_{0.2}$2 reaches about 3.0, and spatially resolved $_{0.2}$3–$_{0.2}$4 maps define a terrace-edge region on the upper terrace roughly 40 nm wide. The current remains tunneling-like rather than ohmic, and transport fits are explained by a reduced effective tunnel-barrier width: in the terrace-plateau region $_{0.2}$5 nm and $_{0.2}$6 eV, whereas at the terrace edge $_{0.2}$7 nm and $_{0.2}$8 eV. First-principles analysis attributes this to terrace-edge-induced electronic reconstruction on a TiO$_{0.2}$9-terminated surface, with electron-rich Ti $_{0.8}$0 states near $_{0.8}$1 and partial metallization of the top surface layer. Termination control in ultrathin STO supports the same conclusion: the effect is present for TiO$_{0.8}$2-terminated STO and strongly suppressed for SrO-terminated STO (Wang et al., 2017).

A conceptually related but electronically distinct case is the Co-terminated surface of CeCoIn$_{0.8}$3(001). At $_{0.8}$4 mV, increasing the set current from 1 nA to 30 nA and then 100 nA transforms round Co protrusions into dumbbells that alternate along [100] and [010]. Slab GGA+$_{0.8}$5 calculations attribute the pattern to a surface-enhanced staggered $_{0.8}$6-$_{0.8}$7 orbital order triggered by reduced screening and enhanced on-site Coulomb interaction at the surface. Bulk Co shows little spin polarization, $_{0.8}$8, whereas surface Co reaches $_{0.8}$9; the $_x$0 orbital becomes almost fully occupied while the $_x$1 orbital is half-filled, with the pattern reversed on neighboring Co sites. The tunneling lesson is that short-distance STM can become selectively sensitive to anisotropic surface-reconstructed $_x$2-orbital tails, so the topography encodes orbital order rather than merely atomic positions (Kim et al., 2017).

Across these reconstructed systems, the assisting state is neither a pre-existing trap nor a simple bulk continuation. It is created or strongly reshaped by the surface itself. A plausible implication is that surface-state-assisted tunneling should often be interpreted together with surface termination, crystalline quality, local coordination, and matrix-element selectivity rather than only with the existence of a nominal surface band.

The literature also makes clear that microscopic assignment is often model-dependent. In Ge/SiGe, the interface charge is reconstructed by an inverse Schrödinger–Poisson procedure and the TAT current uses phenomenological trap distributions and WKB coefficients; the argument for TAT-assisted filling is strong, but the participating defect species are not uniquely identified (Ma et al., 11 Jan 2026). In Au(111) transport, conventional periodic in-plane NEGF can miss nonperiodic surface channels entirely, so the apparent absence of surface-state assistance may reflect the embedding scheme rather than the material (Li et al., 2021). Surface-state-assisted tunneling is therefore best treated as a transport category defined by the active participation of surface or interface electronic structure, not as a single universal mechanism.