Fermi Surface Instability of Quasi-Two-Dimensional Tight Binding Electrons : A Possible Phase Diagram of (La1-xMx)2CuO4

AbstractWe consider the stability of the circular Fermi surface of a two-dimensional electron gas system against an elliptical deformation induced by an anisotropic Coulomb interaction potential. We use the jellium approximation for the neutralizing background and treat the electrons as fully spin-polarized (spinless) particles with a constant isotropic (effective) mass. The anisotropic Coulomb interaction potential considered in this work is inspired from studies of two-dimensional electron gas systems in the quantum Hall regime. We use a Hartree–Fock procedure to obtain analytical results for two special Fermi liquid quantum electronic phases. The first one corresponds to a system with circular Fermi surface while the second one corresponds to a liquid anisotropic phase with a specific elliptical deformation of the Fermi surface that gives rise to the lowest possible potential energy of the system. The results obtained suggest that, for the most general situations, neither of these two Fermi liquid phases represent the lowest energy state of the system within the framework of the family of states considered in this work. The lowest energy phase is one with an optimal elliptical deformation whose specific value is determined by a complex interplay of many factors including the density of the system.

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A Two Dimensional Fermi Liquid. Part 3: The Fermi Surface

Communications in Mathematical Physics ◽

10.1007/s00220-003-0998-y ◽

2004 ◽

Vol 247 (1) ◽

pp. 113-177 ◽

Cited By ~ 8

Author(s):

Joel Feldman ◽

Horst Kn�rrer ◽

Eugene Trubowitz

Keyword(s):

Fermi Surface ◽

Fermi Liquid ◽

Two Dimensional ◽

Liquid Part

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COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018877 ◽

2007 ◽

Vol 17 (09) ◽

pp. 3071-3083 ◽

Cited By ~ 71

Author(s):

J. M. GONZÀLEZ-MIRANDA

Keyword(s):

Phase Diagram ◽

Bifurcation Diagram ◽

Parameter Space ◽

Neuron Model ◽

Two Dimensional ◽

Dimensional Parameter ◽

Rapid Responses ◽

Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

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METAL–INSULATOR TRANSITIONS IN TETRAHEDRAL SEMICONDUCTORS UNDER LATTICE CHANGE

International Journal of Modern Physics B ◽

10.1142/s0217979204024525 ◽

2004 ◽

Vol 18 (07) ◽

pp. 975-988

Author(s):

SHAILESH SHUKLA ◽

DEEPAK KUMAR ◽

NITYA NATH SHUKLA ◽

RAJENDRA PRASAD

Keyword(s):

Dielectric Constant ◽

Fermi Surface ◽

Lattice Constant ◽

Critical Behavior ◽

Tight Binding ◽

Metal Insulator ◽

Wide Range ◽

Insulating Phase ◽

Tetrahedral Semiconductors ◽

Lattice Compression

Although most insulators are expected to undergo insulator to metal transition on lattice compression, tetrahedral semiconductors Si, GaAs and InSb can become metallic on compression as well as by expansion. We focus on the transition by expansion which is rather peculiar; in all cases the direct gap at Γ point closes on expansion and thereafter a zero-gap state persists over a wide range of lattice constant. The solids become metallic at an expansion of 13% to 15% when an electron Fermi surface around L-point and a hole Fermi surface at Γ-point develop. We provide an understanding of this behavior in terms of arguments based on symmetry and simple tight-binding considerations. We also report results on the critical behavior of conductivity in the metal phase and the static dielectric constant in the insulating phase and find common behavior. We consider the possibility of excitonic phases and distortions which might intervene between insulating and metallic phases.

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Universal behavior of the bosonic metallic ground state in a two-dimensional superconductor

npj Quantum Materials ◽

10.1038/s41535-021-00312-x ◽

2021 ◽

Vol 6 (1) ◽

Author(s):

Zhuoyu Chen ◽

Bai Yang Wang ◽

Adrian G. Swartz ◽

Hyeok Yoon ◽

Yasuyuki Hikita ◽

...

Keyword(s):

Magnetic Field ◽

Phase Diagram ◽

Quantum Phase Transitions ◽

Metallic State ◽

Two Dimensional ◽

Metallic Behavior ◽

Universal Behavior ◽

Hall Resistivity ◽

Wide Range ◽

Metal State

AbstractAnomalous metallic behavior, marked by a saturating finite resistivity much lower than the Drude estimate, has been observed in a wide range of two-dimensional superconductors. Utilizing the electrostatically gated LaAlO3/SrTiO3 interface as a versatile platform for superconductor-metal quantum phase transitions, we probe variations in the gate, magnetic field, and temperature to construct a phase diagram crossing from superconductor, anomalous metal, vortex liquid, to the Drude metal state, combining longitudinal and Hall resistivity measurements. We find that the anomalous metal phases induced by gating and magnetic field, although differing in symmetry, are connected in the phase diagram and exhibit similar magnetic field response approaching zero temperature. Namely, within a finite regime of the anomalous metal state, the longitudinal resistivity linearly depends on the field while the Hall resistivity diminishes, indicating an emergent particle-hole symmetry. The universal behavior highlights the uniqueness of the quantum bosonic metallic state, distinct from bosonic insulators and vortex liquids.

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