Cooper-pair-mediated coherence between two normal metals

Abstract

Two electrons bound in a singlet state have long provided a conceptual and pedagogical framework for understanding the non-local nature of entangled quantum objects. As bound singlet electrons separated by a coherence length of up to several hundred nanometres occur naturally in conventional BardeenCooper-Schrieffer superconductors in the form of Cooper pairs, recent theoretical investigations [1][2][3][4][5][6][7][8][9] have focused on whether electrons in spatially separated normal-metal probes placed within a coherence length of each other on a superconductor can be quantum mechanically coupled by the singlet pairs. This coupling is predicted to occur through the non-local processes of elastic cotunnelling and crossed Andreev reflection. In crossed Andreev reflection, the constituent electrons of a Cooper pair are sent into different normal probes while retaining their mutual coherence. In elastic cotunnelling, a sub-gap electron approaching the superconductor from one normal probe undergoes coherent, long-range tunnelling to the second probe that is mediated by the Cooper pairs in the condensate. Here, we present experimental evidence for coherent, non-local coupling between electrons in two normal metals linked by a superconductor. The coupling is observed in non-local resistance oscillations that are periodic in an externally applied magnetic flux.Three key predicted signatures of the elastic cotunnelling and crossed Andreev reflection (CAR) processes, shown schematically in Fig. 1, are (1) the coupling created between the normal probes is non-local-no current need be sent between them, (2) the resultant non-local signals decay rapidly as the probe separation is increased, exponentially over a superconducting coherence length ξ S or faster 4,5,7 and (3) the processes create quantum phase coherence between the two probes. Previous experiments looking for evidence of elastic cotunnelling and CAR have used normal-superconductor-normal and ferromagnetsuperconductor-ferromagnet devices. A current is sent across one normal-superconductor or ferromagnet-superconductor interface and non-local voltages are measured on the other normal or ferromagnet probe located less than a coherence length from the interface [10][11][12] . Although the measured non-local signals exhibit behaviour consistent with predictions (1) and (2), the coherent nature of the non-local signals has not been demonstrated. To establish the presence of non-local coherence, we have attached a hybrid normal-superconducting loop known as an Andreev interferometer [13][14][15] to one of the normal probes in a normal-superconductor-normal device. Modifying the phase of the electrons in the normal part of the Andreev interferometer by threading a magnetic flux through the loop leads to oscillations in the resistance of the loop with a period equal to the superconducting flux quantum Φ 0 = h/2e. Periodic oscillations can also be seen in the non-local resistance measured using normal probes placed off the interferometer, but coupled to it by a supercondu...

Cooper Pair Splitting by Means of Graphene Quantum Dots

“…DOI A Cooper pair, splitting from a superconductor into two different normal metal terminals [1,2], is a natural source of nonlocal entangled electrons, which is an essential resource for quantum information processing [3]. During the past decade, many efforts have been made to split Cooper pairs into metal [4][5][6][7], InAs nanowire [8][9][10], and carbon nanotube [11,12]. In a normal-superconductor-normal (NSN) type of metallic structure, evidence of entangled pairs has been reported using combined conductance and noise correlation measurements in two SN junctions [7].…”

Focused crossed Andreev reflection

“…Resonant enhancement of CAR due to Andreev bound states at an NS interface has been proposed [23,24]. Recently, an Andreev interferometer was used to demonstrate the phase coherent nature of CAR and ET [11]. We show here that electron focusing clearly discriminates between CAR and ET, which might be useful to maximize entanglement generation in artificial solid state devices.…”

“…The second process, involving a virtual excitation, is also referred to as electron co-tunneling. The competition between CAR and ET has been studied for about a decade [1][2][3][5][6][7][8][9][10][11]. Theoretical papers report that ET typically dominates CAR in linear response [3,9].…”

Density of states of chaotic Andreev billiards

“…To obtain the desired generating function of the semiclassical correlation functions, we set F = G(1 − i ) in (22), along with the other substitutions in (25) and (26), (30) so that by expanding g and hence G in powers of r, we obtain all the correlation functions C( ,n). This can be simplified by rearranging (30) and substituting into (29) to get the cubic for G directly,…”

“…17 and 18 and references therein for example), though in this paper we focus instead on closed structures. Naturally, this choice has the consequence of leaving aside some exciting recent results such as, for example, the statistical properties of the conductance, 19 the magnetoconductance in Andreev quantum dots, 20 resonant tunneling, 21 and the thermoelectric effect 22,23 in Andreev interferometers. In closed systems, one of the most noticeable manifestations of the proximity effect is the suppression of the density of states (DOS) of the normal metal just above the Fermi energy.…”