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We present the theoretical results for the Majorana band structure andthermal transport properties in the Kitaev honeycomb model under a staggeredmagnetic field in addition to a uniform one. The Majorana band structure isasymmetrically modulated in momentum space, and the valley degree of freedom isactivated and controlled by the magnitudes and directions of the uniform andstaggered magnetic fields; as a result, the Majorana excitation is eithergapped or gapless, the latter of which in general has Majorana Fermi surfaces,in contrast to the point nodes in the absence of the fields. We show that theasymmetric deformation of the Majorana band induces a nonlinear (nonreciprocal)thermal transport, in addition to the linear one. The field dependence of thelinear thermal current is correlated with the magnitude of the Majorana gap,while that of the nonlinear thermal current is associated with the asymmetry ofthe Majorana excitation spectra. We show the estimates of the thermal currentsand discuss that the linear response is experimentally measurable, whereasfuture improvement is required for the observation of the nonlinear one. Wealso discuss how the thermal currents are modulated by other additional effectsof the magnetic field and contributions from conventional magnons, latter ofwhich are expected in heterostructures to realize an internal staggeredmagnetic field.

Asymmetric modulation of Majorana excitation spectra and nonreciprocal thermal transport in the Kitaev spin liquid under a staggered magnetic field