In situ tuning of symmetry-breaking-induced nonreciprocity in the giant-Rashba semiconductor BiTeBr

Nonreciprocal transport, where the left-to-right-flowing current differs from the right-to-left-flowing one, is an unexpected phenomenon in bulk crystals. BiTeBr is a noncentrosymmetric material, with a giant Rashba spin-orbit coupling which presents this unusual effect when placed in an in-plane magnetic field. It has been shown that this effect depends strongly on the carrier density; however, in situ tuning has not yet been demonstrated. We developed a method where thin BiTeBr flakes are gate tuned via ionic-liquid gating through a thin protective hexagonal boron nitride layer. Tuning the carrier density allows a more than $400\%$ variation of the nonreciprocal response in our sample. Our study demonstrates how a few-atomic-layer-thick van der Waals protection layer allows ionic gating of chemically sensitive, exotic nanocrystals.

Figure 1

(a) Due to the lack of inversion symmetry of the crystal and the presence of an in-plane magnetic field, the current flowing through the sample depends on the polarity of the electric field applied [17, 23]. (b) The crystal structure of BiTeBr (projected on the 001 and 1120 planes) [25, 26, 27]. The dashed lines show the border of a possible unit cell. (c) The band structure of BiTeBr assuming a two-dimensional crystal; however, the theoretical calculations concern both two- and three-dimensional cases [23]. (d) The band structure in an in-plane magnetic field. The direction of the magnetic field $B_y$, electric field $E_x$, and polarization $P$ are indicated. (e) Fermi surfaces near the energy minimum of the antiparallel spins, and color map of the reciprocal of the effective mass $m^{*}$. The cross section of the dispersion relation is at the energy highlighted by the horizontal dashed line in (d).

Figure 2

(a) Schematic image of the sample, with the IL and hBN peeled away from the lower corner to show the BiTeBr flake. (b1)–(b3) Optical images of the BiTeBr samples. ($\mathrm{b}1$) The measured sample, with the BiTeBr flake (orange outline) covered with hBN (blue outline). ($\mathrm{b}2$) An unprotected BiTeBr flake before liquid gating, with planned electrodes. ($\mathrm{b}3$) The above flake with contacts, destroyed by liquid gating. (c) Schematic image of liquid gating. Due to the metallic nature of the sample the bulk is screened, and only a thin surface layer is affected by the gating. (d) Two-point resistance as a function of the gate voltage at $220\mathrm{K}$. The hysteretic behavior is due to the slow motion of the ions.

Figure 3

Second-harmonic measurements before the IL gate is applied, showing the antisymmetrized second-harmonic signal. The relative orientation of the magnetic and electric field is shown in the insets. $\gamma$ can be calculated from the slope of the second-harmonic resistance using Eq. (1). As expected, no signal is detected in the parallel case.

Figure 4

(a) The magnetic field dependence of the second-harmonic signal at different gate voltages. The insets demonstrate the position of the ions in the IL and the induced density changes in the BiTeBr in the different experiments. (b) ${\gamma }^{\prime }$ as a function of the carrier density extracted from Hall measurements. The dashed line shows theory from Ref. [23] without any fitting parameters. The divergence from theory can be explained by considering that the second-harmonic signal comes mainly from the gated surface layer, while the Hall measurements used for determining $n$ measure the whole crystal.

Figure 5

(a) Tuning the electron density with the back gate. The gating is much weaker than what is achievable with the IL gate. (b) AFM image of the sample. The image was taken after the sample was extensively studied, and many leads have failed. The failure has caused visible damage to the two top left contacts and the bottom middle contact. (c) Current dependence of the second-harmonic signal. (d) Second-harmonic measurements with the current flowing parallel and perpendicularly to the magnetic field.

Figure 6

(a) Full gating curve at 220 K. Hysteretic behavior is due to the slow movement of the ions. Part of the same curve is shown in Fig. 2. (b) Gate current as a function of $V_{\mathrm{g}}$. $I_{\mathrm{g}}$ never exceeded 0.3 nA, and no chemical reaction takes place between the BiTeBr and the IL.

Figure 7

(a) Hall measurements before the IL was applied. $R_{xy}$ (solid lines) and its antisymmetrized component $\mathrm{\Delta }{R}_{xy}$ (dotted lines) as a function of the out-of-plane magnetic field. The antisymmetrization is necessary, as the nonoptimal geometry of the sample leads to the mixing of the $R_{xx}$ and $R_{xy}$ components. The insets show the respective geometries for the two measurements. They both yield the same value for $n$. (b) Hall measurements without the IL applied (orange) and $V_{\mathrm{g}}=-4\mathrm{V}$ (blue). The orange curve is the same as in (a). The calculated electron densities are shown in Fig. 4.

Figure 8

All measurements were carried out at $2.5\mathrm{K}$ before applying the IL. (a) $\mathrm{\Delta }{R}^{2\omega }$ as a function of the magnetic field, for different applied current amplitudes. The nonreciprocity is expected to scale with the current as Eq. (C1) shows; the measured change is quite small, however. (b) $\mathrm{\Delta }{R}_{\mathbf{B}=\mathbf{15}\mathbf{T}}^{2\omega }$ acquired from linear fits as a function of the applied current. While the trend is linear, it does not cross the axes at the origin; it has a 0.22 $\mathrm{\Omega }$ offset. (c) The temperature dependence of ${\gamma }^{\prime }$ follows the same trend as the results in Ref. [23].

Figure 9

(a) AFM image of the sample discussed in the main text. The height of the sample was measured by fitting the height distribution of the area highlighted with a dashed red rectangle. The height was measured from the top of the hBN flake to the top of the $\text{hBN}+\mathrm{Bi}\mathrm{Te}\mathrm{Br}$ stack. (b) Raman spectra of different flakes obtained from the same bulk crystals during exfoliation. The gray dashed lines mark the peaks calculated using density functional theory (DFT) in Ref. [55]. The blue spectrum shows good agreement with the results of Refs. [55, 56], and EDS measurements confirmed the presence of Bi, Te, and Br. The green spectrum shows good agreement with the results of Ref. [50] (where it is identified as BiTeBr) and Refs. [52, 53] (where it is identified as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$), while EDS measurements show a lack of Br. The flakes showing the orange spectrum are insulating, displaying different colors based on their thickness. The spectrum aligns with that in Ref. [57], where it is identified as BiOBr. EDS measurements confirm a lack of Te, while the excess O could not be clearly seen due to the background signal of the SiO substrate.