Strain-induced quantum oscillation in Kitaev spin liquid with Majorana-Fermi surface

TL;DR

The paper tackles detecting a charge-neutral Majorana-Fermi surface in Kitaev spin liquids by leveraging strain to induce a pseudo-magnetic field that quantizes Majorana fermions. By perturbing the isotropic Kitaev model to generate Majorana-Fermi surfaces near the Dirac points and applying triaxial strain, the authors induce a strain-generated vector potential $\bm{A}_{\mathrm{eff}}$ and a corresponding pseudo-magnetic field $B_{\mathrm{eff}}$, producing discrete pseudo-Landau levels. They demonstrate clear quantum-oscillation signatures in both the density of states and the specific heat, analogous to de Haas-van Alphen physics, and confirm these features through LDOS analyses on hexagonal flakes. In the two-flux sector, they observe bound states between Landau levels, consistent with Kitaev spin-liquid physics, suggesting that Majorana quantum oscillations provide a local and bulk probe of Majorana-Fermi surfaces in Kitaev materials. The work proposes a route to experimentally detect and study charge-neutral Majorana Fermi surfaces via strain engineering and related thermodynamic and local measurements.

Abstract

We theoretically study Landau quantization of itinerant Majorana quasiparticles induced by lattice strain in a Kitaev spin liquid with Majorana Fermi surfaces. We consider the isotropic spin-1/2 Kitaev model on the honeycomb lattice with a perturbation such as a staggered Zeeman field and an electromagnetic field, which generates small Majorana Fermi surfaces near the Dirac points. By introducing triaxial strain, we create an effective vector potential that couples to Majorana fermions and leads to Landau quantization. Our calculations show that the low-energy spectrum forms discrete pseudo-Landau levels of the Majorana Fermi surface. We further demonstrate that the strain-induced effective vector potential gives rise to pronounced quantum oscillations of the density of states and the specific heat at very low temperatures, in close analogy to the de Haas-van Alphen effect for charged electrons in metals. These results indicate that Landau-quantization-driven "Majorana quantum oscillations" can serve as a probe of the charge-neutral Majorana Fermi surface in Kitaev materials.

Figures (8)

• Figure 1: (a) Geometry of the hexagonal flake with zigzag boundaries used in the calculations ($r=4$). The arrows indicate the directions of the applied triaxial strain. (b) Kitaev model in a staggered Zeeman magnetic field in the Majorana representation. Black lines denote nearest-neighbor hoppings. Red (blue) bonds denote next-nearest-neighbor hoppings with $d_{ij}=+1$ ($d_{ij}=-1$), respectively [see Eq. \ref{['eq::majorana_Hamiltonian']}].
• Figure 2: Energy spectrum at $h_{\mathrm{st}}^3=0.05$ in momentum space. (a) The dispersion as a function of the momenta. (b) The Majorana-Fermi surface. The blue region corresponds to a hole-like pocket of Majorana fermions, while the red region does to an electron-like pocket.
• Figure 3: Local density of states (LDOS) $\rho_{i_0}(\varepsilon)$ at the site $i_0$ located near the center of the flake. The flake radius is $r=20$ and the strain strength is $C=0.01$. We have approximated the delta function by a Lorentzian with broadening width 0.005. (a) and (b): results in the flux-free sector for $h_{\mathrm{st}}^3 = 0.0$ and $h_{\mathrm{st}}^3 = 0.03$, respectively. (c) and (d): results in the two-flux sector for $h_{\mathrm{st}}^3=0.0$ and $h_{\mathrm{st}}^3$, respectively. The black dashed lines indicate that the peaks in the two-flux sector are located between the corresponding peaks in the flux-free sector.
• Figure 4: Strain dependence of the normalized DOS $D(C)/D(C=0)$ at zero energy $\varepsilon=0$. The radius is $r=20$. We have approximated the delta function by a Lorentzian with broadening width 0.005. The black dashed line corresponds to $(h_{\mathrm{st}})^3 = 0.0$, while the green, red and purplelines are for $(h_{\mathrm{st}})^3 = 0.01$, $0.03$, and $0.05$, respectively.
• Figure 5: Normalized specific heat $\mathcal{C}_v(C)/\mathcal{C}_v(C=0)$ as a function of strain for a hexagonal flake with radius $r=20$. The black dashed line corresponds to $h_{\mathrm{st}}^3 = 0.0$, while the green, red and purple lines are for $h_{\mathrm{st}}^3 = 0.01$, $0.03$, and $0.05$, respectively.