Exchange and correlation effects in the three-dimensional electron gas in strong magnetic fields and application to graphite

Takada, Yogo; Okuno, Hiroshi G.

doi:10.1088/0953-8984/10/49/020

Cited by 48 publications

(84 citation statements)

References 20 publications

(18 reference statements)

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“…This approximate form is developed to fulfill the gauge invariance and nineteen sum rules. The VEA formula for a homogeneous system is in quite good agreement with the exchange and correlation energies [34] of the homogeneous electron liquid applied by a uniform magnetic field [31][32][33].…”

Section: Introductionsupporting

confidence: 54%

“…E x [ρ] and E c [ρ] denote the exchange and correlation energy functionals of the conventional DFT, respectively. The dimensionless parametersD x ,C 0 ,ᾱ, and δ are 3.76 × 10 −4 , −4.669 × 10 −4 , 0.653, and 1.0 × 10 −30 , respectively [31][32][33], which have been determined by utilizing the exchange and correlation energies of the homogeneous electron liquid applied by a uniform magnetic field [34]. These formulas are constructed so as to comply with the gauge invariance and nineteen sum rules that are derived from coordinate scaling of electrons [31][32][33].…”

Section: Sum Rules For the Exchange-correlation Energy Functionalmentioning

confidence: 99%

“…Thus, the VEA formula has wellbehaved form in comparison with the CDFT-LDA formula. At the end of this section, we give a brief comment on twelve sum rules that are not satisfied by the VEA formula (33)(34)(35)(36)(37)(38)(42)(43)(44)(45)(46)(47). Since the sum rule generally gets rid of the difficulties that lead to unphysical results, we may expect that the more sum rules the VEA formula fulfils, the better it works for describing the ground-state properties of solids where the orbital current is induced.…”

Section: B Exhaustive Checks Of the Vea Formula Via A Total Of Sixtymentioning

confidence: 99%

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Sum rules for the exchange-correlation energy functional of the extended constrained-search theory: Application to checking the validity of the vorticity expansion approximation of the current-density functional theory

Higuchi

2010

Phys. Rev. A

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We present four kinds of sum rules for the exchange-correlation energy functional of the extended constrainedsearch theory. They are applicable even to the conventional density functional theory. As an application of these sum rules, we utilize them to check the validity of the vorticity expansion approximation (VEA) of the current-density functional theory (CDFT). The VEA formula fulfils three of them, though the local density approximation formula of the CDFT fulfills only one. The validity of the VEA formula is thus confirmed successfully from the viewpoint of the sum rules.

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Section: Introductionsupporting

confidence: 54%

Section: Sum Rules For the Exchange-correlation Energy Functionalmentioning

confidence: 99%

Section: B Exhaustive Checks Of the Vea Formula Via A Total Of Sixtymentioning

confidence: 99%

See 1 more Smart Citation

Sum rules for the exchange-correlation energy functional of the extended constrained-search theory: Application to checking the validity of the vorticity expansion approximation of the current-density functional theory

Higuchi

2010

Phys. Rev. A

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“…If we choose C 0 Ͻ 0, ␣ Ͼ 0, and 0 Ͻ ␦ Ӷ a H 3 , then all sum rules and bounds which are listed in Table I The validity of the above VEA formulas has already been confirmed by comparing them with the exchange and correlation energies of the homogeneous electron liquid under a uniform magnetic field. 29,37 B. Does the VEA formula satisfy Levy's asymptotic bound?…”

Section: C͑ ͒mentioning

confidence: 99%

Evaluation of vorticity expansion approximation of current-density functional theory by means of Levy’s asymptotic bound

Higuchi

2007

Phys. Rev. B

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“…Therefore, the (n=-1,↓) sub-level is expected to become empty at a lower magnetic field than the (n=0,↑) sub-level (as sketched in Fig.4). However, according to Takada and Goto [19], electron correlations modify the SWM spectrum at high magnetic field. Thus, the identity of the occupied sub-level between 53 T and 75 T remains an open question.…”

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confidence: 98%

Two Phase Transitions Induced by a Magnetic Field in Graphite

et al. 2013

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Different instabilities have been speculated for a three-dimensional electron gas confined to its lowest Landau level. The phase transition induced in graphite by a strong magnetic field, and believed to be a Charge Density Wave (CDW), is the only experimentally established case of such instabilities. Studying the magnetoresistance in graphite for the first time up to 80 T, we find that the magnetic field induces two successive phase transitions, consisting of two distinct ordered states each restricted to a finite field window. In both states, an energy gap opens up in the out-ofplane conductivity and coexists with an unexpected in-plane metallicity for a fully gap bulk system. Such peculiar metallicity may arise as a consequence of edge-state transport expected to develop in presence of a bulk gap.Graphite is a compensated semi-metal with a tiny three-dimensional Fermi surface and is described by the Slonczewski-Weiss-McClure (SWM) band model [1,2]. A modest magnetic field of 7.5 T perpendicular to the graphene layers confines electrons and holes to their lowest Landau levels (LLs). It is therefore an ideal candidate to explore the nature of the electronic ground state of a three-dimensional electron gas pushed beyond the socalled quantum limit. In this regime [3], the electronic spectrum becomes analogue to a one-dimensional system with a variety of possible instabilities [4][5][6]. In the early eighties, a phase transition in this system was discovered by Tanuma and co-workers who reported a sharp increase in the in-plane magnetoresistance of graphite at B≈25 T [8]. Numerous experimental studies followed [9][10][11][12][13][14][15] and confirmed the existence of a field-induced many-body state beyond a temperature-dependent critical magnetic field. Soon after the initial experimental discovery, Yoshioka and Fukuyama (YF) [16] ascribed this instability to a charge-density-wave (CDW). Such an instability is favored by one-dimensionality, because of the availability of a suitable (2k F ) nesting vector. In the original YF scenario, the CDW in adjacent valleys are out of phase, creating a valley density wave state [17], in order to minimize Coloumb energy. In 1998, by further increasing the magnetic field, Yaguchi and Singleton found that the field-induced state is eventually destroyed beyond 53 T [13]. This destruction was attributed to the depopulation of a Landau sub-level within the framework of YF scenario. The possible multiplicity of induced phases and their signatures in the in-plane and out of-plane charge transport remain open questions (for a review see [18]). Therefore, despite a large body of research on graphite at high magnetic field, the nature of its electronic ground state is not settled. In addition, these investigations can * benoit.fauque@espci.fr provide interesting input to the debate on the importance of many-body physics and its evolution with dimensionality in graphene [7].In this letter, we extend the previous measurements up to a magnetic field as strong as 80 T and focus on the contr...

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Exchange and correlation effects in the three-dimensional electron gas in strong magnetic fields and application to graphite

Cited by 48 publications

References 20 publications

Sum rules for the exchange-correlation energy functional of the extended constrained-search theory: Application to checking the validity of the vorticity expansion approximation of the current-density functional theory

Sum rules for the exchange-correlation energy functional of the extended constrained-search theory: Application to checking the validity of the vorticity expansion approximation of the current-density functional theory

Evaluation of vorticity expansion approximation of current-density functional theory by means of Levy’s asymptotic bound

Two Phase Transitions Induced by a Magnetic Field in Graphite

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