Evidence for the Fulde–Ferrell–Larkin–Ovchinnikov state in bulk NbS2

Abstract

We present measurements of the magnetic torque, specific heat and thermal expansion of the bulk transition metal dichalcogenide (TMD) superconductor NbS2 in high magnetic fields, with its layer structure aligned strictly parallel to the field using a piezo rotary positioner. The upper critical field of superconducting TMDs in the 2D form is known to be dramatically enhanced by a special form of Ising spin orbit coupling. This Ising superconductivity is very robust to the Pauli paramagnetic effect and can therefore exist beyond the Pauli limit for superconductivity. We find that superconductivity beyond the Pauli limit still exists in bulk single crystals of NbS2 for a precisely parallel field alignment. However, the comparison of our upper critical field transition line with numerical simulations rather points to the development of a Fulde-Ferrell-Larkin-Ovchinnikov state above the Pauli limit as a cause. This is also consistent with the observation of a magnetic field driven phase transition in the thermodynamic quantities within the superconducting state near the Pauli limit.

Probing the interlayer coupling in 2$H$-NbS$_2$ via soft x-ray angle-resolved photoemission spectroscopy

“…At 2 K, the ratio H c2, /H c2,⊥ ≈ 6.3 is similar to reported values of 7.5-8 for NbS 2 and larger than reported values of 2.3-3.2 for NbSe 2 [31]. H c2, also exceeds the Pauli limit of 1.84 T c , as previously reported and discussed [26].…”

“…Theoretical studies point to NbS 2 hosting stronger many-body effects than NbSe 2 , including competing Coulomb and electron-phonon interactions, and lying on the verge of instability to charge or even spin ordering [19][20][21][22][23][24][25]. Most surprisingly, when a magnetic field is carefully aligned parallel to the NbS 2 layers, the upper critical field shows an upturn above the Pauli limit, reminiscent of the Fulde-Ferrell-Larkin-Ovchinnikov state with finite-momentum Cooper pairs [26]. However, Ising spin-orbit coupling in TMDC monolayers may provide an alternative means for the system to exceed the Pauli limit, and one deciding factor is the dimensionality of bulk NbS 2 ; i.e., how strong the individual layers are coupled.…”

Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

“…As we argue below, anisotropic kinetic terms allow for stabilizing the FFLO phases. This conclusion actually seems in line with experimental findings, since the most convincing evidence for FFLO-like features was reported for highly anisotropic situations both in the solid state [29][30][31][32][33] and ultracold gases contexts. We therefore do not restrict to any specific form of the dispersion.…”

Competition between orbital effects, Pauli limiting, and Fulde–Ferrell–Larkin–Ovchinnikov states in 2D transition metal dichalcogenide superconductors

“…Capacitance was measured using a General Radio 1615-A capacitance bridge and a SR830 digital lock-in amplifier. Note that even with parallel alignment, τ usually does not completely vanish because of quadrupole moments [7,16,17]. All data present the magnitude τ of the torque.…”

“…We recently reported the observation of an FFLO state in 2H-NbS 2 bulk samples when we applied the magnetic field exactly parallel to its layer structure with an accuracy of one millidegree using a piezo rotary stage in combination with magnetic torque, specific heat and thermal expansion experiments [17]. In this article, we report magnetic torque measurements for 2H-NbSe 2 for precisely parallel alignment of the magnetic field with respect to the layer structure and compare the magnetic field phase diagram with the one of 2H-NbS 2 .…”