Bosonic Anomalies in Boron-Doped Polycrystalline Diamond

Gufei Zhang, Tomas Samuely, Jozef Kačmarčík, Evgeny A. Ekimov, Jun Li, Johan Vanacken, Pavol Szabó, Junwei Huang, Paulo J. Pereira, Dorin Cerbu, and Victor V. Moshchalkov

Phys. Rev. Applied 6, 064011 – Published 21 December 2016

Abstract

Quantum confinement and coherence effects are considered the cause of many specific features for systems which are generally low dimensional, strongly disordered, and/or situated in the vicinity of the metal-insulator transition. Here, we report on the observation of anomalous resistance peak and specific heat peaks superimposed at the superconducting transition of heavily boron-doped polycrystalline bulk diamond, which is a three-dimensional system situated deep on the metallic side of the boron-doping-driven metal-insulator transition in diamond. The anomalous resistance peak and specific heat peaks are interpreted as a result of confinement and coherence effects in the presence of intrinsic and extrinsic granularity. Our data, obtained for superconducting diamond, provide a reference for understanding the superconductivity in other granular disordered systems. Furthermore, our study brings attention to the significant influence of granular disorder on the physical properties of boron-doped diamond, which is considered a promising candidate for electronics applications.

Received 28 June 2016

DOI:https://doi.org/10.1103/PhysRevApplied.6.064011

Physics Subject Headings (PhySH)

Bosons Localization Superconducting phase transition Superconductivity Thermal properties Transition temperature Transport phenomena

Doped semiconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gufei Zhang^1,*, Tomas Samuely², Jozef Kačmarčík², Evgeny A. Ekimov³, Jun Li⁴, Johan Vanacken¹, Pavol Szabó², Junwei Huang¹, Paulo J. Pereira¹, Dorin Cerbu¹, and Victor V. Moshchalkov^1,†

¹INPAC-Insititute for Nanoscale Physics and Chemistry, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
²Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences & Faculty of Science, P. J. Šafárik University, 04001 Košice, Slovakia
³Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 142190 Troitsk, Moscow Region, Russia
⁴RISE, Nanjing University, 210093 Nanjing, China

^*Gufei.Zhang@fys.kuleuven.be
^†Victor.Moshchalkov@fys.kuleuven.be

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Vol. 6, Iss. 6 — December 2016

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Images

Figure 1
The dirty metallic normal state and the resistive superconducting transition of heavily boron-doped polycrystalline diamonds synthesized with the high-pressure high-temperature (HPHT) method. (a) Despite the negative temperature coefficient of resistivity, the normal-state $ρ (T)$ increases when lowering temperature is far smaller than the criterion of $Δ ρ |_{per 10 K} > 10 %$ for an insulating state, suggesting the dirty metallic normal state induced by weak disorder. Inset: sample HPHT2 exhibits a two-step superconducting transition, while sample HPHT1 demonstrates an anomalous $ρ (T)$ peak superimposed in its resistive superconducting transition. (b) In magnetic fields, the anomalous $ρ (T)$ peak of HPHT1 diminishes into a bump, leaving behind a two-step feature of the superconducting transition.
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Figure 2
The anomalous resistance peak observed when measuring the resistivity as a function of magnetic field $ρ (B)$ . (a) Consistent with the $ρ (T)$ measurements, the anomalous resistance peak, situated in the low field regime, is suppressed and shifted in higher magnetic fields. (b) The 3D view of the interpolated data of (a).
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Figure 3
Anomalous specific heat peaks found below the onset critical temperature of the superconducting transition. (a) The temperature dependence of specific heat over $T$ , $C / T$ . Rather than a single jump, two broad $C / T$ peaks are observed for the polycrystalline bulk diamond. The behavior of the $C / T$ peaks in magnetic fields is tracked up to 5 T. Inset: With the linear fitting of $C / T$ ( $B = 5 T$ ) vs $T^{2}$ , we disclose that our HPHT diamond has a normal state of classic BCS superconductors. (b) The 3D view of the interpolated data of (a). (c) When plotting $ρ (T)$ and $C / T$ together, the anomalous $ρ (T)$ peak is found to be within the temperature window of the $C / T$ peak at $T_{p 1}^{hc}$ , and the other $C / T$ peak is located at the tail of the resistive superconducting transition with its maximum temperature $T_{p 2}^{hc} < T_{c}^{offset}$ . The magnetic field dependence of the characteristic temperatures as determined in (c) is summarized in (d), yielding accordingly the phase boundaries.
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Figure 4
Topography and temperature-induced evolution of the superconducting gap width and the zero-bias conductance (ZBC) map. (a) The topographic image of a $(500 \times 500)$ -nm-sized surface area, on which the grain boundary in between grain 1 ( $G 1$ ) and grain 2 ( $G 2$ ) is marked with dashed white lines. (b) The superconducting gap measured at three different locations labeled as $A$ , $B$ , and $C$ in (a). (c) Temperature-induced evolution of the superconducting gap. The solid curves are the BCS fit to the half-width of the superconducting gap $Δ$ (hollow symbols) at different location. (d)–(g) Temperature-induced evolution of the ZBC map, providing information about the depth variation of the superconducting gap. Intrinsic granularity is found to play a role in defining the modulations of $Δ$ on a scale much smaller than the size of physical grains (extrinsic granularity).
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Figure 5
The resistor–superconductor-insulator-superconductor ( $S − I − S$ ) junction network model, based on which the bosonic $ρ (T)$ and $C / T$ anomalies are interpreted. Note that the solid circles (red for normal state and blue for superconducting state) should be viewed as intrinsic and/or extrinsic grains. The percolation and condensation path is highlighted by glowing polylines. Blue crosses denote the $S − I − S$ junctions. (a)–(c) illustrate the physics picture for normal-state, resistive superconducting transition, and superconducting state ( $ρ = 0$ ) in the presence of intrinsic and extrinsic granularity-correlated disorder, respectively.
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Figure 6
Modeling of the anomalous resistive superconducting transition by using different multichannel circuits. Considering that a resistive superconducting transition is a process in which Cooper pairs take over the control of electrical transport from single quasiparticles, we borrow the switchlike function of parallel circuits for the development of three different models. (a) The two-channel model, composed of one fermionic channel $ρ_{N}$ and one bosonic channel $ρ_{S}$ , fails to describe our $ρ (T)$ peak superimposed in the two-step superconducting transition, although it can generally provide good fits to resistance peaks situated at the very onset of resistive superconducting transitions. (b) The three-channel model, composed of one fermionic channel $ρ_{N}$ and two bosonic channels $ρ_{S 1}$ and $ρ_{S 2}$ , describes the anomalous resistive superconducting transition fairly well, as shown in (d). (c) The three-channel model, composed of two fermionic channels $ρ_{N 1}$ and $ρ_{N 2}$ and one bosonic channel $ρ_{S}$ , ended up with a failure when fitting the resistive superconducting transition.
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