Promoted current-induced spin polarization in inversion symmetry broken topological insulator thin films

TL;DR

We study current-induced spin polarization in inversion-symmetry-broken topological insulator thin films under an in-plane electric field using the Kubo formalism with self-consistent Born approximation and ladder (vertex) corrections to treat disorder. The low-energy model describes two hybridized TI surfaces with $H_0(k)$ and eigenvalues $E_{lp}(k)$, enabling a topological transition at $V_c=v\sqrt{|\Delta_0/\Delta_1|}$. We show that the transverse spin susceptibility $\chi_{yx}$ is nonzero in a finite chemical-potential window near the Dirac point, with the window broadening as $μ$ increases, and that both momentum-dependent hybridization $Δ_1$ and inversion breaking $V$ amplify spin polarization; vertex corrections further enhance the response. The results offer a tunable mechanism for spin–charge interconversion in TI thin films and are consistent with first-principles parameter regimes for Bi$_2$Se$_3$, Bi$_2$Te$_3$, and Sb$_2$Te$_3$, suggesting relevance for spintronic devices.

Abstract

We theoretically investigate current-induced spin polarization in disordered topological insulator thin films with broken inversion symmetry under an applied in-plane electric field. Utilizing the Kubo formalism within the self-consistent Born approximation and incorporating vertex corrections to account for multiple scattering events, we analyze how disorder, chemical potential, the electrostatic potential difference between the top and bottom surfaces, and momentum-dependent hybridization affect the spin susceptibility. Our results reveal that the spin susceptibility exhibits nonzero values within a finite range around a zero gap, and this range broadens as the chemical potential increases. A higher hybridization strength induces asymmetry in the spin response. A stronger potential difference, breaking inversion symmetry, significantly enhances polarization. This enhancement is a trend attributable to band inversion and is further refined by vertex corrections. These findings provide a theoretical framework for tuning spin-charge conversion in topological thin films, with implications for spintronic device applications.

Figures (10)

• Figure 1: (Color online) Schematic diagram of a TI thin film subjected to a parallel applied electric field $E$ in the $x$-direction and an electrostatic potential $V$ between the top and bottom surfaces. Also, $\Delta_{0}$ and $\Delta_{1}$ are hybridization parameters between the two surface states. The homogeneous spin polarization of electrons across the sample, resulting from the CISP effect, is depicted in blue.
• Figure 2: (Color online) The band structure of the system is shown for different values of $V$: (a) $V=0.0$ ($V<V_c$), (b) $V=0.447$ ($V=V_c$), (c) $V=0.9$ ($V>V_c$) and (d) $V=1.5$ ($V>V_c$). Here $\Delta_0=0.1$ and $\Delta_1=0.5$.
• Figure 3: (Color online) (a) Real and (b) imaginary parts of $\Sigma_{00}^{-}$, $\Sigma_{0y}^{-}$ and $\Sigma_{zz}^{-}$, for $V=0.1$, $\Delta_{0}=0.1$, $\Delta_{1}=0.5$, and $n_i V_{0}^{2}=0.02$.
• Figure 4: (Color online) The spin susceptibility $\chi_{yx}$ as a function of $\mu$ for different values of potentials. Here $\Delta_0=0.1$ and $\Delta_1=0.5$. The inset shows the abrupt sign change near the Dirac point, which signals the closing of the energy gap.
• Figure 5: (Color online) The spin susceptibility versus $\mu$ and $\Delta_0$ with $V=0.1$, $V=0.6$, and $V=0.9$ for the left, middle, and right columns, respectively. Also, $\Delta_1=0.1$ and $\Delta_1=0.5$ for the top and bottom rows, respectively.