Electronic structure of indium selenide probed by magnetoabsorption spectroscopy under high pressure

We report on an investigation of the peculiar electronic structure of the layered semiconductor InSe by magneto-optical experiments under high pressure up to 5 GPa. Magneto-absorption spectroscopy is performed under pulsed magnetic field up to 53 T using a specific setup. Excitonic magnetofingerprints and high-field oscillatory magnetoabsorption yield significant details on the band structure. In addition, the application of an external pressure unveils phenomena that confirm the specific $\mathbf{k}\cdot \mathbf{p}$ model proposed for this compound on the basis of earlier measurements.

Figure 1

(Color online) Schematic view of the magnetoabsorption setup, featuring the high-pressure cell and the specific coupling adaptor, allowing the $U$-turn of the optical fibers feeding the white light (white large arrow) to the bottom diamond side of the sample, in the Faraday configuration. A special focus is provided (left) on the aligned fiber connector to enhance the optical coupling with the entrance slit of the spectrometer and (right) on the two-step hole defining the pressure chamber and ensuring that the light driven to the spectrometer (rainbow large arrow) has traveled through the sample.

Figure 2

(Color online) Typical absorption coefficient spectra in the fundamental InSe band-gap region measured in the diamond-anvil cell at 4 K. Pérot-Fabry oscillations are clearly noticeable below the gap as well as the $n=1$ excitonic peak. Inset: raw transmitted light data.

Figure 3

(Color online) Low-temperature OMA of InSe at ambient pressure up to 53 T contour map. The normalized absorption intensity is shown in color scale. Excitonic peak around 1.34 eV and OMA bands (arrows) with linear magnetic blueshift are evidenced.

Figure 4

(Color online) Typical OMA data at 4 K and 49 T. (a) $I_t$ and $I_t\left(E,B=0\right)$. (b) Normalized intensity $I_t\left(E,B\right)/I_t\left(E,B=0\right)$. (c) ${\alpha }_B-{\alpha }_0$.

Figure 5

(Color online) OMA fan chart at ambient pressure and low temperature.

Figure 6

(Color online) Excitonic peak magnetic behavior. Our data (black squares) and low-field data from Ref. 33 (red dots) are shown as well as three different purely $B^2$ fits: in the full magnetic range (dotted black line), in the low-field region $B\le 20\text{T}$ (black solid line) and on low-field data (red dotted line).

Figure 7

(Color online) Conduction-band nonparabolicity estimation from OMA values of $1/m_e^{\ast }\left(E\right)$ measured at 52.0 T plotted as a function of $\tilde{E}$ and linear fit (solid line).

Figure 8

(Color online) Normalized intensity oscillatory magnetoabsorption spectra at selected pressure.

Figure 9

(Color online) Energy-dependent reduced effective mass ${\mu }_{\perp }\left(N\right)$ pressure behavior: $N=1$ (black squares), $N=2$ (red dots), and $N=3$ (blue triangles).

Figure 10

(Color online) Reentrant exciton behavior at high magnetic field under high pressure. Inset: critical field values $B_C$ (squares) as a version of pressure and linear fit (solid line).