在過去的二十年里，單原子層的生長和剝離技術取得了突破性進展，為科學發現和技術創新開辟了新時代。繼石墨烯之后，過渡金屬二硫屬化物（TMDs）受到了廣泛關注，成為眾多新穎量子現象的寶庫。近年來，一種名為Ising超導性的現象在NbSe₂等材料中被觀察到，這種現象主要由自旋-軌道耦合和中心反演對稱性破缺驅動。

Fig. 1 Electron–phonon interaction and intra/inter-pocket Eliashberg spectral function.?

Ising超導體與其他層狀材料（如拓撲材料、單層TMDs和二維磁性層狀材料）之間的鄰近效應和界面效應有望被應用在量子信息存儲和自旋電子學等器件上。最近，關于這類材料，除了占主導地位的電聲耦合（EPC）之外，人們還關注了自旋漲落（SF）在Ising超導現象中可能發揮的作用，討論了三重態占主導的可能性，并引出了一個關于單重態-三重態Leggett振蕩的猜想。然而，這些假設尚未經過定量檢驗。

Fig. 2 Superconducting gap without and with spin-fluctuation?interaction.

來自美國弗吉尼亞州喬治梅森大學物理與天文學系的S. Das等，基于第一性原理計算，針對Ising超導體NbSe₂進行了詳細研究，探討了EPC和SF的作用。作者發現：(1)EPC具有強烈的各向異性，主要來自于K-K’散射，因此排除了三重態對稱性作為激發態的可能性；(2)超導性由SF顯著削弱，但各向異性保持不變；(3)作者發現了Leggett模式的可能性，不是在單重態-三重態之間，而是在s₊₊– s_±通道中。

Fig. 3 Schematic illustration of the Ising superconductor pairing?symmetry.

作者通過對電聲耦合和自旋漲落貢獻的自洽分析，估計了平均的BCS能隙ΔBCS、Leggett模式頻率Ω_L、以及Ω_L/2ΔBCS，與實驗結果比較接近。本研究為理解NbSe₂及其他Ising超導體的超導現象提供了較為全面的定量分析，為今后的實驗和理論研究提供了有力支持。相關論文近期發布于npj?Computational Materials9:?66?(2023)。

Fig. 4 Analytical solution of the two-gap BCS equations.

Editorial Summary

Unraveling the Ising Superconductivity in NbSe₂: Electron-Phonon Coupling and Spin Fluctuations

Revolutionary progress in the growth and exfoliation of single atomic layers over the last two decades has led to a new era of scientific discoveries and technological innovation. Following graphene, transition metal dichalcogenides (TMDs) have taken the spotlight, as a treasure trove for a plethora of novel quantum phenomena. In recent years, a phenomenon called Ising superconductivity has been observed in materials such as NbSe₂, driven primarily by spin-orbit coupling and the absence of inversion symmetry. The proximity and interface effects between Ising superconductors and other layered materials, such as topological materials, single-layer TMDs, and two-dimensional magnetic layered materials, could lead to interesting device applications for quantum information storage and spintronics. Recently, attention was called to the possible role that spin fluctuations (SF) play in this phenomenon, in addition to the dominant electron–phonon coupling (EPC); the possibility of a predominantly triplet state was discussed and led to a conjecture of viable singlet–triplet Leggett oscillations. However, these hypotheses have not been put to a quantitative test.?

S. Das et al. from the Department of Physics and Astronomy, George Mason University, USA, conducted an in-depth study on the Ising superconductor NbSe₂, and explored the roles of EPC and SF based on first-principles calculations. The authors found that: (1) EPC is strongly anisotropic, largely coming from the K?K’ scattering, and therefore excludes triplet symmetry even as an excited state; (2) superconductivity is substantially weakened by SF, but anisotropy remains as above; and, (3) the possibility of a Leggett mode was found, not in a singlet–triplet but in an s++ – s± channel. Based on the self-consistent analytical solution and first-principles calculations including electron–phonon coupling and spin-fluctuation contribution, the authors estimated the average BCS gap ΔBCS, Leggett mode frequency Ω_L, and the ratio Ω_L/2ΔBCS, showing good agreement with experimental results. This study provides a fairly comprehensive quantitative analysis for understanding the superconductivity in NbSe₂ and other Ising superconductors, offering valuable insights for future experimental and theoretical research.Thisarticle was recently?published in?npj?Computational Materials?9:?66?(2023).

原文Abstract及其翻譯

Electron-phonon coupling and spin fluctuations in the Ising superconductor NbSe₂ (Ising超導體NbSe₂中的電聲耦合與自旋漲落)

S. Das, H. Paudyal, E. R. Margine, D. F. Agterberg & I. I. Mazin

Abstract

Ising superconductivity, observed in NbSe₂ and similar materials, has generated tremendous interest. Recently, attention was called to the possible role that spin fluctuations (SF) play in this phenomenon, in addition to the dominant electron–phonon coupling (EPC); the possibility of a predominantly triplet state was discussed and led to a conjecture of viable singlet–triplet Leggett oscillations. However, these hypotheses have not been put to a quantitative test. In this paper, we report first principle calculations of the EPC and also estimate coupling with SF, including full momentum dependence. We find that: (1) EPC is strongly anisotropic, largely coming from the K?K′? scattering, and therefore excludes triplet symmetry even as an excited state; (2) superconductivity is substantially weakened by SF, but anisotropy remains as above; and, (3) we do find the possibility of a Leggett mode, not in a singlet–triplet but in an s₊₊ – s_±channel.

摘要

在NbSe₂和類似材料中觀察到的Ising超導性引起了極大的關注。最近，除了占主導地位的電聲耦合（EPC）之外，人們還關注了自旋漲落（SF）在這一現象中可能發揮的作用，討論了三重態占主導的可能性，并引出了一個關于單重態-三重態Leggett振蕩的猜想。然而，這些假設尚未經過定量檢驗。在本文中，我們報道了電聲耦合的第一性原理計算，還估算了與自旋漲落的耦合，包括完全動量依賴性。我們發現：(1) EPC呈強烈的各向異性，主要來自于K-K’散射，因此，即使作為激發態，也排除了三重態對稱性；(2)超導性受到自旋漲落的顯著削弱，但各向異性仍然存在；(3)我們確實發現了Leggett模式的可能性，不是在單重態-三重態之間，而是在s₊₊– s_±通道中。