Origin of sublattice particle-hole asymmetry in monolayer FeSe superconductors

Abstract

In iron-based superconductors, the two Fe atoms in the unit cell are typically related by crystal symmetries; therefore, we expect no intra-unit cell variations in the superconducting gap. However, recent experiments have challenged this expectation, reporting intra-unit cell variations in the gap with an unusual particle-hole asymmetry. Here, we examine the origin of this asymmetry between the two Fe sublattices in monolayer FeSe grown on SrTiO$_3$. We reveal that, in addition to the substrate-induced broken inversion symmetry, substrate nematic symmetry breaking is key to observing this asymmetry. We further identify two possible mechanisms through which this can occur. The first is through an odd-parity gap function that coexists with an extended $s$-wave function. The second is via a nodeless $d$-wave gap function that develops in the presence of a symmetry-breaking substrate. We argue that the latter mechanism is more physical. To test our theory, we performed scanning tunneling spectroscopy measurements across the nematic domain walls, which exhibit a clear enhancement of the asymmetry between the two Fe sublattices. In addition, we reveal that the observed sublattice particle-hole asymmetry is associated with odd-frequency pairing correlations, providing an experimental realization of this unusual pairing correlation.

Figures (4)

• Figure 1: (a) Sketch of the monolayer FeSe lattice illustrating the center of inversion (denoted by the X mark) and the four-fold rotation about the $z$ axis ($C_{4z}$) through one Se site relating the A and B Fe sublattices. (b) Schematic representation of the normalized DOS as a function of frequency $\omega$ in units of the superconducting gap $\Delta_0$, displaying a difference between the Fe A and Fe B sublattices.
• Figure 2: Two domains of monolayer FeSe grown on STO, inducing different substrate symmetry breakings. The O atoms that are below Fe or Se atoms are illustrated by a dashed circle with a light red interior. (a) The mirror symmetry $m_z$ relating the two Fe sublattices is broken. (b) Only one Fe sublattice is on the Ti atoms and, consequently, both the mirror and four-fold symmetry relating the two Fe sites are broken.
• Figure 3: Map showing the two scenarios that give rise to a sublattice particle-hole asymmetry for the nodeless $d$-wave and extended $s$-wave gap.
• Figure 4: STM/STS of the single-layer FeSe/STO(100) and sublattice resolved DOS from the effective model. (a) Large-scale STM image showing two types of domain boundaries orientated along the [10] and [11] directions (V$_{\rm bias}$ = 3V, I = 10 pA). (b) Atomic resolution image acquired at the boxed area in (a), V$_{\rm bias}$ = 75 mV, I = 100 pA. (c) A series of dI/dV tunneling spectra acquired along the blue arrow in (b) across a [10] domain boundary, V$_{\rm bias}$ = 30 mV, I = 500 pA, V$_{\rm mod}$ = 0.6 mV, tunneling spectra are vertically shifted for clarity. (d) Atomic resolution STM image of the single-layer FeSe/STO(100) (V$_{\rm bias}$ = 30 mV, I = 100 pA), including the ball-stick model showing the top Se lattice (red), four-iron sites and bottom Se (black). (e) dI/dV tunneling spectra acquired at sites indicated in (d), V$_{\rm bias}$ = 30 mV, I = 500 pA, V$_{\rm mod}$ = 0.6 mV, tunneling spectra are vertically shifted for clarity. H and L denote the high and low peaks, respectively. (f) Sublattice-resolved DOS considering the full model including $d_{x^2-y^2}$ and $d_{xz,yz}$ orbitals and the hybridization between them, see the SM Supplementary.