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Register a new userThermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid
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A sufficiently large perpendicular magnetic field quenches the kinetic (Fermi) energy of an interacting two-dimensional (2D) system of fermions, making them susceptible to the formation of a Wigner solid (WS) phase in which the charged carriers organize themselves in a periodic array in order to minimize their Coulomb repulsion energy. In low-disorder 2D electron systems confined to modulation-doped GaAs heterostructures, signatures of a magnetic-field-induced WS appear at low temperatures and very small Landau level filling factors ($ usimeq1/5$). In dilute GaAs 2D textit{hole} systems, on the other hand, thanks to the larger hole effective mass and the ensuing Landau level mixing, the WS forms at relatively higher fillings ($ usimeq1/3$). Here we report our measurements of the fundamental temperature vs. filling phase diagram for the 2D holes WS-liquid textit{thermal melting}. Moreover, via changing the 2D hole density, we also probe their Landau level mixing vs. filling WS-liquid textit{quantum melting} phase diagram. We find our data to be in good agreement with the results of very recent calculations, although intriguing subtleties remain.
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Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers.
We report the first experimental observation of a characteristic nonlinear threshold behavior from dc dynamical response as an evidence for a Wigner crystallization in high-purity GaAs 2D hole systems in zero magnetic field. The system under increasing current drive exhibits voltage oscillations with negative differential resistance. They confirm the coexistence of a moving crystal along with striped edge states as observed for electrons on helium surfaces. However, the threshold is well below the typical classical levels due to a different pinning and depinning mechanism that is possibly related to a quantum process.
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.
Spin splitting in the integer quantum Hall effect is investigated for a series of Al$_{x}$Ga$_{1-x}$As/GaAs heterojunctions and quantum wells. Magnetoresistance measurements are performed at mK temperature to characterize the electronic density of states and estimate the strength of many body interactions. A simple model with no free parameters correctly predicts the magnetic field required to observe spin splitting confirming that the appearance of spin splitting is a result of a competition between the disorder induced energy cost of flipping spins and the exchange energy gain associated with the polarized state. In this model, the single particle Zeeman energy plays no role, so that the appearance of this quantum Hall ferromagnet in the highest occupied Landau level can also be thought of as a magnetic field induced Stoner transition.
We identify three-dimensional higher-order superconductors characterized by the coexistence of one-dimensional Majorana hinge states and gapless surface sates. We show how such superconductors can be obtained starting from the model of a spinful quadrupolar semimetal with two orbitals and adding an s-wave superconducting pairing term. By considering all the possible s-wave pairings satisfying Fermi-Dirac statistics we obtain six different superconducting models. We find that for two of these models a flat-band of hinge Majorana states coexist with surface states, and that these models have a non-vanishing quadrupole-like topological invariant. Two of the other models, in the presence of a Zeeman term, exhibit helical and dispersive hinge states localized only at two of the four hinges. We find that these states are protected by combinations of rotation and mirror symmetries, and that the pair of corners exhibiting hinge states switches upon changing the sign of the Zeeman term. Furthermore, we show that these states can be localized to a single hinge with suitable perturbations. The remaining two models retain gapless bulk and surface states that spectroscopically obscure any possible hinge states.
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