Liquids crystallize as they cool; however, when crystallization is avoided in some way, they supercool, maintaining their liquidity, and freezing into glass at low temperatures, as ubiquitously observed. These metastable states crystallize over time through the classical dynamics of nucleation and growth. However, it was recently found that Coulomb interacting electrons on charge-frustrated triangular lattices exhibit supercooled liquid and glass with quantum nature and they crystallize, raising fundamental issues : what features are universal to crystallization at large and specific to that of quantum systems? Here, we report our experimental challenges that address this issue through the spatiotemporal observation of electronic crystallization in an organic material. With Raman microspectroscopy, we are the first to successfully perform real-space and real-time imaging of electronic crystallization. The results directly capture strongly temperature-dependent crystallization profiles indicating that nucleation and growth proceed at distinctive temperature-dependent rates, which is common to conventional crystallization. Remarkably, however, the growth rate is many orders of magnitude larger than that in the conventional case, which is attributable to the quantum effect. The temperature characteristics of nucleation and growth are universal, whereas unusually fast growth kinetics features quantum crystallization where a quantum-to-classical catastrophe occurs in interacting electrons.
One-dimensional (1D) electron-hole (e-h) systems in a high-density regime is investigated by means of bozonization techniques. It turned out that the systems are insulating even at the high density limit and that the exciton Mott transition (insulator-to-metal transition) never occurs at absolute zero temperature. The insulating ground state exhibits a strong instability towards the crystallization of biexcitons.
Wigner crystallization of electrons in a 2D quantum dots is reported. It proceeds in two stages: I) via radial ordering of electrons on shells and II) freezing of the inter-shell rotation. The phase boundary of the crystal is computed in the whole temperature--density plane, and the influence of quantum effects and of the particle number is analyzed.
Charge ordering (CO) is a phenomenon in which electrons in solids crystallize into a periodic pattern of charge-rich and charge-poor sites owing to strong electron correlations. This usually results in long-range order. In geometrically frustrated systems, however, a glassy electronic state without long-range CO has been observed. We found that a charge-ordered organic material with an isosceles triangular lattice shows charge dynamics associated with crystallization and vitrification of electrons, which can be understood in the context of an energy landscape arising from the degeneracy of var…
The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives rise to a rich sequence of structural transitions upon varying the particle density. In addition, the concurrence of low-dimensional electron motion and isotropic Coulomb interactions leads to a sizeable stabilization of the Wigner crystal, which could be one of the mechanisms at the origin of the charge ordered phases frequently observed in such compounds.
Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and the orientational correlation functions are calculated for the first time. We have found an indication that the solid phase has a quasi-long-range (power-law) positional order along with a long-range orientational order. This indicates that, although the long-range Coulomb interaction is outside the scope of Mermin's theorem, the absence of ordinary crystallin…
We consider a \textit{mass-asymmetric} electron and hole bilayer. Electron and hole Coulomb correlations and electron and hole quantum effects are treated on first princles by path integral Monte Carlo methods. For a fixed layer separation we vary the mass ratio $M$ of holes and electrons between 1 and 100 and analyze the structural changes in the system. While, for the chosen density, the electrons are in a nearly homogeneous state, the hole arrangement changes from homogeneous to localized, with increasing $M$ which is verified for both, mesoscopic bilayers in a parabolic trap and for a macr…
We investigate the effects of coupling between the two zigzag edges of graphene nanoribbons on the Wigner crystallization of electrons and holes using a combination of tight-binding, mean field Hubbard and many-body configuration interaction methods. We show that the thickness of the nanoribbon plays a crucial role in the formation of Wigner crystal. For ribbon widths smaller than 16 \mboxÅ, increased kinetic energy overcomes the long-range Coulomb repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38 \mboxÅ wide, strong Wigner localization is observed for even number…
A femtosecond laser-irradiated crystallizing technique is tried to convert amorphous Sb2Te3 film into crystalline film. Sensitive coherent phonon spectroscopy (CPS) is used to monitor the crystallization of amorphous Sb2Te3 film at the original irradiation site. The CPS reveals that the vibration strength of two phonon modes that correspond to the characteristic phonon modes of crystalline Sb2Te3, enhances with increasing laser irradiation fluence (LIF), showing the rise of the degree of crystallization with LIF and that femtosecond laser irradiation is a good post-treatment technique. Time-re…
We introduce a new approach for the correlation energy of one- and two-valley two-dimensional electron gas (2DEG) systems. Our approach is based on a random phase approximation at high densities and a classical approach at low densities, with interpolation between the two limits. This approach gives excellent agreement with available Quantum Monte Carlo (QMC) calculations. We employ the two-valley 2DEG model to describe the electron correlations in monolayer transition metal dichalcogenides (TMDs). The zero-temperature transition from a Fermi liquid to a quantum Wigner crystal phase in monolay…
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb $U/r$ potential. The studies of models without disorder and spin and including disorder and spin show that the electron solid is formed in two stages, giving rise to an intriguing solid-liquid regime at intermediate couplings
We consider the fate of the Wigner crystal state in a two dimensional system of massive Dirac electrons as the effective fine structure constant $α$ is increased. In a Dirac system, larger $α$ naively corresponds to stronger electron-electron interactions, but it also implies a stronger interband dielectric response that effectively renormalizes the electron charge. We calculate the critical density and critical temperature associated with quantum and thermal melting of the Wigner crystal state using two independent approaches. We show that at $α\gg 1$, the Wigner crystal state is best underst…
When electrons in a solid are excited to a higher energy band they leave behind a vacancy (hole) in the original band which behaves like a positively charged particle. Here we predict that holes can spontaneously order into a regular lattice in semiconductors with sufficiently flat valence bands. The critical hole to electron effective mass ratio required for this phase transition is found to be of the order of 80.
Using a periodic train of Lorentzian voltage pulses, which generates soliton-like electronic excitations called Levitons, we investigate the charge density backscattered off a quantum point contact in the fractional quantum Hall regime. We find a regular pattern of peaks and valleys, reminiscent of analogous self-organization recently observed for optical solitons in non-linear environments. This crystallization phenomenon is confirmed by additional side dips in the Hong-Ou-Mandel noise, a feature that can be observed in nowadays electron quantum optics experiments.
The ground state energy of the 2-D Wigner crystal is determined as a function of the thickness of the electron layer and the crystal structure. The method of evaluating the exchange-correlation energy is tested using known results for the infinitely-thin 2D system. Two methods, one based on the local-density approximation(LDA), and another based on the constant-density approximation (CDA) are established by comparing with quantum Monte-Carlo (QMC) results. The LDA and CDA estimates for the Wigner transition of the perfect 2D fluid are at $r_s=38$ and 32 respectively, compared with $r_s=35\pm5$…
The competition between kinetic energy and Coulomb interactions in electronic systems can lead to complex many-body ground states with competing superconducting, charge density wave, and magnetic orders. Here we study the low temperature phases of a strongly interacting zinc-oxide-based high mobility two dimensional electron system that displays a tunable metal-insulator transition. Through a comprehensive analysis of the dependence of electronic transport on temperature, carrier density, in-plane and perpendicular magnetic fields, and voltage bias, we provide evidence for the existence of com…
Critical gate distance for Wigner crystallization in the two-dimensional electron gas
Center for Computational Quantum Physics, Flatiron Institute（Flatiron Institute 计算量子物理中心）；Department of Physics, Stanford University（斯坦福大学物理系）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Department of Physics and Astronomy, Hofstra University（霍夫斯特拉大学物理与天文系）；Department of Physics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校物理系）
The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the non-perturbative fixed phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the $ν-κ$ plane, where $ν$ is the filling factor and $κ$ is the strength of Landau level mixing. The phase boundary is seen to exhibit a striking $ν$ dependence, with the states away from the magic filling factors $ν=n/(2pn+1)$ being much more susceptible to crystallization due to Landau level mixing t…
Dynamic Moiré Potentials and Robust Wigner Crystallization in Large-Scale Twisted Transition Metal Dichalcogenides
Hefei National Research Center for Physical Sciences at the Microscale, and Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家物理科学（微观）研究中心和合肥国家实验室）；Graduate School of Science and Technology, Keio University（庆应义塾大学理工学部研究生院）；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC), Keio University（庆应义塾大学可持续量子人工智能中心）；State Key Laboratory of Precision and Intelligent Chemistry, Department of Chemical Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China（中国科学技术大学精密与智能化学国家重点实验室、化学物理系和安徽应用数学中心）
Indirect excitons -- pairs of electrons and holes spatially separated in semiconductor bilayers or quantum wells -- are known to undergo Bose-Einstein condensation and to form a quantum fluid. Here we show that this superfluid may crystallize upon compression. However, further compression results in quantum melting back to a superfluid. This unusual behavior is explained by the effective interaction potential between indirect excitons which strongly deviates from a dipole potential at small distances due to many-particle and quantum effects. Based on first principle path integral Monte Carlo s…
A system of confined charged electrons interacting via the long-range Coulomb force can form a Wigner crystal due to their mutual repulsion. This happens when the potential energy of the system dominates over its kinetic energy, i.e., at low temperatures for a classical system and at low densities for a quantum one. At $T=0$, the system is governed by quantum mechanics, and hence, the spatial density peaks associated with crystalline charge localization are sharpened for a lower average density. Conversely, in the classical limit of high temperatures, the crystalline spatial density peaks are …
Quantum dots may display fascinating features of strong correlation such as finite-size Wigner crystallization. We here review a few electron spectroscopies and predict that both inelastic light scattering and tunneling imaging experiments are able to capture clear signatures of crystallization.
In a certain regime of low carrier densities and strong correlations, electrons can crystallize into a periodic arrangement of charge known as Wigner crystal. Such phases are particularly interesting in one dimension (1D) as they display a variety of charge and spin ground states which may be harnessed in quantum devices as high-fidelity transmitters of spin information. Recent theoretical studies suggest that the strong Coulomb interactions in Mott insulators and other flat band systems, may provide an attractive higher temperature platform for Wigner crystallization, but due to materials and…
We present a variational study of the 2D and 3D Wigner crystal phase of large polarons. The method generalizes that introduced by S. Fratini,P.\ Qu{é}merais [Mod. Phys. Lett. B {\bf 12} 1003 (1998)]. We take into account the Wigner crystal normal modes rather than a single mean frequency in the minimization procedure of the variational free energy. We calculate the renormalized modes of the crystal as well as the charge polarization correlation function and polaron radius. The solid phase boundaries are determined via a Lindemann criterion, suitably generalized to take into account the classic…
We consider temperature-induced melting of a Wigner solid in one dimensional (1D) and two dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we f…
We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the…
The existence of Wigner crystallization, one of the most significant hallmarks of strong electron correlations, has to date only been definitively observed in two-dimensional systems. In one-dimensional (1D) quantum wires Wigner crystals correspond to regularly spaced electrons; however, weakening the confinement and allowing the electrons to relax in a second dimension is predicted to lead to the formation of a new ground state constituting a zigzag chain with nontrivial spin phases and properties. Here we report the observation of such zigzag Wigner crystals by use of on-chip charge and spin…
The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, i…
We study Wigner crystallization of electron systems in phosphorene quantum dots with confinement of an electrostatic origin with both circular and elongated geometry. The anisotropy of the effective mass allows for the formation of Wigner molecules in the laboratory frame with a confined charge density that has lower symmetry than the confinement potential. We find that in circular quantum dots separate single-electron islands are formed for two and four confined electrons but not for three trapped carriers. The spectral signatures of the Wigner crystallization to be resolved by transport spec…
