Andreev reflection and strongly enhanced magnetoresistance oscillations in ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{As}∕\mathrm{In}\mathrm{P}$ heterostructures with superconducting contacts

We study the magnetotransport in small hybrid junctions formed by high-mobility ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{As}∕\mathrm{In}\mathrm{P}$ heterostructures coupled to superconducting (S) and normal metal (N) terminals. Highly transmissive superconducting contacts to a two-dimensional electron gas (2DEG) located in a ${\mathrm{Ga}}_x{\mathrm{In}}_{1-x}\mathrm{As}∕\mathrm{In}\mathrm{P}$ heterostructure are realized by using a $\mathrm{Au}∕\mathrm{Nb}\mathrm{N}$ layer system. The magnetoresistance of the S/2DEG/N structures is studied as a function of dc bias current and temperature. At bias currents below a critical value, the resistance of the S/2DEG/N structures develops a strong oscillatory dependence on the magnetic field, with an amplitude of the oscillations considerably larger than that of the reference N/2DEG/N structures. The experimental results are qualitatively explained by taking into account Andreev reflection in high magnetic fields.

Figure 1

(Color online) Schematics of the sample cross section. The size of the mesa is $3\times 3\mu {\mathrm{m}}^2$. For the first type of structures, a superconducting $\mathrm{Au}∕\mathrm{Nb}\mathrm{N}$ electrode and a normally conducting $\mathrm{Cr}∕\mathrm{Au}$ electrode face each other. For the second sample type, two $\mathrm{Cr}∕\mathrm{Au}$ electrodes were used.

Figure 2

(Color online) Magnetoresistance oscillations $\Delta R$ of the S/2DEG/N sample for various dc bias currents $I_{\mathit{dc}}$: 0, 0.25, 0.5, and $0.75\mu \mathrm{A}$ at a temperature of $0.5\mathrm{K}$. The oscillation amplitude was extracted for Fig. 3 at the magnetic field value of $0.51\mathrm{T}$ indicated by a circle. The filling factors $\nu$ are indicated by arrows.

Figure 3

(Color online) Oscillation amplitude $\Delta R$ at $B=0.51\mathrm{T}$ as a function of the dc bias current $I_{\mathit{dc}}$ for the S/2DEG/N sample (squares) and for the N/2DEG/N structure (triangles). The inset shows the normalized differential resistance $(dV∕dI)∕R_i$ of the S/2DEG/N structure as a function of $I_{\mathit{dc}}$.

Figure 4

(Color online) Magnetoresistance oscillations $\Delta R$ of the S/2DEG/N sample at $I_{\mathit{dc}}=0$ for various temperatures: 0.5, 1.0, 2.0, and $3.0\mathrm{K}$.

Figure 5

(Color online) Normalized amplitude $A∕A_0$ as a function of temperature at $B=0.47\mathrm{T}$ (squares). Here, $A_0$ is the amplitude at $T=0.5\mathrm{K}$. The solid line represents the calculated amplitude according to Ref. 19. The inset shows the schematics of the Andreev-reflection process at S/2DEG interface, with a magnetic field applied perpendicular to the plane of the 2DEG. The electrons and holes acquire phase shifts ${\varphi }_B^e$ and ${\varphi }_B^h$, respectively, between two successive Andreev reflections. The quantities $r_c$ and $L$ denote the cyclotron radius and the length of the S/2DEG interface, respectively.