Dynamics of Vortices and Charges in Two Dimensional Arrays of Small Josephson Junctions
Doctoral thesis, 1994
This thesis is based on experimental work on two dimensional (2D) Josephson junction arrays. The junctions are small (~ 0.004~0.04 µm2) so that the charging energy E~ e2/2C associated with the junction capacitance C is large. In this case, charging effect becomes important and leads to a zero-current state called Coulomb blockade of Cooper pair tunneling. This zero-current state is complementary to the zero- voltage state seen in the Josephson effect. Emphasis in this work is placed on the competition between the Josephson effect and the charging effect; A competition which results in a rich behavior of both the current-voltage (IV) characteristics and the temperature dependence of zero bias resistance RO(T). This thesis explores fundamental properties in this new field and the experimental results probe the vortex dynamics, the charge dynamics and the region where they overlap. The arrays are characterized by two parameters, x ~ EJ/EC and .alpha.N ~ RQ/RN,where EJ ~ (.DELTA.O/2)(RQ/RN) is the Josephson coupling energy, RN is the junction normal state resitance. RQ ~ 6.45 k.OMEGA. is the quantum resistance, .DELTA.0 is the superconducting gap.
In a region where x>=0.8 and .alpha.N >=0.5, the characteristics of the arrays can be described by the motion of vortices. The R0(T) at high temperatures display a Kosterlitz-Thouless vortex pair-unbinding transition. Below the transition temperature, we observe a thermal activation behavior, R0 ~ exp(Eb/kBT), where the effective barrier height, Eb, is proportional to EJ and is magnetic field dependent. At low temperatures, quantum fluctuations dominate and the resistance flattens off, becoming temperature independent. The flattening-off resistance is lower for arrays with large x and for arrays of larger size. The effective damping resistance which characterizes the flux-flow motion is found to be close to RN.
In the region where x>=0.27 and .alpha.N >=0.26, the transport properties are described by the motion of charges. The RO(T) behavior follows a simple Arrhenius form, RO ~exp(Ea/kBT), where the activation energy Ea is 1/4Ec in the normal state, and is between 1/4Ec and 1/4Ec + .DELTA.0 in the superconducting state. When in the normal state, the resistance at low temperatures (T<100mK) also flattens off and becomes temperature independent, which is attributed to quantum fluctuations of the charge. The flattening- off resistance decreases exponentially with decreasing RN.
For the samples with 0.8<=x<=1.7, 0.5<=.alpha.N<=0.8, R0(T) can be tuned from a superconducting-like to insulating-like behavior by applying a small magnetic field. This superconductor-insulator transition was analyzed within the context of a scaling theory. We show resistance scaling curves over 5 orders of magnitude, from which the zero temperature fixed point resistance at the S-I transition is precisely determined.