Abstract
We study the origin of Lorentz force on the spinons in a U(1) spin liquid. We are partly inspired by the previous observation of gauge field correlation in the pairwise spin correlation using the neutron scattering measurement by P.A. Lee an N. Nagaosa [PhysRevB 87,064423(2013)] when the Dzyaloshinskii-Moriya interaction intertwines with the lattice geometry. We extend this observation to the Lorentz force that exerts on the (neutral) spinons. The external magnetic field, that polarizes the spins, effectively generates an internal U(1) gauge flux for the spinons and twists the spinon motion through the Dzyaloshinskii-Moriya interaction. Such a mechanism for the emergent Lorentz force differs fundamentally from the induction of the internal U(1) gauge flux in the weak Mott insulating regime from the charge fluctuations. We apply this understanding to the specific case of spinon metals on the kagome lattice. Our suggestion of emergent Lorentz force generation and the resulting topological thermal Hall effect may apply broadly to other non-centrosymmetric spin liquids with Dzyaloshinskii-Moriya interaction. We discuss the relevance with the thermal Hall transport in kagome materials volborthite and kapellasite.
Highlights
Quantum spin liquid (QSL) is an exotic quantum state of matter in which spins are highly entangled quantum mechanically and remain disordered down to zero temperature [1,2,3]
In this Letter, we develop a theory of the topological thermal Hall effect (TTHE) for U(1) QSLs with spinon Fermi surfaces in the strong Mott regime
We have demonstrated that the external magnetic field induces an internal U(1) gauge flux through the combination of Zeeman coupling and Dzyaloshinskii-Moriya interaction for a strong Mott insulator QSL
Summary
In this Supplementary material, following the main text, we adopt the canonical Abrikovsov fermion representation. S3, i.e., sin Φ is onehalf of the solid angle subtended by three spins Si(i = 1, 2, 3), as depicted in Fig. 1 (b) in the main text. In this sense, the fluctuations in the gauge field can be interpreted as fluctuations in the chirality through each plaquette. 〈S4 × S5〉 = λD45 = λD23, where λ is a constant estimated at λ ∼ 1/J It is readily verify there exists a linear coupling between the spin chirality Si · Sj × Sk and Si · Djk. Averaging the total chirality through the two attached up and down triangles, the in-plane component D of the Dzyaloshinskii-Moriya vectors will be canceled out and one can obtain 〈sin Φ〉 = 1/2λDz〈Sz〉. A more formal proof about the above relations can be proceeded within the first order perturbation theory [38]
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