Quantum Crystals Research Articles

Unified Analytic Melt-Shear Model in the Limit of Quantum Melting

Quantum melting is the phenomenon of cold (zero-temperature) melting of a pressure-ionized substance which represents a lattice of bare ions immersed in the background of free electrons, i.e., the so-called one-component plasma (OCP). It occurs when the compression of the substance corresponds to the zero-point fluctuations of its ions being so large that the ionic ordered state can no longer exist. Quantum melting corresponds to the classical melting curve reaching a turnaround point beyond which it starts going down and eventually terminates, when zero temperature is reached, at some critical density. This phenomenon, as well as the opposite phenomenon of quantum crystallization, may occur in dense stellar objects such as white dwarfs, and may play an important role in their evolution that requires a reliable thermoelasticity model for proper physical description. Here we suggest a modification of our unified analytic melt-shear thermoelasticity model in the region of quantum melting, and derive the corresponding Grüneisen parameters. We demonstrate how the new functional form for the cold shear modulus can be combined with a known equation of state. One of the constituents of the new model is the melting curve of OCP crystal which we also present. The inclusion of quantum melting implies that the modified model becomes applicable in the entire density range of the existence of the solid state, up to the critical density of quantum melting above which the solid state does not exist. Our approach can be generalized to model melting curves and cold shear moduli of different solid phases of a multi-phase material over the corresponding ranges of mechanical stability.

Equilibrium and Non-Equilibrium Lattice Dynamics of Anharmonic Systems.

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation-dissipation theorem and the Donsker-Furutsu-Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures.

White lead: A new naturally occurring 2D material

Atomic scale crystallographic structures of a quantum crystals depend on substrate, interfacial strain, defects, surface functionalities etc., which make it challenging to precisely control. To achieve high quality material, UHV conditions are prerequisite, which makes it costly. Naturally occurring 2D materials have tremendous significance in this regard. White lead, having weak interlayer coupling and easily found in natural ores have never been exfoliated. Keeping the novelty in mind, one needs to explore its physical as well as chemical behaviour and look out for appropriate applications. We for the first time, therefore, have sonochemically exfoliated white lead, and established its physical and chemical behaviour. We have also blended it with graphene oxide and explored its gas sensing applications and found the hybrid system to be very selective for NH3 gas. White lead, a naturally occurring 2D material; has been exfoliated for the first time and its hybrid with graphene oxide has been explored for gas sensing.Graphical abstractWhite lead, a naturally occurring 2D material; has been exfoliated for the first time and its hybrid with graphene oxide has been explored for gas sensing.

Band repulsion in periodically modulated lattice models and electromagnetic systems

Periodically modulated quantum crystals and their photonic analogs---also known as Floquet crystals (FCs)---are characterized by continuous quasienergy bands separated from each other by spectral gaps. Meanwhile, a separate class of periodically driven systems---the so-called time crystals (TCs)---have an entirely different band structure characterized by gaps in their Bloch momenta. The reasons for such starkly different properties of the FCs and TCs are uncovered and time-averaged perturbation theory is used to derive the criteria for band gaps opening in quasienergy, Bloch momentum, or both. Examples from electrodynamics and from a Su-Schrieffer-Heeger lattice model illustrate the emergence of non-Hermiticity, exceptional points, and amplified edge states in periodically driven systems.

Anomalous and normal dislocation modes in Floquet topological insulators

Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial insulator into a Floquet topological insulator (FTI) that accommodates nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe FTIs as well as unconventional π-trivial insulator in the bulk of driven quantum systems by supporting normal and anomalous modes, localized near the defect core. Respectively, normal and anomalous dislocation modes reside at the Floquet zone center and boundaries. We exemplify these outcomes specifically for two-dimensional (2D) Floquet Chern insulator and px + ipy superconductor, where the dislocation modes are respectively constituted by charged and neutral Majorana fermions. Our findings should be, therefore, instrumental in probing Floquet topological phases in the state-of-the-art experiments in driven quantum crystals, cold atomic setups, and photonic and phononic metamaterials through bulk topological lattice defects.

Fractonic gauge theory of smectics

Motivated by striped correlated quantum matter, and the recently developed duality between elasticity of a two-dimensional (2D) crystal and a gauge theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional (2D) quantum smectic, where the disclination is mapped onto the fractonic charge, that we demonstrate can only move transversely to smectic layers. This smectic gauge theory dual also emerges from a gauge dual of a quantum crystal through a Higgs transition corresponding to a single flavor of its dipole condensation, an anisotropic quantum melting via dislocation proliferation. A condensation of the second flavor of dislocations a corresponds to another Higgs transition describing the smectic-to-nematic melting. We also utilize the electrostatic limit of this duality to formulate a melting of a 2D classical smectic in terms of a higher derivative sine–Gordon model, demonstrating its instability to a nematic at any nonzero temperature. Generalizing this classical duality to a 3D smectic, gives formulation of a 3D nematic-to-smectic transition in terms of an anisotropic Abelian-Higgs model.

The Nonlinear Schrödinger Equation for Orthonormal Functions: Existence of Ground States

We study the nonlinear Schr\"odinger equation for systems of $N$ orthonormal functions. We prove the existence of ground states for all $N$ when the exponent $p$ of the non linearity is not too large, and for an infinite sequence $N_j$ tending to infinity in the whole range of possible $p$'s, in dimensions $d\geq1$. This allows us to prove that translational symmetry is broken for a quantum crystal in the Kohn-Sham model with a large Dirac exchange constant.

Activation-Tunneling Dynamics of Extended Systems in a Periodic Potential Relief

The dynamics of objects of various physical origins in barrier structures of superconductors, magnetic materials, quantum crystals and other solids is determined by the rate of fluctuation decay of metastable states in intermediate minima of a potential barrier. In a low-temperature region important for many nanotechnological applications, thermal fluctuations are frozen and are replaced by quantum fluctuations, which lead to a specific phase transition in the dynamics. The character of this transition in various systems is an analog of second-order or first-order transitions. The transition temperature is dependent on the degree of metastability and can be controlled by external load. This dependence is calculated for an extended nanosystem in an oblique periodic relief like a “washboard” in a wide range of varying the load, and the results generalize the results known before.

Quantum crystals, Kagome lattice, and plane partitions fermion-boson duality

In this work, we study quantum crystal melting in three space dimensions. Using an equivalent description in terms of dimers in a hexagonal lattice, we recast the crystal melting Hamiltonian as an occupancy problem in a Kagome lattice. The Hilbert space is spanned by states labeled by plane partitions and writing them as a product of interlaced integer partitions, we define a fermion-boson duality for plane partitions. Finally, based upon the latter result we conjecture that the growth operators for the quantum Hamiltonian can be represented in terms of the affine Yangian ${\cal Y}[\widehat{\mathfrak{gl}}(1)]$.

АНАЛИЗ ПЕРСПЕКТИВ РАЗВИТИЯ ИСТОЧНИКОВ ОДИНОЧНЫХ ФОТОНОВ В СИСТЕМАХ КВАНТОВОГО РАСПРЕДЕЛЕНИЯ КЛЮЧЕЙ

Introduction: The analysis of the main directions of research in the field of creating sources of single photons for communication systems with quantum key distribution is carried out. Scientometric analysis based on Scopus database is used to identify the most promising areas and predict the trends in the field of single photon sources. Methods of single photon sources development and their applications in commercial communication systems with quantum key distribution is shown. At the time single photons sources based on quantum dots are the most developed and presented on the market. However, color centers in nanocrystals and carbon nanotubes are intensively studied. The prospects of creating compact and easy-to-use sources of single photons on telecommunication wavelengths is analyzed. There are many ways of realization of single photon sources design. Significant funding in China and Germany leads to notable growth of the technology. It was detected the main journals, author groups and organizations working in direction of single photon sources. Methods and Results: The research field of communication systems using sources of single photons is growing. It is available single photon sources on quantum dots and crystals. Applying of carbon nanotubes is promising for this problem according to some famous authors. It is revealed significant overlap of the research areas: single photon sources, quantum random number generators and quantum key distribution. At the time fundamental studies are implemented in technical devices with high potential for commercial applications.

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born-Oppenheimer approximation.

We develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born-Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron-ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born-Oppenheimer approximation. Based on the Kubo-Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.

Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models

This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals Hamiltonian becomes more transparent, and we determine expressions for the first 3 levels of plane partition states. A classical statistical model associated to local configurations in the Kagome lattice is also defined, and we show that a reduction of this classical system gives two Yang-Baxter integrable subsystems analogous to a descendant of the 6-vertex model.

Dynamics of a $$^4$$He Quantum Crystal in the Superfluid Liquid

The motion of helium crystals has been experimentally studied when the crystals fall in the superfluid liquid owing to gravity at temperatures above the roughening transitions where the whole crystal surface is in the atomically rough state. The rate of crystal fall at T = 1.25 K is higher than at T = 1.54 K. This is proof of the essential role of the normal component of superfluid helium in the deceleration of crystal motion. The pressure measurements in the container have shown the effect of surface kinetics on the motions of the crystal and its size. The fall of crystals with the low surface mobility at T = 1.54 K does not change the pressure significantly. The high surface mobility at T = 1.25 K results in decreasing the pressure in the container in the course of the fall of a crystal. The pressure drop exceeds the difference in the hydrostatic pressure between the initial and final positions of the crystal. After the stop, the pressure in the container relaxes to the difference mentioned above. This fact demonstrates an additional growth of the crystal in the flow of a superfluid liquid.

Many-body electronic structure of LaScO3 by real-space quantum Monte Carlo

We present real-space quantum Monte Carlo (QMC) calculations of the scandate ${\mathrm{LaScO}}_{3}$ that proved to be challenging for traditional electronic structure approaches due to strong correlation effects resulting in inaccurate band gaps from DFT and $GW$ methods when compared with existing experimental data. Besides calculating an accurate QMC band gap corrected for supercell size biases and in agreement with numerous experiments, we also predict the cohesive energy of the crystal using the standard fixed-node QMC without any empirical or nonvariational parameters. We show that promotion (optical) gap and fundamental gap agree with each other illustrating a clear absence of significant excitonic effects in the ideal crystal. We obtained these results in perfect consistency in two independent tracks that employ different basis sets (plane wave versus localized Gaussians), different codes for generating orbitals (quantum espresso versus crystal), different QMC codes (qmcpack versus qwalk) and different high-accuracy pseudopotentials (ccECPs versus Troullier-Martins) presenting the maturity and consistency of QMC methodology and tools for studies of strongly correlated problems.

High-frequency rectification via chiral Bloch electrons.

Rectification is a process that converts electromagnetic fields into a direct current. Such a process underlies a wide range of technologies such as wireless communication, wireless charging, energy harvesting, and infrared detection. Existing rectifiers are mostly based on semiconductor diodes, with limited applicability to small-voltage or high-frequency inputs. Here, we present an alternative approach to current rectification that uses the intrinsic electronic properties of quantum crystals without using semiconductor junctions. We identify a previously unknown mechanism for rectification from skew scattering due to the inherent chirality of itinerant electrons in time-reversal invariant but inversion-breaking materials. Our calculations reveal large, tunable rectification effects in graphene multilayers and transition metal dichalcogenides. Our work demonstrates the possibility of realizing high-frequency rectifiers by rational material design and quantum wave function engineering.

Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure.

We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum MonteCarlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion MonteCarlo methods. Nuclear zero point effects cause a large reduction in the gap (∼2 eV). Depending on the structure, the fundamental indirect gap closes between 380 and 530GPa for ideal crystals and 330-380GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ∼450-500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.

From optical lattices to quantum crystals

Optical lattices can be loaded with atoms which can have strong interactions, such that the interaction of atoms at different lattice sites cannot be neglected. Moreover, the intersite interactions can be so strong that it can force the atoms to form a self-organized lattice, such that exists in crystals. With increasing intersite interactions, there can appear several lattice states, including conducting optical lattices, insulating optical lattices, delocalized quantum crystals, and localized quantum crystals.

Fractons from Vector Gauge Theory.

Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and restricted mobility emerge as a result of an unusual Gauss law where electric field lines of one gauge field act as sources of charge for others. At low energies this vector gauge theory reduces to the previously studied fractonic symmetric tensor gauge theory. We construct the corresponding lattice model and a number of generalizations, which realize fracton phases via a condensation of stringlike excitations built out of charged particles, analogous to the p-string condensation mechanism of the gapped X-cube fracton phase.

Destiny of optical lattices with strong intersite interactions

Optical lattices are considered loaded by atoms or molecules that can exhibit strong interactions between different lattice sites. The strength of these interactions can be sufficient for generating collective phonon excitations above the ground-state energy level. Varying the interaction strength makes it possible to create several equilibrium three-dimensional phases, including conducting optical lattices, insulating optical lattices, delocalized quantum crystals, and localized quantum crystals. Also, there can exist finite one- and two-dimensional lattices of chains and planes.

Crystal-to-fracton tensor gauge theory dualities

Fractons are a new class of emergent quasiparticles with restricted mobility. Previously, fractons were only known to occur in complicated spin models without direct material realization. Here, the authors detail various duality relationships, which map directly the physics of fractons onto topological defects of quantum crystals. Fractons and dipoles correspond to disclinations and dislocations, respectively, while elastic phonons map onto tensor gauge modes. The authors discuss several applications of the duality, such as a simplified reformulation of two-dimensional melting.