Kramers Dichroism in PT Symmetric Magnets

TL;DR

The paper shows that in PT-symmetric magnets, circularly polarized light can coherently couple Kramers partner states, generating a Kramers dichroism that reveals a tunable Kramers degree of freedom beyond the ground-state bookkeeping. By formulating a systematic quantum Liouville approach and a covariant $\lambda$-formulation, it identifies four PT-odd second-order nonlinearities (KI, KFS, SR, SFS) and demonstrates that KI and KFS track the Kramers coherence, whereas SR mostly vanishes under PT symmetry. The MnBi$_2$Te$_4$ bilayer serves as a concrete platform where Kramers nonlinearities dominate interlayer polarization and reveal Neél-order–dependent, helicity-sensitive responses, offering a route to optically control and diagnose Kramers states. Overall, the work provides a geometric and dynamical framework linking light helicity to Kramers coherence with potential applications in Kramers-based optoelectronics and quantum materials diagnostics.

Abstract

Superpositions between states in doubly degenerate Kramers pairs can act as an internal degree of freedom. Here we uncover a Kramers dichroism in PT symmetric magnets: interband transitions induced by circularly polarized light irradiation produce a coherent superposition between Kramers partnered states. This allows to optically control the Kramers degree of freedom. In contrast, Kramers pairs optically excited by linearly polarized light remain in a completely mixed state. Strikingly, we find a class of second-order nonlinear responses that directly track the coherence between Kramers partnered states. Such Kramers nonlinearities can be pronounced producing large second-order nonlinear layer polarization responses activated by Kramers degeneracy in layered antiferromagnets. Together with Kramers dichroism, these render optical responses a novel means for accessing the Kramers degree of freedom and diagnosing their quantum coherent state.

Figures (3)

• Figure 1: Kramers Pair Optical Transitions.a. Optical interband transitions in PT electronic bands involve Kramers pairs of degenerate states from ($v, \bar{v}$) to ($c, \bar{c}$). b,c The quantum state after interband transition can be visualized in a Bloch sphere of the Kramers subspace e.g., for ($c, \bar{c}$). b. Linearly polarized light produces a completely mixed state in the Kramers subspace; black blurred dot denotes the trace of the density matrix in the Kramers subspace, Eq. (\ref{['eq:kramersDOF']}) c. In contrast, circularly polarized light produces a coherence between the Kramers partnered states characterized by a Kramers Bloch vector $\boldsymbol{\kappa}$ (red, purple), Eq. (\ref{['eq:kramersDOF']}); $\boldsymbol{\kappa}$ can be switched by the helicity of light denoted by red and purple. We term the contrast between the quantum states induced by different light polarizations: "Kramers Dichroism".
• Figure 2: Kramers activated second order nonlinear responses in MBT. (a) Helicity dependent non-linear interlayer polarization susceptibility tensor of bilayer $\rm Mn Bi_2 Te_4$ ($\tau = 0.25$ps ma2022photocurrent, $\mu =0.01$eV, for the complete set of parameters see SI). Note that the KI response is the only circular response in the absorptive regime. While Fermi sea shift responses also display circular polarization sensitivity (orange), their effect is small as compared with KI (blue) and KFS (purple). Bilayer MBT band structure (left inset). (b) Schematic illustration of the interlayer polarization and spin responses for distinct circular (LH/RH) polarizations (red circular arrows) and Néel order parameters $x = \pm 1$, alternating according to the boxed arrow direction.
• Figure S3: Second order nonlinear responses for PT-odd observables in MBT. Helicity dependent non-linear interlayer polarization susceptibility tensor of bilayer $\rm Mn Bi_2 Te_4$ for $\mu =0.01$eV and (a)$\tau = 1$ ps, (b)$\tau = 50$ fs; for the complete set of parameters see section "MBT Hamiltonian"). Similarly to the result displayed on Fig.\ref{['FIG2']}a of the main text, for both relaxation parameters, Kramers nonlinearities (KI and KFS) are consistently dominant. Notice that shift resonant contribution is helicity blind, as a result $\frac{1}{2}\delta O^{(2)}_{\rm SFS} ({\rm LH}) - \frac{1}{2}\delta O^{(2)}_{\rm SFS} ({\rm RH})$ vanishes in a PT symmetric material .