Quantum Theory of Defects in Crystals

Andreev, Aleksandr F.; Lifshitz, I.M.

doi:10.1070/pu1971v013n05abeh004235

Cited by 391 publications

(832 citation statements)

References 4 publications

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“…The existence of an exotic supersolid crystalline phase with combined solid and superfluid characteristics has been long conjectured 16,17,18 for solid 4 He under appropriate conditions. The recent experimental discovery 19 that solid 4 He exhibits a nonclassical (nonrigid) rotational inertia (NCRI 18 ) has revived an intense interest 20,21,22,23,24 in the existence and properties of the supersolid phase in this system, as well as in the possible emergence of exotic phases in other systems.…”

Section: B Nonclassical (Non-rigid) Rotational Inertiamentioning

confidence: 99%

“…In the context of the appearance of supersolid behavior of 4 He under appropriate conditions, formation of a supersolid fraction is often discussed in conjunction with the presence of (i) real defects and (ii) real vacancies. 16,17 Our REM wave function [Eq. 2] belongs to a third possibility, namely to virtual defects and vacancies, with the number of particles equal to the number of lattice sites (in the context of 4 He, the possibility of a supersolid with equal number of particles and lattice sites is mentioned in Ref.…”

Section: Lmmentioning

confidence: 99%

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From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Yannouleas

Landman

2006

Phys. Rev. B

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Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N -electron parabolic quantum dots in strong magnetic fields in the medium-size range 10 ≤ N ≤ 30. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. An analytic expression for the energetics of such non-rigid multi-ring REMs is derived; it is applicable to arbitrary sizes given the corresponding equilibrium configuration of classical point charges. We show that the rotating electron molecules have a non-rigid (non-classical) rotational inertia exhibiting simultaneous crystalline correlations and liquid-like (non-rigidity) characteristics. This mixed phase appears in high magnetic fields and contrasts with the picture of a classical rigid Wigner crystal in the lowest Landau level.

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Section: B Nonclassical (Non-rigid) Rotational Inertiamentioning

confidence: 99%

Section: Lmmentioning

confidence: 99%

From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Yannouleas

Landman

2006

Phys. Rev. B

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“…high-quality resonances of torsional oscillations at two different frequencies could be excited and monitored, and the heat flux along the axis could be used to measure the thermal conductivity. The moments of inertia of the annular cell (torsion head) and dummy bob are labelled 1 I and 2 , I respectively. The rigidity of the "head" torsion rod is 1 K and that of the "bob" torsion rod is 2 .…”

Section: Methodsmentioning

confidence: 99%

“…The former include freeparticle-like dynamics of point defects (vacancies and impurities) [1,2], multiple exchange causing competing ferroand antiferromagnetic ordering of nuclear spins [3], crystallization waves [4]. Further exotic properties of this quantum crystal might be expected, such as supersolidity (coexistence of solid rigidity and non-dissipative coherent mass transport) [1]. Many of the mentioned properties are only meaningful for perfect monocrystals of solid helium.…”

Section: Solid Heliummentioning

confidence: 99%

“…At low temperatures and densities, substantial zero-point kinetic energy and quantum tunneling of atoms lead to a range of unconvential properties, both observed and predicted. The former include freeparticle-like dynamics of point defects (vacancies and impurities) [1,2], multiple exchange causing competing ferroand antiferromagnetic ordering of nuclear spins [3], crystallization waves [4]. Further exotic properties of this quantum crystal might be expected, such as supersolidity (coexistence of solid rigidity and non-dissipative coherent mass transport) [1].…”

Section: Solid Heliummentioning

confidence: 99%

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Thermal conductivity and torsional oscillations of solid 4He

Brazhnikov

Zmeev

Golov

2012

Low Temperature Physics

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Polycrystalline samples of hcp 4 He of molar volume V m = 19.5 cm 3 with small amount of 3 He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of 3 He, x 3 , were studied: isotopically purified 4 He with the estimated x 3 < 10 -10 , commercial 'well-grade' helium with x 3 ~ 3⋅10 -7 and a mixture with x 3 = 2.5⋅10 -6. Torsional oscillations at two frequencies, 132.5 and 853.6 Hz, and thermal conductivity were investigated before and after annealing. The solid helium under investigation was located not only in the annular container but also in the axial fill line inside two torsion rods and dummy bob of the doublefrequency torsional oscillator. The analysis of the frequency shifts upon loading with helium and changing temperatures of different parts of the oscillator suggests that the three techniques probe the properties of solid helium in three different locations: the two different torsion modes respond to the changes of the shear modulus of solid helium in either of the two torsion rods while the thermal conductivity probes the phonon mean free path in solid helium inside the annular container. The temperature and width of the torsional anomaly increase with increasing frequency and x 3 . The phonon mean free path increases with increasing x 3 . Annealing typically resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them. PACS: 67.80.bd Superfluidity in solid 4 He, supersolid 4 He; 65.40.-b Thermal properties of crystalline solids.

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The One‐Dimensional Bose–Fermi–Hubbard Model in the Limit of Fast Fermions

Mering

Fleischhauer

2019

Physica Status Solidi (b)

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The authors discuss the ground‐state phase diagram of the one‐dimensional Bose–Fermi–Hubbard model (BFHM) in the limit of fast fermions based on an effective boson model. The authors give a detailed derivation of the effective model with long‐range Rudermann–Kittel–Kasuya–Yosida (RKKY)‐type interactions, discuss its range of validity, and provide a deeper insight into its implications. In particular, they show that integrating out the fast fermion degrees of freedom in a naive way results in an ill‐behaved effective Hamiltonian and a proper renormalization is required. Based on the effective Hamiltonian, the phase diagram in the thermodynamic limit is constructed by analytic means and is compared to numerical results obtained by density matrix renormalization group (DMRG) techniques for the full BFHM. The most prominent feature of the phase diagram, the existence of a phase separation between Mott insulator (MI) and charge density wave (CDW) is discussed in depth including boundary effects.

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Quantum Theory of Defects in Crystals

Cited by 391 publications

References 4 publications

From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

From a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings

Thermal conductivity and torsional oscillations of solid 4He

The One‐Dimensional Bose–Fermi–Hubbard Model in the Limit of Fast Fermions

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