Unusual pressure-induced metallic state in the correlated narrow band-gap semiconductor FeSi

Compressing FeSi induces a progressive semiconductor to metal transition, onset at $P$≥15 GPa at temperatures below $T_{\max }$ determined by the degree of disorder in the sample. At high pressure preceding charge-gap closure, a broad maximum manifests in the ρ($T$) data at $T_{\max }$ and is a feature which persists into the metallic state. The extremum in ρ($T$) occurs at $T_{\max }\sim 40\mathrm{K}$ at ∼11 GPa and shifts monotonically to ∼240 K as pressure is increased to ∼32 GPa, in the most detailed example of three series of measurements involving pressurized FeSi with different degrees of disorder. The transition to a metallic phase is an electronic change only, in that the B20-type crystal structure is retained up to 30 GPa, with no evidence of a discontinuity in the volume-pressure equation of state data. Samples from the same ingot subjected to different quasihydrostatic conditions reveal different values of the critical pressure of the electronic transition, its width, and pressure dependences of $T_{\max }$. This attests to sensitivity of the electronic transition to the degree of disorder in the investigated sample. The metallic state has neither Fermi-liquid nor non-Fermi-liquid behavior. Such an unusual pressure-induced correlated metallic state in FeSi is attributed to extended states within the $3d-3p$ hybridization gap originating from disorder and compression tuning of the mobility edge relative to the Fermi level. The metallic state has also been investigated in external magnetic fields up to 8 T at low temperatures $(2\mathrm{K}\le T\le 20\mathrm{K})$ at 15 and 19 GPa. This reveals a positive magnetoresistance, as observed in doped $\mathrm{F}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\mathrm{Si}$ samples at ambient pressure, suggesting that in the majority and minority spin bands there is a field-induced modification of the respective magnitudes of charge-carrier populations which have different mobilities.

Figure 1

Crystal structure of ε-FeSi, showing the B20-type cubic unit cell with four formula units. Each Fe atom has a sevenfold coordination of Si atoms involving three sets of Fe–Si near-neighbor bond lengths [26].

Figure 2

Temperature dependence of the resistivity in the range 300–2 K of the FeSi sample [28], which involved a DC four-probe measurement at ambient pressure on a bar cut from the original polycrystalline ingot. Top inset shows data in the 200–100 K regime and solid line fit involving Arrhenius thermally activated behavior $\rho \propto exp\left(E_{\mathrm{g}}/\phantom{E_{\mathrm{g}}2k_{\mathrm{B}}T}2k_{\mathrm{B}}T\right)$, where $E_{\mathrm{g}}=63\mathrm{meV}$ is the derived charge gap. Bottom inset is a linearized plot of the variable range-hopping formulation $\rho \propto exp\left[{\left(T_0/\phantom{T_{0}T}T\right)}^{1/4}\right]$, where the solid line is a linear fit in the range 20–4 K to yield a Mott temperature $T_0=1.1\times {10}^5\mathrm{K}$. The residual resisitivty ratio $\rho \left(4.2\mathrm{K}\right)/\rho \left(300\mathrm{K}\right)\approx 14000$ [24].

Figure 3

(a) Temperature dependence of resistivity of sample FeSi-UK up to maximum pressurization of 32.1 GPa. Resistivity curves below 11.2 GPa have $d\rho /dT<0$. (b) Temperature dependence of resistivity in the HP metallic electronic phase at $P>15\mathrm{GPa}$, where the charge gap $E_{\mathrm{g}}\approx 0$, exemplifying a broad maximum at $T_{\max }$ delineated by arrows in some curves.

Figure 4

(a) Example of extraction of $E_{\mathrm{g}}$ at 6.5 GPa of the LP phase of sample FeSi-UK, from a linear fit (solid line) to the high-temperature data range 150–200 K assuming activated hopping transport $ln\rho =\frac{E_{\mathrm{g}}}{2k_{\mathrm{B}}T}+\mathrm{const}$. (b) Evolution of LT resistivity ρ(2 $K$) to identify the semiconductor→metal transition. (c) Analysis of HP data of metallic behavior of sample FeSi-UK, using a power-law formulation $\rho \left(T\right)={\rho }_0+A{T}^n$. Derivative $d\left[\ln (\rho \left(T\right)-{\rho }_0)\right]/d\left(\ln T\right)$ provides the exponent $n$ at any LT [36]. There is no extended LT range as $T\to 0\mathrm{K}$ where either Fermi-liquid behavior ($n=2$) or non-Fermi-liquid characteristics ($1\le n\le 1.5$) are exhibited.

Figure 5

(a) Comparison of the trend of $E_{\mathrm{g}}$ for the three series of measurements on samples derived from the same synthesized ingot, subjected to both different degrees of grinding prior to loading in the DAC and hydrostaticity under pressure. Solid lines guide the eye. (b) Pressure evolution of the extremum $T_{\max }$ in ρ($T$) data (e.g., Fig. 3) for the three series of measurements. Vertical error bars for $T_{\max }$ are the size of the symbols. Arrows on the horizontal axis and hatched bars indicate pressures where $E_{\mathrm{g}}$ extrapolates to zero (see top panel) and beyond which the HP metallic electronic phase is stabilized. Solid lines guide the eye.

Figure 6

(a) Representative selection of ED-XRD patterns of sample FeSi-UK measured up to 30 GPa at RT. Peaks not indexed are from fluorescence events in the detector or solidified nitrogen pressure-transmitting medium. (b) Corresponding unit-cell volume behavior of the B20 lattice structure retained throughout the pressure range. Solid line through data points is the Murnaghan equation of state.

Figure 7

Schematic DOS of FeSi near the Fermi level $E_{\mathrm{F}}$ at ambient conditions. Mobility edges $E_{\mu }$ arising from crystal lattice heterogeneity (i.e., disorder) separate the localized (shaded) states from extended states in band-edge tails in the region $E_{\mathrm{VBE}}$ to $E_{\mathrm{CBE}}$ [24, 39]. This demonstrates how the gap $E_{\mathrm{g}}$ is manifest in the DOS.

Figure 8

Temperature dependence of the normalized resistivity $\rho \left(T\right)/\rho \left(60\mathrm{K}\right)$ for $6.5\mathrm{GPa}\le P\le 11.2\mathrm{GPa}$ at low temperatures ($\rho <60\mathrm{K}$). Red arrow marks a kink/upturn in $\rho \left(T\right)$ at $T^{*}\sim 12\mathrm{K}$; black arrow marks the maximum in $\rho \left(T\right)$ for 11.2 GPa at ∼38 K.

Figure 9

(a) Temperature dependence of the electrical resistivity for $2\mathrm{K}\le T\le 20\mathrm{K}$ in various magnetic fields beyond the onset pressure to the metallic state ($E_{\mathrm{g}}\sim 0$) for FeSi-UK at 15 and 19 GPa. (b) Magnetic-field dependence of the temperature $T_{\min }$ where a minimum in the electrical resistivity is observed at LT in (a), and (c) the magnetoresistance at 4 and 8 T.