@article{19852,
  abstract     = {Technology involving hybrid superconductor–semiconductor materials is a promising avenue for engineering quantum devices for information storage, manipulation, and transmission. Proximity-induced superconducting correlations are an essential part of such devices. While the proximity effect in the conduction band of common semiconductors is well understood, its manifestation in confined hole gases, realized for instance in germanium, is an active area of research. Lower-dimensional hole-based systems, particularly in germanium, are emerging as an attractive platform for a variety of solid-state quantum devices, due to their combination of efficient spin and charge control and long coherence times. The recent experimental realization of the proximity effect in germanium thus calls for a theoretical description that is tailored to hole gases. In this work, we propose a simple model to describe proximity-induced superconductivity in two-dimensional hole gases, incorporating both the heavy-hole (HH) and light-hole (LH) bands. We start from the Luttinger–Kohn model, introduce three parameters that characterize hopping across the superconductor–semiconductor interface, and derive explicit intraband and interband effective pairing terms for the HH and LH bands. Unlike previous approaches, our theory provides a quantitative relationship between induced pairings and interface properties. Restricting our general model to an experimentally relevant case where only the HH band crosses the chemical potential, we predict the coexistence of 𝑠-wave and 𝑑-wave singlet pairings, along with triplet-type pairings, and modified Zeeman and Rashba spin–orbit couplings. Our results thus present a starting point for theoretical modeling of quantum devices based on proximitized hole gases, fueling further progress in quantum technology.},
  author       = {Babkin, Serafim and Joecker, Benjamin and Flensberg, Karsten and Serbyn, Maksym and Danon, Jeroen},
  issn         = {2469-9969},
  journal      = {Physical Review B},
  number       = {21},
  publisher    = {American Physical Society},
  title        = {{Superconducting proximity effect in two-dimensional hole gases}},
  doi          = {10.1103/k4jh-pnxy},
  volume       = {111},
  year         = {2025},
}

@article{15367,
  abstract     = {Two-dimensional semiconductor-superconductor heterostructures form the foundation of numerous nanoscale physical systems. However, measuring the properties of such heterostructures, and characterizing the semiconductor in-situ is challenging. A recent experimental study by [Phys. Rev. Lett. 128, 107701 (2022)] was able to probe the semiconductor within the heterostructure using microwave measurements of the superfluid density. This work revealed a rapid depletion of superfluid density in semiconductor, caused by the in-plane magnetic field which in presence of spin-orbit coupling creates so-called Bogoliubov Fermi surfaces. The experimental work used a simplified theoretical model that neglected the presence of non-magnetic disorder in the semiconductor, hence describing the data only qualitatively. Motivated by experiments, we introduce a theoretical model describing a disordered semiconductor with strong spin-orbit coupling that is proximitized by a superconductor. Our model provides specific predictions for the density of states and superfluid density. Presence of disorder leads to the emergence of a gapless superconducting phase, that may be viewed as a manifestation of Bogoliubov Fermi surface. When applied to real experimental data, our model showcases excellent quantitative agreement, enabling the extraction of material parameters such as mean free path and mobility, and estimating g-tensor after taking into account the orbital contribution of magnetic field. Our model can be used to probe in-situ parameters of other superconductor-semiconductor heterostructures and can be further extended to give access to transport properties.},
  author       = {Babkin, Serafim and Higginbotham, Andrew P and Serbyn, Maksym},
  issn         = {2542-4653},
  journal      = {SciPost Physics},
  number       = {5},
  publisher    = {SciPost Foundation},
  title        = {{Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field}},
  doi          = {10.21468/scipostphys.16.5.115},
  volume       = {16},
  year         = {2024},
}