Strain Response as a Probe of Spinons in Quantum Spin Liquids

Abstract

Quantum spin liquids (QSLs) host emergent, fractionalized fermionic excitations that are charge-neutral. Identifying clear experimental signatures of these excitations remains a central challenge in the field of strongly correlated systems, as they do not couple to conventional electromagnetic probes. Here, we propose lattice strain as a powerful and tunable probe: Mechanical deformation of the lattice generates large pseudomagnetic fields, inducing pseudo-Landau levels that serve as distinctive spectroscopic signatures of these excitations. Using the Kitaev model on the honeycomb lattice, we show that distinct QSL phases exhibit strikingly different strain responses. The semimetallic Kitaev spin liquid and the gapped chiral spin liquid display pronounced Landau quantization and a diamagnetic-like response to strain, whereas the Majorana metal phase shows a paramagnetic-like response without forming Landau levels. These contrasting behaviors provide a direct route to experimentally identifying and distinguishing QSL phases hosting fractionalized excitations. We further outline how local resonant ultrasound spectroscopy can detect the strain-induced resonances associated with these responses, offering a practical pathway towards identifying fractionalized excitations in candidate materials.

Figures (5)

• Figure 1: (a) Phase diagram of the antiferromagnetic Kitaev honeycomb model under an external magnetic field [see Eq.\ref{['eq:H']}] and the strain responses of the three quantum spin liquid phase. KSL denotes the Kitaev spin liquid at the exactly solvable limit $h=0$, while CSL denotes the chiral spin liquid phase at small $h$. LRUS denotes local resonant ultrasound spectroscopy. (b) Strain configuration described by Eq.\ref{['eq:strain']} and strain induced pseudomagnetic field. Black dots and circles represent the unstrained lattice, while gray ones show the deformed positions after applying strain. The strain induces opposite pseudomagnetic field at $K$ and $K'$.
• Figure 2: Majorana hoppings on the honeycomb lattice depicted in Eq. \ref{['eq:tbH']}.
• Figure 3: Local density of states (LDOS) for region $\mathcal{R}$, defined as the central hexagon, in the (a) Kitaev spin liquid (KSL), (b) chiral spin liquid (CSL), and (c) Majorana metal phases. Red lines correspond to strained systems with $\beta \mathcal{S} = 0.4$, while black lines represent unstrained systems ($\beta \mathcal{S} = 0$). Insets show the LDOS difference between strained and unstrained systems. In the Majorana metal phase, we use $\lambda = 0.15 J_{0}$, disorder is introduced by flipping the sign of each bond with probability 0.2. The results are averaged over 100 samples. In all calculations we use $J_{0}=1$ and lattice with $60\times 60$ unit cells. (d) Momentum-resolved Majorana spectral function at zero energy ($E = 0$) and the dispersion near the $K$ point.
• Figure 4: Local strain susceptibility for region $\mathcal{R}$, defined as the central hexagon, in the (a) KSL and (b) CSL phases. Circles represent numerically data, solid line represents fittings of the data according to Eq. \ref{['eq:suscsl']}. In both calculations we use $J_{0}=1$ and lattice with $60\times 60$ unit cells. (c) Strain susceptibility of a system with $4\times 2$ unit cells calculated from the spin model with and without the flux penalty and the Majorana-hopping model, respectively. (d) Strain susceptibility of a system with $4\times 2$ unit cells calculated from the spin model with $h=0.6$, which is in the Majorana metal phase.
• Figure 5: Schematic of a LRUS measurement using focused surface acoustic waves. A focused surface acoustic wave beam is launched from the left transducer, directed through a strained graphene region on a surface acoustic wave-supporting substrate, and detected by the right transducer. Inter–pseudo-Landau-level excitations induced by strain lead to resonant absorption, visible as pronounced features in the transmitted surface acoustic wave attenuation.