[Paper Review] Proximity-induced superconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor

Tudor D. Stanescu, S. Das Sarma|arXiv (Cornell University)|Jun 27, 2022

Topological Materials and PhenomenaPhysics and Astronomy61 references19 citations

TL;DR

This paper investigates how disorder in thin superconducting (SC) films affects proximity-induced superconductivity in semiconductor (SM) systems, using a 3D microscopic model and recursive Green's function methods. It finds that SC disorder enhances proximity pairing and suppresses its strong thickness dependence, but simultaneously induces effective disorder in the SM, which critically impacts topological superconductivity and Majorana modes.

ABSTRACT

We investigate the effects of disorder characterising a superconducting thin film on the proximity-induced superconductivity generated by the film (in, e.g., a semiconductor) based on the exact numerical analysis of a three-dimensional microscopic model. To make the problem numerically tractable, we use a recursive Green's function method in combination with a patching approach that exploits the short-range nature of the interface Green's function in the presence of disorder. As a result of the Fermi surface mismatch between the superconductor (SC) and the semiconductor (SM) in combination with the confinement-induced quantization of the transverse SC modes, the proximity effect induced by a clean SC film is typically one to three orders of magnitude smaller that the corresponding quantity for a bulk SC and exhibits huge thickness-dependent variations. The presence of disorder has competing effects: on the one hand it enhances the proximity-induced superconductivity and suppresses its strong thickness dependence, on the other hand it generates proximity-induced effective disorder in the SM. The effect of proximity-induced disorder on the topological superconducting phase and the associated Majorana modes is studied nonperturbatively.

Motivation & Objective

• To understand the impact of disorder within thin superconducting films on proximity-induced superconductivity in adjacent semiconductors.
• To address the long-ignored role of strong disorder in the superconductor, especially surface disorder, which is typically much stronger than semiconductor disorder.
• To investigate how SC disorder competes with Fermi surface mismatch and finite-size quantization in thin films, which otherwise severely suppress proximity effects.
• To nonperturbatively assess the effect of proximity-induced disorder on topological superconductivity and Majorana zero modes.
• To provide a quantitative, numerically exact analysis of the interplay between Fermi surface mismatch, film thickness, and SC disorder in hybrid SC-SM systems.

Proposed method

• Uses a three-dimensional microscopic model to describe the SC-SM hybrid system with realistic parameters.
• Applies a recursive Green's function method to solve the Kitaev-type Hamiltonian numerically.
• Employs a 'patching approach' that exploits the short-range nature of the interface Green's function in disordered systems to make the problem computationally tractable.
• Treats the superconducting film as a finite-thickness system with transverse quantization, capturing the effects of finite-size confinement.
• Models disorder in the SC via a random potential with energy scales of 10–100 meV, significantly exceeding the induced SM gap (~0.1 meV).
• Performs nonperturbative analysis of the proximity-induced superconducting gap and the emergence of Andreev bound states.

Experimental results

Research questions

• RQ1 How does disorder in a thin superconducting film affect the strength and thickness dependence of proximity-induced superconductivity in a semiconductor?
• RQ2 To what extent does SC disorder enhance or suppress the proximity effect compared to a clean superconductor?
• RQ3 How does the combination of Fermi surface mismatch and finite-size quantization in thin SC films limit the proximity effect in clean systems?
• RQ4 What is the nonperturbative effect of proximity-induced disorder on the stability of topological superconductivity and Majorana zero modes?
• RQ5 Can the presence of strong SC disorder explain the observed soft gaps in experimental systems, even when the SM interface is clean?

Key findings

• Disorder in the superconducting film enhances the proximity-induced superconducting gap by up to one to two orders of magnitude compared to the clean case.
• SC disorder suppresses the strong thickness dependence of the proximity effect, which in clean films varies by orders of magnitude with just one atomic layer change.
• The Fermi surface mismatch between the SC (E_F ~ 10 eV) and SM (E_F ~ 10–100 meV) combined with transverse quantization in thin films severely suppresses the proximity effect in clean systems.
• Proximity-induced disorder in the semiconductor, generated by SC disorder, can destabilize topological superconductivity and obscure the signature of Majorana zero modes.
• The induced gap remains soft in the presence of SC disorder, consistent with experimental observations of subgap states and zero-bias conductance peaks.
• Nonperturbative analysis shows that while SC disorder enhances pairing, it also introduces effective disorder in the SM that competes with topological protection, limiting the feasibility of realizing robust Majorana modes.