Negative Vicinity Resistance

Updated 17 September 2025

Negative vicinity resistance is defined as the occurrence of local voltage or effective resistance reversal near a current injection point, challenging conventional Ohmic behavior.
It arises from diverse mechanisms such as electron hydrodynamics, ballistic transport, edge-state mixing, and nonlinear tunneling phenomena in nanoscale devices.
This effect offers practical insights for designing low-dissipation devices, THz oscillators, and quantum electronics by exploiting nonlocal feedback mechanisms.

Negative vicinity resistance refers to the phenomenon where, in a specific nonlocal electronic or thermal measurement geometry, the measured voltage or effective resistance near a current injection point or within a local region of a device becomes negative—i.e., a reversal of the expected sign relating local potential (or temperature) gradient to the current direction. This concept arises in several contexts, such as hydrodynamic electronic transport, ballistic systems, molecular devices, Josephson junctions, nanostructured materials, and engineered thermal systems. While mechanisms differ, all realizations share the defining feature that the local (vicinity) response runs counter to naive expectations from Ohm’s law, Fourier’s law, or basic tunneling models.

1. Definition and Experimental Manifestations

Negative vicinity resistance is most precisely characterized by a negative measured voltage at a probe close to a current injector in geometries where homogeneous dissipative or diffusive transport predicts a positive voltage drop. The resistance is often operationally defined as

$R_v = \frac{V_{\text{probe}}}{I_{\text{inj}}}$

where $V_{\text{probe}}$ is the local voltage and $I_{\text{inj}}$ is the injected current. Negative $R_v$ indicates that the local potential increases in the direction of net current flow.

Manifestations include:

Negative local (vicinity) resistance in proximity to current injectors in high-quality graphene Hall bars (Bandurin et al., 2015), GaAs quantum wells (Levin et al., 2018), and ballistic graphene nanostructures (Wang et al., 2019).
Negative contact resistance extracted via transmission line models in Dirac-cone systems (Nouchi et al., 2012).
Negative differential resistance in I–V characteristics of molecular junctions or Josephson junctions, often associated with regions where increased bias voltage leads to reduced current (Dzhioev et al., 2011, Dubi, 2013, Filatrella et al., 2014, Pedersen et al., 2023, Nath et al., 2019).
Negative longitudinal resistance in quantum Hall transport due to edge-state intersections mediated by local disorder (Kaverzin et al., 9 May 2024).

2. Physical Mechanisms

The emergence of negative vicinity resistance arises through diverse but well-defined microscopic mechanisms:

Electron Hydrodynamics

In the hydrodynamic regime, strong electron–electron (ee) collisions enable local equilibrium and collective flow. When a current is injected through a narrow contact, viscous forces can produce whirlpools or vortices in the electron flow (Bandurin et al., 2015, Levin et al., 2018). This produces backflow regions where the current locally circulates against the main direction, causing local potential reversals. The negative resistance is intrinsic to the hydrodynamic (viscous-dominated) regime and is enhanced as electron viscosity (e.g., $v \sim 0.1\,{\rm m^2/s}$ for graphene) increases or as the geometry sharpens velocity gradients.

Ballistic and Boundary Effects

In the ballistic regime $d \ll l_{ee}$ , where $d$ is the probe distance and $l_{ee}$ the ee mean free path, negative vicinity resistance arises from long electron trajectories and backscattering events (Shytov et al., 2018). Collisions “remove” background electrons that would otherwise reach the probe, resulting in a negative local voltage. The effect is log-enhanced due to the broad phase space for long ballistic excursions:

$V(d) \sim - J_0 \gamma_{ee} \ln(l_{ee}/d),$

where $J_0$ is the injected current and $\gamma_{ee}$ the collision rate (Shytov et al., 2018).

Boundary-induced vortex formation, even without significant interactions, generates a negative voltage via the creation of ballistic current loops between voltage probes, as evidenced by local-current flow maps from non-equilibrium Green’s function calculations in ballistic graphene (Wang et al., 2019). The presence (or suppression) of such vortices can be tuned by Rashba spin-orbit coupling in these devices.

Contact and Structural Effects

Strong metal-induced doping near contacts can create a local region where the effective resistivity becomes so low that the extrapolated contact resistance appears negative (Nouchi et al., 2012). In highly anisotropic or multiply connected conductor networks, current can reroute such that, depending on probe geometry, the measured voltage drop runs counter to the current (G et al., 2023).

Quantum Hall/Landauer–Büttiker Edge-State Mixing

In quantum Hall systems, edge channels typically carry current unidirectionally. Local impurity-induced intersections or enhanced doping domains can enable coupling of counter-propagating edge states on a single edge of a Hall bar. Such mixing inverts the local potential drop, resulting in negative longitudinal resistance (Kaverzin et al., 9 May 2024). The critical criterion is that transmission probabilities between contacts become re-ordered by impurity-mediated shortcuts, so that in Landauer–Büttiker formalism, the numerator in

$R_{41,56} = \frac{h}{e^2} \frac{T_{54} T_{61} - T_{51} T_{64}}{D}$

can become negative.

Nonlinear and Resonant Tunneling Mechanisms

Negative differential resistance—regions where $dI/dV < 0$ —are prevalent in molecular junctions and Josephson devices. Mechanisms include:

Solvent-induced mean-field shifts and multistability (Dzhioev et al., 2011).
Coulomb interaction–induced nonlinearities and bias-dependent molecule–electrode coupling (Dubi, 2013).
Conformational switching or mechanical motion in nanoelectromechanical systems (Sadeghi et al., 2016).
Nonlinear quasiparticle dissipation in Josephson junctions, especially under cavity coupling or external load (Filatrella et al., 2014, Pedersen et al., 2023).
Localized heating and core–shell conduction in oxides modulated by Schottky barrier asymmetry (Nath et al., 2019).

3. Mathematical Formulation and Diagnostic Criteria

Several analytical and computational formalisms capture the onset and character of negative vicinity resistance:

System/Effect	Key Equations	Diagnostic Signatures
Hydrodynamic regime (graphene, GaAs)	$\nabla \cdot J = 0$ , $\sigma_0\nabla\phi + D_v^2 \nabla^2 J - J = 0$	$R_v < 0$ near injector; negative nonlocal voltage
Ballistic regime	$V(d) \sim -J_0 \gamma_{ee} \ln(l_{ee}/d)$	Log-enhanced negative response
Landauer–Büttiker (quantum Hall)	$R_{41,56} = (h/e^2)(T_{54}T_{61} - T_{51}T_{64})/D$	Negative $r_{xx}$ in four-terminal geometry
Molecular NDR	$J = (4/\pi)\int d\omega \Gamma_L\Gamma_R [f_L - f_R]/[(\omega-\epsilon-2\Lambda)^2 + \Gamma^2]$	Current drops with increasing $V$

In molecular or resonant tunneling devices, a key requirement is the existence of a controllable parameter (dielectric constant, bias, impurity configuration) that can tune the system into a nonlinear response region where the feedback between local occupation (or state density) and the transmission probability drives the effective resistance negative, often accompanied by hysteresis and multiple steady states.

4. Experimental Realizations and Applications

Negative vicinity resistance has been experimentally observed in various platforms:

Graphene Hall bars and GaAs quantum wells with high mobility, using multiterminal “vicinity” geometries (Bandurin et al., 2015, Levin et al., 2018).
Ballistic graphene systems, employing H-shaped devices to probe vortex-induced negative $R_{NL}$ (Wang et al., 2019).
Dirac-cone systems like graphene FETs, where contact resistance extracted via transmission line model can be negative due to metal-induced local doping (Nouchi et al., 2012).
Mesoscopic devices in the quantum Hall regime, with tailored disorder to reveal edge-state crossings and negative longitudinal resistance (Kaverzin et al., 9 May 2024).
Josephson junctions (BSCCO stacks) and NEMS, where NDR regions are associated with transition points for high-power THz emission or conformational switching (Filatrella et al., 2014, Pedersen et al., 2023, Sadeghi et al., 2016).
Polycrystalline, nanostructured hybrids such as Ni–TiO₂, exhibiting negative resistance due to anisotropic current routing (G et al., 2023).

Applications include the engineering of low-dissipation or high-gain device elements, THz oscillators, memory and logic devices exploiting NDR for switching, and sensitive probes for diagnosing hydrodynamic or quantum-coherent transport regimes.

5. Implications for Device Design and Theoretical Interpretation

Negative vicinity resistance serves as both a diagnostic and control tool:

Its presence, while suggestive of hydrodynamic or ballistic effects, is not a unique signature; careful analysis of temperature, density, and scaling dependencies is required to attribute the origin to either viscous or ballistic mechanisms (Shytov et al., 2018, Bandurin et al., 2015, Levin et al., 2018).
In hybrid or anisotropic systems, standard interpretations of four-probe resistance become ambiguous; detailed modeling using full conductivity tensors or network analysis is necessary (G et al., 2023).
For molecular electronics, NDR features can be tuned by solvent polarity, contact geometry, Coulomb interactions, or bias, offering routes to custom-tailored device behaviors (Dzhioev et al., 2011, Dubi, 2013).
In quantum Hall systems, the sensitivity of negative resistance to local disorder furnishes a potent method for probing edge-state topology, impurity effects, and local doping fluctuations (Kaverzin et al., 9 May 2024).

The interplay between nonlocal transport, nonlinear feedback, and device geometry implies that negative vicinity resistance is a system-agnostic phenomenon requiring precise experimental control and rigorous theoretical analysis for correct interpretation.

Negative vicinity resistance shares conceptual and formal links with:

Negative differential thermal resistance (NDTR), where engineered interfaces in heterojunctions can yield a decrease in thermal flux with rising temperature difference, oppositely signed to the expected behavior (Kobayashi, 2023).
Negative magnetoresistance features in systems exhibiting resonance states or interfacial electronic structure effects (Huang et al., 2023).
Circuit theory of negative incremental resistance, where the interplay of active and passive elements in nonlinear networks generates global negative response, leading to oscillatory, bistable, or chaotic behavior (Miranda-Villatoro et al., 2019).

This suggests a broader unifying principle: negative vicinity (or nonlocal) resistance generically arises where local dissipation or nonlocal coupling mechanisms drive feedback such that the system’s response opposes or even reverses the sign expected from the dominant direction of current, voltage, or temperature gradient.

The paper of negative vicinity resistance, in its diverse realizations, continues to illuminate the intricate interplay of geometry, interaction, disorder, and nonlinearity in advanced electronic, spintronic, superconducting, and phononic materials and devices.