Electrically and magnetically switchable nonlinear photocurrent in РТ-symmetric magnetic topological quantum materials

Abstract

Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems such as ferroelectric semimetals sparked tremendous interest of utilizing nonlinear optics to characterize condensed matter with exotic phases. Here we provide a microscopic theory of two types of second-order nonlinear direct photocurrents, magnetic shift photocurrent (MSC) and magnetic injection photocurrent (MIC), as the counterparts of normal shift current (NSC) and normal injection current (NIC) in time-reversal symmetry and inversion symmetry broken systems. We show that MSC is mainly governed by shift vector and interband Berry curvature, and MIC is dominated by absorption strength and asymmetry of the group velocity difference at time-reversed ±k points. Taking $${\cal{P}}{\cal{T}}$$ P T -symmetric magnetic topological quantum material bilayer antiferromagnetic (AFM) MnBi2Te4 as an example, we predict the presence of large MIC in the terahertz (THz) frequency regime which can be switched between two AFM states with time-reversed spin orderings upon magnetic transition. In addition, external electric field breaks $${\cal{P}}{\cal{T}}$$ P T symmetry and enables large NSC response in bilayer AFM MnBi2Te4, which can be switched by external electric field. Remarkably, both MIC and NSC are highly tunable under varying electric field due to the field-induced large Rashba and Zeeman splitting, resulting in large nonlinear photocurrent response down to a few THz regime, suggesting bilayer AFM-z MnBi2Te4 as a tunable platform with rich THz and magneto-optoelectronic applications. Our results reveal that nonlinear photocurrent responses governed by NSC, NIC, MSC, and MIC provide a powerful tool for deciphering magnetic structures and interactions which could be particularly fruitful for probing and understanding magnetic topological quantum materials.

Basic formulation and first-principles implementation of nonlinear magneto-optical effects

“…above results are consistent with literature [13,25], and additionally we generalized the formulae of NSC and MSC to a U(N )-invariant form in the presence of N -fold degeneracy.…”

“…( 5), P inter (ω Σ = 0) (2) is finite, with ω Σ P inter (ω Σ = 0) (2) = 0, and j(ω Σ = 0) (2) = j intra (ω Σ = 0) (2) according to Eq. ( 3), which can reduce to the well-known U(1)-invariant formulae of rectification current densities [13,25]. However, if band degeneracy occurs, e.g.…”

“…The conventional formulae for second-order photocurrent and electric polarization only consider nondegenerate bands, and therefore are only U(1)-gauge invariant [13,25]. However, in magnetic materials with PT symmetry, Kramers-like degeneracy appears at every k point and the choice of eigenstates in the doubly degenerate subspace has a gauge freedom determined by a 2 × 2 unitary matrix.…”

“…In the linear regime, the plane of polarization can be rotated when light is reflected by or transmitted through magnetic materials, which is called the linear magneto-optical Kerr effect or Faraday effect. In the nonlinear regime, the magnetization-sensitive rectification current has recently been proposed in antiferromagnetic (AFM) bilayers of CrI 3 and MnBi 2 Te 4 with parity-time (PT ) symmetry [12][13][14], whose non-magnetic counterparts are absent. Magnetization-sensitive SHG has long been a tool to probe surface and interface magnetization in metallic materials since 1990s [15][16][17][18] and later used to investigate complex magnetic orders in bulk magnetic oxides, such as in Cr 2 O 3 [19].…”

“…Firstly, the conventional formalism of nonlinear magnetooptical effects is ill-defined in the presence of PT symmetry due to the Kramers-like degeneracy at each k point in the band structure. The conventional expressions of nonlinear conductivity and electric susceptibility [12,13,22] only consider non-degenerate bands with an arbitrary phase freedom for eigenstates at each k point, which is also called the U(1)-gauge freedom. However, due to the Kramers-like degeneracy, formulations under PT symmetry should be invariant under an arbitrary 2 × 2 unitary transformation in the subspace spanned by the doubly degenerate eigenstates, corresponding to a U(2)-gauge freedom.…”