Environment-Assisted Tunneling as an Origin of the Dynes Density of States

Abstract

We show that the effect of a high-temperature environment in current transport through a normal metalinsulator-superconductor tunnel junction can be described by an effective density of states in the superconductor. In the limit of a resistive low-Ohmic environment, this density of states reduces into the well-known Dynes form. Our theoretical result is supported by experiments in engineered environments. We apply our findings to improve the performance of a single-electron turnstile, a potential candidate for a metrological current source. DOI: 10.1103/PhysRevLett.105.026803 PACS numbers: 73.40.Gk, 06.20.Jr, 72.70.+m, 73.20.At Introduction.-The density of states (DOS) of the carriers governs the transport rates in a mesoscopic conductor [1], e.g., in a tunnel junction. Understanding the current transport in a junction in detail is of fundamental interest, but it plays a central role also in practical applications, for instance, in the performance of superconducting qubits [2], of electronic coolers and thermometers [3], and of a singleelectron turnstile to be discussed in this Letter [4]. When one or both of the contacts of a junction are superconducting, the one-electron rates at small energy bias should vanish at low temperatures because of the gap in the Bardeen-Cooper-Schrieffer (BCS) DOS [5]. Yet, a small linear in voltage leakage current persists in the experiments [3,6-10] that can often be attributed to the Dynes DOS, a BCS-like expression with lifetime broadening [11,12]. A junction between two leads admits carriers to pass at a rate that depends on the DOS of the conductors, the occupation of the energy levels, and the number of conduction channels in the junction [13]. In general, basic one-electron tunneling coexists with many-electron tunneling, for instance, cotunneling in multijunction systems [14], or Andreev reflection in superconductors [15,16]. However, when the junction is made sufficiently opaque, a common situation in practice, only one-electron tunneling governed by the Fermi golden rule should persist. We demonstrate experimentally that the subgap current in a high-quality opaque tunnel junction between a normal metal and a superconductor can be ascribed to photon-assisted tunneling. We show theoretically that this leads exactly to the Dynes DOS with an inverse lifetime of e 2 k B T env R=@ 2 , where T env and R are the temperature and effective resistance of the environment.We employ a tunnel junction with a normal metalinsulator-superconductor (NIS) structure; see Fig. 1(a). The essentially constant DOS in the normal metal renders

Andreev current for low temperature thermometry

“…6). In addition, their responsivity tends to saturate at low temperature due to particular tunneling processes such as environment assisted tunneling 7 or Andreev reflections. 8 We are proposing to use the disorder enhanced Andreev current as a temperature probe.…”

Superconducting tantalum nitride-based normal metal-insulator-superconductor tunnel junctions

“…The DOS broadening seen in our Al-AlO x -Cu junctions is comparable to the results by other labs. 28,30,31 However, if extreme measures are taken to reduce environmental radiation coupling to the junction, much lower broadening has been demonstrated in Al-AlO x -Cu junctions, 30,32 explained by photon-assisted tunneling. According to that picture C/D $ 1/D, which suggests that the broadening in our higher gap junctions (Nb,NbN,TaN) is due to some other mechanism.…”

Proximity nanovalve with large phase-tunable thermal conductance

“…where D is the wire diffusion coefficient, the parameter Γ accounts for the inelastic scattering rate within the relaxation time approximation [16][17][18][19] , andτ z is the third Pauli matrix in the Nambu space. The Green's function g is a matrix in this space with the formĝ = gτ z +f , beingf the anomalous Green's function that is off-diagonal in Nambu space.…”