Formation of defects in multirow Wigner crystals

We study the structural properties of a quasi-one-dimensional classical Wigner crystal, confined in the transverse direction by a parabolic potential. With increasing density, the one-dimensional crystal first splits into a zigzag crystal before progressively more rows appear. While up to four rows the ground state possesses a regular structure, five-row crystals exhibit defects in a certain density regime. We identify two phases with different types of defects. Furthermore, using a simplified model, we show that beyond nine rows no stable regular structures exist.Comment: 11 pages, 8 figure

Optical exciton Aharonov-Bohm effect, persistent current, and magnetization in semiconductor nanorings of type I and II

The optical exciton Aharonov-Bohm effect, i. e. an oscillatory component in the energy of optically active (bright) states, is investigated in nanorings. It is shown that a small effective electron mass, strong confinement of the electron, and high barrier for the hole, achieved e. g. by an InAs nanoring embedded in an AlGaSb quantum well, are favorable for observing the optical exciton Aharonov-Bohm effect. The second derivative of the exciton energy with respect to the magnetic field is utilized to extract Aharonov-Bohm oscillations even for the lowest bright state unambiguously. A connection between the theories for infinitesimal narrow and finite width rings is established. Furthermore, the magnetization is compared to the persistent current, which oscillates periodically with the magnetic field and confirms thus the non-trivial (connected) topology of the wave function in the nanoring.Comment: 12 pages, 11 figure

Some Exact Solutions For The Classical Hall Effect In Inhomogeneous Magnetic Field

The classical Hall effect in inhomogeneous systems is considered for the case of one-dimensional inhomogeneity. For a certain geometry of the problem and for the magnetic field linearly depending on the coordinate the density of current distribution corresponds to the skin-effect.Comment: 5 pages, LaTe

Quantum phase transition in quantum wires controlled by an external gate

We consider electrons in a quantum wire interacting via a long-range Coulomb potential screened by a nearby gate. We focus on the quantum phase transition from a strictly one-dimensional to a quasi-one-dimensional electron liquid, that is controlled by the dimensionless parameter $n x_0$, where $n$ is the electron density and $x_0$ is the characteristic length of the transverse confining potential. If this transition occurs in the low-density limit, it can be understood as the deformation of the one-dimensional Wigner crystal to a zigzag arrangement of the electrons described by an Ising order parameter. The critical properties are governed by the charge degrees of freedom and the spin sector remains essentially decoupled. At large densities, on the other hand, the transition is triggered by the filling of a second one-dimensional subband of transverse quantization. Electrons at the bottom of the second subband interact strongly due to the diverging density of states and become impenetrable. We argue that this stabilizes the electron liquid as it suppresses pair-tunneling processes between the subbands that would otherwise lead to an instability. However, the impenetrable electrons in the second band are screened by the excitations of the first subband, so that the transition is identified as a Lifshitz transition of impenetrable polarons. We discuss the resulting phase diagram as a function of $n x_0$.Comment: 18 pages, 8 figures, minor changes, published versio

First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy

We analyze in detail the fermionic self-energy \Sigma(\omega, T) in a Fermi liquid (FL) at finite temperature T and frequency \omega. We consider both canonical FLs -- systems in spatial dimension D >2, where the leading term in the fermionic self-energy is analytic [the retarded Im\Sigma^R(\omega,T) = C(\omega^2 +\pi^2 T^2)], and non-canonical FLs in 1<D <2, where the leading term in Im\Sigma^R(\omega,T) scales as T^D or \omega^D. We relate the \omega^2 + \pi^2 T^2 form to a special property of the self-energy -"the first-Matsubara-frequency rule", which stipulates that \Sigma^R(i\pi T,T) in a canonical FL contains an O(T) but no T^2 term. We show that in any D >1 the next term after O(T) in \Sigma^R(i\pi T,T) is of order T^D (T^3\ln T in D=3). This T^D term comes from only forward- and backward scattering, and is expressed in terms of fully renormalized amplitudes for these processes. The overall prefactor of the T^D term vanishes in the "local approximation", when the interaction can be approximated by its value for the initial and final fermionic states right on the Fermi surface. The local approximation is justified near a Pomeranchuk instability, even if the vertex corrections are non-negligible. We show that the strength of the first-Matsubara-frequency rule is amplified in the local approximation, where it states that not only the T^D term vanishes but also that \Sigma^R(i\pi T,T) does not contain any terms beyond O(T). This rule imposes two constraints on the scaling form of the self-energy: upon replacing \omega by i\pi T, Im\Sigma^R(\omega,T) must vanish and Re\Sigma^R (\omega, T) must reduce to O(T). These two constraints should be taken into consideration in extracting scaling forms of \Sigma^R(\omega,T) from experimental and numerical data.Comment: 22 pages, 3 figure