Antisymmetric transport coefficients of magnetic monopoles in quantum spin ice under an electric field

Unambiguously detecting magnetic monopoles in classical or quantum spin ice has been an intriguing issue. Of our interest is the bosonic U(1) quantum spin liquid phase of quantum spin ice, which accomodates emergent magnetic monopoles as fractionalized quasiparticles and hosts deconfined emergent U(1) gauge fields. It has recently been recognized that the emergent electric gauge flux in this quantum spin liquid can be generated by a real electric field and electric polarization [1,2]. Here, solving the Harper equation [3] for a prototypical quantum spin ice, we show that magnetic monopoles can form Landau levels under an electric field, bending the orbital motion of magnetic monopoles and thus producing antisymmetric transport coeffiients in response to the temperature gradient and the magnetic field gradient [4]. Possible experimental setups are also discussed.
[1] E. Lantagne-Hurtubise, S. Bhattacharjee, and R. Moessner, Phys. Rev. B 96, 125145 (2017).
[2] S. Nakosai and S. Onoda, arXiv:1801.03117.
[3] P. G. Harper, Proc. Phys. Soc. Lond. A68, 874 (1955); D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
[4] S. Onoda, unpublished.