Persistent Currents in Normal Metal Rings

Abstract

Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. To address these issues we have developed a new technique for detecting persistent currents which offers greatly improved sensitivity and reduced measurement back action. This allows us to measure the persistent current in metal rings over a wider range of temperature, ring size, and magnetic field than has been possible previously. We find that measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons. An electrical current induced in a resistive circuit will rapidly decay in the absence of an applied voltage. This decay reflects the tendency of the circuit's electrons to dissipate energy and relax to their ground state. However quantum mechanics predicts that the electrons' many-body ground state (and, at finite temperature, their thermal equilibrium state) may itself contain a "persistent" current which flows through the resistive circuit without dissipating energy or decaying. A dissipationless equilibrium current flowing through a resistive circuit is highly counterintuitive, but it has a familiar analog in atomic physics: some atomic species' electronic ground states possess non-zero orbital angular momentum, equivalent to a current circulating around the atom. Theoretical treatments of persistent currents (PC) in resistive metal rings have been developed over a number of decades (see [1,2] and references therein). Calculations which take 1

Searching for thermal signatures of persistent currents in normal-metal rings

“…Due to the weak magnitude of the persistent current, only the first two harmonics m = 1, 2 in Eq. (1) were observed experimentally [4][5][6][7][8][9][10]. They were also in the focus of numerous theoretical studies (see Refs.…”

“…If early observations were somewhat contradictory [5,7], more recent works have demonstrated an impressive agreement between experiment and the noninteracting electron theory [9,10,18]. The second harmonics I 2 , on the contrary, still represents a challenge for both theory and experiment.…”

“…The ensemble of the existing literature indicates that the statistical properties of the first harmonics I 1 can be understood within the model of noninteracting electrons, whereas the second harmonics I 2 is dominated by interaction effects. In the experiments performed on single rings [5,9] or on small ensembles of identical rings [7,10], both the first and the second harmonics of I have been detected. Hence, the measured period of current oscillation with Φ is Φ 0 .…”

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

“…It is possible that the dependence of the averaged pumped current on the initial state and on the overall phase of the oscillating potentials on a ring with no mechanisms for momentum and phase relaxation can be observed experimentally. For mesoscopic rings which have a large number of impurities which lead to elastic scattering, the transport is diffusive and is characterized by a diffusive round-trip time τ d which is equal to 3L 2 /(v F l c ), where l c is the mean free path and L is the circumference of the ring [65]. Another important length scale for ring systems is the phase coherence length l φ which depends strongly on the temperature [64,66,67].…”

Magnetic response of non-interacting and interacting electrons in a Möbius strip

“…This is the so-called persistent current, an obvious demonstration of AB effect, and was first proposed by Büttiker et al 8 during early 80's. Following this pioneering work, substantial theoretical and experimental works [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] have been done along this line to understand different aspects of persistent current and other related issues in isolated conducting loops. In particular, the physics of quantum rings has always been the subject of intense research due to its potential applications in designing electronic, spintronic, optoelectronic and information processing devices.…”