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Quantum Interference Breaks Bias Symmetry at Extended Superconducting Interfaces

Vishal Tripathi, Goutam Sheet

Abstract

Particle-hole symmetry of the Bogoliubov-de~Gennes Hamiltonian is widely assumed to enforce bias-symmetric transport at superconducting interfaces. We show that this expectation fails generically for interfaces with finite spatial extent due to quantum interference. Using a tight-binding scattering formalism that preserves exact particle-hole symmetry, we demonstrate that propagation through an extended interface causes electrons and holes to accumulate unequal phases, leading to intrinsic bias-asymmetric conductance. The interface thereby acts as an effective Andreev interferometer with characteristic damped oscillations arising from coherent multiple reflections within the barrier. While the asymmetry originates from normal-state interference, its bias dependence is governed by the superconducting gap, which emerges as a sharp crossover scale that can be clearly resolved even when conventional coherence peaks are weak or absent. Thus we present bias asymmetry as an interferometric, spectroscopic probe of nonlocal interface physics and superconducting energy scales in hybrid and topological systems where extended interfaces are unavoidable.

Quantum Interference Breaks Bias Symmetry at Extended Superconducting Interfaces

Abstract

Particle-hole symmetry of the Bogoliubov-de~Gennes Hamiltonian is widely assumed to enforce bias-symmetric transport at superconducting interfaces. We show that this expectation fails generically for interfaces with finite spatial extent due to quantum interference. Using a tight-binding scattering formalism that preserves exact particle-hole symmetry, we demonstrate that propagation through an extended interface causes electrons and holes to accumulate unequal phases, leading to intrinsic bias-asymmetric conductance. The interface thereby acts as an effective Andreev interferometer with characteristic damped oscillations arising from coherent multiple reflections within the barrier. While the asymmetry originates from normal-state interference, its bias dependence is governed by the superconducting gap, which emerges as a sharp crossover scale that can be clearly resolved even when conventional coherence peaks are weak or absent. Thus we present bias asymmetry as an interferometric, spectroscopic probe of nonlocal interface physics and superconducting energy scales in hybrid and topological systems where extended interfaces are unavoidable.
Paper Structure (9 equations, 3 figures)

This paper contains 9 equations, 3 figures.

Figures (3)

  • Figure 1: Asymmetry and Interferometry: (a) $G(E)$ vs $E$ normalized at $E=+3\Delta$ for varying $\Delta$. (b) $\mathcal{A}(E)$ extracted from (a) (inset upper: corresponding derivative and inset lower: $\mathcal{A}_E$ vs $\Delta$) (c) $G(E)$ vs $E/\Delta$ for varying $L$ normalized at $E=+3\Delta$. (d) $\mathcal{A}(E)$ extracted from (c) (inset: corresponding derivative). (e) $\mathcal{A}(E)$ for varying $L$. inset: A representative trace at $E = 3\Delta$. (f) $\mathcal{A}_E$ vs $L/\lambda_{\mathrm{osc}}$ showing the characteristic fan-diagram and the triangular phase-space domain corresponding to propagating modes.
  • Figure 2: Barrier-strength evolution: (a) Normalized $G(E)$ vs $E/\Delta$ for varying $Z$ (inset: $\Delta_{\mathrm{fit}}$ vs $Z$). (b) Corresponding asymmetry $\mathcal{A}(E)$.
  • Figure 3: Symmetrization and BTK fitting: (a) Normalized $G(E)$ for different $L$: Symmetrized spectra and BTK fits. (b) Fitted $Z_{\mathrm{fit}}$ vs $L$; inset: $\Delta_{\mathrm{fit}}$ and $\Gamma_{\mathrm{fit}}$ vs $L$.