Session X1: Persistent Currents in Normal Metals

Capacitance, entanglement energetics and persistent currents of mesoscopic rings

Small rings are a quintessential mesoscopic system. As a consequence of quantum coherence small normal metal rings support a persistent current. Novel experimental techniques will permit to investigate rings with geometries which highlight the effects of interactions. We discuss rings with in-line and side quantum dots. In the Coulomb blockade regime we derive an effective two-state Hamiltonian and discuss the flux dependence of the Coulomb blockade peaks in the capacitance and the persistent current [1]. Different nearly degenerate charge configurations of the ring-dot system become entangled with an electrical environment. With an environment consisting of an external resistor capacitively coupled to the ring and dot the entire system maps on a spin boson problem. Analysis shows that the visibility of the persistent current decreases with increasing coupling to the environment [2]. The system-bath entanglement which is at the origin of this phenomenon can be detected by projective measurements of the energy of the ring-dot subsystem or the persistent current: even in the ground state of the total system the ring can be found with some probability in the energetically higher lying state [3]. The distribution of energy or of the persistent currents is a direct measure of the system bath entanglement. \\[4pt] [1] M. Buttiker and C. A. Stafford, Phys. Rev. Lett. 76, 495 (1996); \\[0pt] [2] P. Cedraschi, V. V. Ponomarenko, and M. Buttiker, Phys. Rev. Lett. 84, 346 (2000); P. Cedraschi and M. Buttiker, Annals of Physics, 289, 1 (2001). \\[0pt] [3] A. N. Jordan and M. Buttiker, Phys. Rev. Lett. 92, 247901 (2004); M. Buttiker and A. N. Jordan, Physica E 29, 272 (2005); K. Le Hur, Annals of Physics, 323, 2208 (2008).   

Persistent currents in superconducting rings well above their critical magnetic field

A striking manifestation of quantum mechanics is the existence of a dissipationless current in a non-superconducting metal ring. The persistent current is analogous to electrons orbiting the nucleus in an atom. The prediction that an atom-like persistent current could be observed in a micron size metal ring generated considerable interest. The persistent current is a signature of electronic phase coherence around the ring and offers insight into many issues in mesoscopic physics such as coherence and electron interactions in metals. The small magnitude of the current and the necessity of measuring it through its associated magnetic moment make persistent current experiments challenging. Few measurements have been reported and inconsistent results have left an unclear picture of the properties of persistent currents. In a novel approach to studying persistent currents we have developed a cantilever based torsional magnetometer capable of detecting a magnetic moment of 1 $\mu _B /Hz^{1/2}$and a force of 1.6 $aN/Hz^{1/2}$ at 300 mK. I present measurements of persistent currents in normal aluminum rings in the presence of large magnetic fields. We have measured single rings and arrays of rings. I discuss the temperature, ring size, and magnetic field dependence of the persistent current and compare it to theory and previous experiments.   

Observation of persistent currents in thirty metal rings, one at a time

It is a central prediction of quantum mechanics that a thermodynamically stable or ``persistent'' current should exist in sufficiently small electronic structures, even if they have a finite resistance as semiconducting or metallic samples do. The magnitude and even the sign of this current should vary greatly from sample to sample, but it should always have a periodic dependence on the applied magnetic field in ring-shaped samples. Due to the extremely high sensitivity required to measure persistent currents in normal metals, only a handful of experiments exist, and most measure ensemble-averaged properties. I will present measurements of the magnetic response of 33 gold rings, measured one ring at a time with a sensitive scanning SQUID technique. We find that the amplitude distribution and temperature dependence of the $h/e$-periodic persistent current is in good agreement with theoretical predictions. This result is in disagreement with the only previous experiment [1] measuring individual metal rings, which found a much larger response than expected in the three measured rings. Our results confirm predictions for the typical, disorder-realization dependent $h/e$ persistent current in diffusive rings at the single ring level, and thus address a major open question in mesoscopic physics. \\[4pt] [1] V. Chandrasekhar et al., PRL \bf{67}, 3578 (1991).   

Effect of pair-breaking on superconductivity and on persistent currents well above the transition temperature

We consider the mesoscopic normal persistent current (PC) in a very low-temperature superconductor with a bare transition temperature much smaller than the Thouless energy. We show that in a rather broad range of pair-breaking strength, in-between the bare transition temperature and the Thouless energy, the transition temperature is renormalized to zero, but the PC is hardly affected. This may provide an explanation for the magnitude of the average PC's in the noble metals, as well as a way to determine their bare transition temperatures.   

Paramagnetic or diamagnetic persistent currents? A topological point of view

A persistent current flows at low temperatures in small conducting rings when they are threaded by a magnetic flux. I will discuss the sign of this persistent current (diamagnetic or paramagnetic response) in the special case of $N$ electrons in a one dimensional ring [1]. One dimension is very special in the sense that the sign of the persistent current is entirely controlled by the topology of the system. I will establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett using another topological argument. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). The situation is more interesting with unpolarized electrons where Leggett upper bound breaks down: rings with $N=4n$ exhibit either paramagnetic behavior or a superconductor-like current-phase relation. The topological argument provides a rigorous justification for the phenomenological Huckel rule which states that cyclic molecules with $4n + 2$ electrons like benzene are aromatic while those with 4n electrons are not. \\[4pt] [1] Xavier Waintal, Genevi\`eve Fleury, Kyryl Kazymyrenko, Manuel Houzet, Peter Schmitteckert, and Dietmar Weinmann {\it Phys. Rev. Lett.}{\bf 101}, 106804 (2008).