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Register a new userThe Crossover between Liquid and Solid Electron Phases in Quantum Dots: A Large-Scale Configuration-Interaction Study
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Authors
Massimo Rontani
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We study the crossover between liquid and solid electron phases in a two-dimensional harmonic trap as the density is progressively diluted. We infer the formation of geometrically ordered phases from charge distributions and pair correlation functions obtained via a large scale configuration interaction calculation.
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The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover only governed by the density parameter $r_s$. For $r_s>r_c$, the data are consistent with a Wigner molecule description, while for $r_s<r_c$, Fermi liquid behavior is recovered. The crossover value $r_c approx 4$ is surprisingly small.
The nature of the state at low Landau-level filling factors has been a longstanding puzzle in the field of the fractional quantum Hall effect. While theoretical calculations suggest that a crystal is favored at filling factors $ ulesssim 1/6$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $ u=$ 1/7, 2/11, 2/13, 3/17, 3/19, 1/9, 2/15 and 2/17, which belong to the standard sequences $ u=n/(6npm 1)$ and $ u=n/(8npm 1)$. To address this paradox, we investigate the nature of some of the low-$ u$ states, specifically $ u=1/7$, $2/13$, and $1/9$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.
The melting temperature ($T_m$) of a solid is generally determined by the pressure applied to it, or indirectly by its density ($n$) through the equation of state. This remains true even for helium solidscite{wilk:67}, where quantum effects often lead to unusual propertiescite{ekim:04}. In this letter we present experimental evidence to show that for a two dimensional (2D) solid formed by electrons in a semiconductor sample under a strong perpendicular magnetic fieldcite{shay:97} ($B$), the $T_m$ is not controlled by $n$, but effectively by the textit{quantum correlation} between the electrons through the Landau level filling factor $ u$=$nh/eB$. Such melting behavior, different from that of all other known solids (including a classical 2D electron solid at zero magnetic fieldcite{grim:79}), attests to the quantum nature of the magnetic field induced electron solid. Moreover, we found the $T_m$ to increase with the strength of the sample-dependent disorder that pins the electron solid.
We report electron transport studies in an encapsulated few-layer WTe$_2$ at low temperatures and high magnetic fields. The magnetoconductance reveals a temperature-induced crossover between weak antilocalization (WAL) and weak localization (WL) in quantum diffusive regime. We show that the crossover clearly manifests coexistence and competition among several characteristic lengths, including the dephasing length, the spin-flip length, and the mean free path. In addition, low temperature conductance increases logarithmically with the increase of temperature indicating an interplay of electron-electron interaction (EEI) and spin-orbit coupling (SOC). We demonstrate the existences and quantify the strengths of EEI and SOC which are considered to be responsible for gap opening in the quantum spin hall state in WTe2 at the monolayer limit.
We perform projective quantum Monte Carlo simulations of zigzag graphene nanoribbons within a realistic model with long-range Coulomb interactions. Increasing the relative strength of nonlocal interactions with respect to the on-site repulsion does not generate a phase transition but has a number of nontrivial effects. At the single-particle level we observe a marked enhancement of the Fermi velocity at the Dirac points. At the two-particle level, spin- and charge-density-wave fluctuations compete. As a consequence, the edge magnetic moment is reduced but the edge dispersion relation increases in the sense that the single-particle gap at momentum $q=pi/|{pmb a}_1|$ grows. We attribute this to nonlocal charge fluctuations which assist the spin fluctuations to generate the aforementioned gap. In contrast, the net result of the interaction-induced renormalization of different energy scales is a constant spin-wave velocity of the edge modes. However, since the particle-hole continuum is shifted to higher energies---due to the renormalization of the Fermi velocity---Landau damping is reduced. As a result, a roughly linear spin-wave-like mode at the edge spreads out through a larger part of the Brillouin zone.
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