Quantum tunneling of the interfaces between normal-metal and superconducting regions of a type-I Pb superconductor

Abstract

Evidence of a non-thermal magnetic relaxation in the intermediate state of a type-I superconducor is presented. It is attributed to quantum tunneling of interfaces separating normal and superconducting regions. Tunneling barriers are estimated and temperature of the crossover from thermal to quantum regime is obtained from Caldeira-Leggett theory. Comparison between theory and experiment points to tunneling of interface segments of size comparable to the coherence length, by steps of order one nanometer. When placed in the magnetic field, type-I superconductors do not develop flux lines. Instead, they exhibit intermediate state in which the sample splits into normal and superconducting regions separated by planar interfaces of positive energy [12][13][14]. Recently, there has been a renewed interest to the equilibrium structure, pinning, and dynamics of interfaces in type-I superconductors [15][16][17][18][19][20]. Pure lead has been mostly used as a prototypical experimental system. In the presence of pinning centers the interfaces adjust to the pinning potential by developing curvature as is schematically shown in Fig. 1. Pinning by point or small-volume defects should result in a broad distribution of energy barriers. It is, therefore, plausible that at low temperature type-I superconductors continue to relax towards equilibrium via quantum diffusion of interfaces. This situation is similar to the diffusion of domain walls in disordered ferromagnets with one essential difference. Contrary to a ferromagnetic domain wall, the dynamics of the planar interface in a superconductor should be dominated by dissipation.At low temperature the decay of metastable states created by pinning provides slow relaxation of magnets and superconductors towards thermal equilibrium. This relaxation is known as magnetic after-effect. At finite temperature it may occur via thermal activation with a probability proportional to exp(−U B /T ) where U B is the energy barrier. As T → 0 thermal processes die out and the only channel of escape from the metastable state becomes underbarrier quantum tunneling. Its probability is proportional to exp(−I ef f /h) where I ef f is the effective action associated with tunneling. The pre-exponential factors in the two expressions are of lesser importance because the dependence of the probability on the parameters is dominated by the exponents. Equating the two exponents, one finds that the crossover from thermal activation to quantum tunneling occurs at T Q ≈hU B /I ef f . Experimental evidence of such a crossover in type-II su-

Equilibrium intermediate-state patterns in a type-I superconducting slab in an arbitrarily oriented applied magnetic field

“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. For further background we refer the reader to several books and reviews.…”

Magnetic field dependence of the quantum tunneling of normal-superconductor interfaces in a type-I Pb superconductor

“…The sample investigated was a thin disk of extremely pure (99.999 at.%) type-I superconducting Pb with a surface area of 40 mm 2 and a thickness of 0.2 mm, whose preparation and magnetic characterization have been given elsewhere [14]. Magnetic measurements were carried out in a commercial superconducting quantum interference device (SQUID) magnetometer at temperature values from T = 1.80 K to T = 7.00 K with a low temperature stability better than 0.01 K [17], by applying the magnetic field, H, always parallel to the revolution axis of the sample, with intensities up to 1 kOe.…”

“…Evidence of a mechanism of quantum nature as responsible for the relaxation of the system was found below a certain crossover temperature. Resemblances between the movement of normal-superconductor interfaces (NSI) in type-I superconductors and that of domain walls in ferromagnets suggest that the logarithmic relaxation observed so far in Pb samples is brought about by the dissipation of the NSI traversing a broad distribution of local pinning potentials associated with the defects of the sample [14]. A model for quantum tunneling of interfaces (QTI) based on the Caldeira-Leggett theory for quantum dissipation [16] was recently developed considering that the magnetization evolves with time due to the formation and decay of mesoscopic bumps in the NSI, and was found to fit rather well the experimental data [14].…”

“…Resemblances between the movement of normal-superconductor interfaces (NSI) in type-I superconductors and that of domain walls in ferromagnets suggest that the logarithmic relaxation observed so far in Pb samples is brought about by the dissipation of the NSI traversing a broad distribution of local pinning potentials associated with the defects of the sample [14]. A model for quantum tunneling of interfaces (QTI) based on the Caldeira-Leggett theory for quantum dissipation [16] was recently developed considering that the magnetization evolves with time due to the formation and decay of mesoscopic bumps in the NSI, and was found to fit rather well the experimental data [14]. The pinning barriers act as a source for metastability along the descending branch of the hysteresis cycle and are responsible for the temperature-dependent irreversibility exhibited by the samples in which both geometrical barrier and stress defects are present [15].…”

“…The properties of type-I superconductors have been studied, both theoretically and experimentally, for nearly one century [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Historically, the presence of irreversible phenomena in the magnetic hysteresis cycle had been associated to physical or chemical defects such as dislocations or impurities [2].…”