Quantum rings for beginners: Energy spectra and persistent currents

The energy and persistent current spectra for a relativistic fermion on a ring is studied in details. The nonlinear nature of persistent current in relativistic regime and its dependence on particle mass and ring radius are analysed thoroughly. For a particular ring radius we find the existence of a critical mass at which the single ring current doesn't depend on the flux. In lower mass regime the total current spectrum shows plateaus at different height which appears periodi...

We explore the behavior of persistent current and low-field magnetic response in mesoscopic one-channel rings and multi-channel cylinders within the tight-binding framework. We show that the characteristic properties of persistent current strongly depend on total number of electrons $N_e$, chemical potential $\mu$, randomness and total number of channels. The study of low-field magnetic response reveals that only for one-channel rings with fixed $N_e$, sign of the low-field c...

We show exactly that small Hubbard rings exhibit unusual kink-like structures giving anomalous oscillations in persistent current. Singular behavior of persistent current disappears in some cases. In half-filled systems mobility gradually drops to zero with interaction, while it converges to some finite value in non-half-filled cases.

We analytically study the magnetic response of persistent current (PC) in normally non-interacting mesoscopic rings of bimodal potential with nearest neighboring interactions (t) and alternating site energies. It is shown that a ring of perimeter (N) and width (M) generally shows weak diamagnetic, breaking the even-odd rule of electron filling. Especially, a maximal paramagnetic current in primary F0/2 period is predicted at N=(2p+1)(M+1) with odd M and integer p, while a max...

We theoretically analyze equilibrium fluctuations of persistent current (PC) in nanorings. We demonstrate that these fluctuations persist down to zero temperature provided the current operator does not commute with the total Hamiltonian of the system. For a model of a quantum particle on a ring we explicitly evaluate PC noise power which has the form of sharp peaks at frequencies set by the corresponding interlevel distances. In rings with many conducting channels a much smoo...

We calculate the persistent current of 1D rings of spinless fermions with short-range interactions on a lattice with up to 20 sites, and in the presence of disorder, for various band fillings. We find that {\it both} disorder and interactions always decrease the persistent current by localizing the electrons. Away from half-filling, the interaction has a much stronger influence in the presence of disorder than in the pure case.

Persistent current in one-dimensional non-superconducting mesoscopic rings threaded by a slowly varying magnetic flux $\phi$ is studied based on the tight-binding model. The behavior of the persistent current is discussed in three aspects: (a) single hopping impurity, (b) in-plane electric field and (c) in presence of some foreign atoms.

Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect, a paradigm of quantum mechanical phase coherence. The phase coherence of transport through a quantum dot embedded in one arm of an open ring has been demonstrated. The energy spectrum of closed rings has only recently been analysed by optical experiments and is the basis for the prediction of persistent curre...

In the present review we make a comprehensive analysis of our understanding on electron transport in mesoscopic single-channel rings and multi-channel cylinders within a tight-binding framework. A spectacular mesoscopic phenomenon where a non-decaying current circulates in a small conducting loop is observed upon the application of an Aharonov-Bohm flux $\phi$. To understand its behavior one has to focus attention on the interplay of quantum phase coherence, electron-electron...

We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux and temperature dependence of the persistent current in a perfect ring is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier that pins the Wigner crystal, the current is suppressed and its temperature dependence is...