Andreev reflection near the Dirac point at the graphene-${\mathrm{NbSe}}_{2}$ junction

Andreev reflection near the Dirac point at the graphene- ${NbSe}_{2}$ junction

Manas Ranjan Sahu, Pratap Raychaudhuri, and Anindya Das

Phys. Rev. B 94, 235451 – Published 30 December 2016

Abstract

Despite extensive search for about a decade, specular Andreev reflection (SAR) has only recently been realized in the bilayer graphene-superconductor interface. The experimental observation of retro to specular Andreev reflection is not only fundamentally important, but also has potential application in quantum computing, etc. Here we have carried out the transport measurements at the van der Waals interface of single-layer graphene and ${NbSe}_{2}$ superconductor. We investigate the Andreev reflection near the Dirac point by measuring the differential conductance as a function of Fermi energy and bias energy. We find that the normalized conductance ( $G_{T < T_{c}} / G_{T > T c}$ ) becomes suppressed as we pass through the Dirac cone, which manifests the transition from retro to nonretro-type Andreev reflection. The suppression indicates the blockage of Andreev reflection beyond a critical angle ( $θ_{c}$ ) of the incident electron with respect to the normal between the single-layer graphene and the superconductor junction. However, the observation of SAR was restricted due to the finite Fermi-energy broadening. The results are compared with a theoretical model of the corresponding setup.

Received 31 May 2016
Revised 22 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.235451

Physics Subject Headings (PhySH)

Andreev reflection Proximity effect Quantum transport

Graphene

Transport techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Manas Ranjan Sahu¹, Pratap Raychaudhuri², and Anindya Das^1,*

¹Department of Physics, Indian Institute of Science, Bangalore 560012, India
²Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India

^*anindya@physics.iisc.ernet.in

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Vol. 94, Iss. 23 — 15 December 2016

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Figure 1
(a) Top left: AR for a semiconductor-superconductor junction. Bottom left: schematic of corresponding retro reflection process. Top right: In the case of graphene, another type of AR appears when the Fermi energy is very close to the Dirac point. Bottom right: schematic of the corresponding specular AR process. (b) Left: optical image of graphene on hBN; right: the device with ${NbSe}_{2}$ . Scale bar 2 $μ m$ . (c) Schematic of the measurement setup.
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Figure 2
(a) 10 K gate responses of two devices. (b) Log-log plot of the gate responses showing the charge inhomogeneity of device 1 and device 2, respectively. (c) The red curve is the four-probe measured resistance of the device which contains SLG and SLG- ${NbSe}_{2}$ parts. The black curve is the resistance of the SLG part only. The SLG- ${NbSe}_{2}$ junction resistance is shown in the inset (top) as a function of gate voltage. The quantum Hall plateau at $B = 4$ T is shown in the lower inset.
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Figure 3
(a) Differential conductance ( $G$ ) as a function of $V_{S D}$ in a ${NbSe}_{2}$ device showing BCS peaks at $\pm 1 mV$ and its evolution with temperature. (b) Evolution of $G$ vs $V_{S D}$ in the actual Au-SLG- ${NbSe}_{2}$ with temperature showing the appearing superconductivity below 6 K. (c) The black line is the gate response at 236 mK and the red line is averaged over 1000 data points. (d) Two-dimensional color map of differential conductance at 10 K as a function of $V_{B G}$ and $V_{S D}$ . (e) $G_{10 K}$ vs $V_{S D}$ plot at a given $V_{B G}$ showing no change of differential conductance. (f) Two-dimensional color map of differential conductance at 236 mK as a function of $V_{B G}$ and $V_{S D}$ . (g) $G_{236 mK}$ vs $V_{S D}$ plot at a given $V_{B G}$ showing the nonmonotonic change of differential conductance due to superconductivity. The dotted horizontal lines indicate the superconducting gap.
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Figure 4
(a) Two-dimensional color map of normalized differential conductance as a function of $V_{B G}$ and $V_{S D}$ . (b) $G_{236 mK} / G_{10 K}$ vs $V_{B G}$ plots for different values of $V_{S D}$ . The brown solid line corresponds to the average over 20 raw data points (red line) at $V_{S D} = 0$ mV. The vertical dashed line indicates the Dirac point. (c) $G_{236 mK} / G_{10 K}$ vs $V_{S D}$ plots for different values of $V_{B G}$ at $- 1.65, - 0.65$ , and 0.65 V, which correspond to $E_{F}$ at $- 30$ , 0, and 35 meV, respectively. The horizontal solid lines schematically indicate those energies in a Dirac cone.
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Figure 5
(a) Top: Schematic of AR for an electron having different Fermi-energy positions. Here we have used only the electronic picture, i.e., the Andreev reflected hole is represented as a vacancy in the electronic band at an appropriate position. Middle/bottom: The position of the incident electron and Andreev reflected hole in the $K_{x} - K_{y}$ plane for RAR (middle) and SAR (bottom). In all of these representations, arrows indicate the real-space velocity of the quasi particles. (b) Top: Schematic of the RAR process when $θ_{inc} = θ_{c}$ . Bottom: The normalized value of the critical angle as a function of $E_{F}$ for $V_{S D} = 0.2$ meV. Inset shows the zoomed one around the Dirac point. (c) Differential conductance of a NS interface as a function of excitation energy for different Fermi energies. (d) $1 / G \times d I / d V$ as a function of Fermi energy for different $δ E_{F}$ .
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Figure 6
(a) Top: The experimental $G_{236 mK} / G_{10 K}$ data (black line) as a function of $V_{B G}$ for device 2, similar to Fig. 4. The red solid line corresponds to the average over 200 raw data points. Bottom: Theoretically calculated normalized differential conductance of SLG- ${NbSe}_{2}$ as a function of $V_{B G}$ with $δ E_{F} \sim 15$ meV for $V_{S D} = 0.2$ meV. (b) The black line is the experimental data of SLG- ${NbSe}_{2}$ device 1 (red shows the average) with higher $δ E_{F} \sim 35$ meV. (c) The black line corresponds to $G_{236 mK} / G_{10 K}$ of SLG alone (red shows average) and there is no suppression around the Dirac point. The vertical dashed line indicates the position of the Dirac point.
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Physical Review B

covering condensed matter and materials physics

Andreev reflection near the Dirac point at the graphene- ${NbSe}_{2}$ junction

Manas Ranjan Sahu, Pratap Raychaudhuri, and Anindya Das

Phys. Rev. B 94, 235451 – Published 30 December 2016

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Physical Review B

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Andreev reflection near the Dirac point at the graphene-NbSe2 junction

Manas Ranjan Sahu, Pratap Raychaudhuri, and Anindya Das

Phys. Rev. B 94, 235451 – Published 30 December 2016

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Andreev reflection near the Dirac point at the graphene- ${NbSe}_{2}$ junction