Charge Density Waves in Graphite: Towards the Magnetic Ultraquantum Limit

Arnold, Frank; Isidori, Aldo; Kampert, Erik; Yager, B.; Eschrig, Matthias; Saunders, J.

doi:10.1103/physrevlett.119.136601

Cited by 25 publications

(58 citation statements)

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“…8). It is generally expected that electron-electron interactions can trigger a variety of phase transitions in the form of density waves, excitonic condensation or Wigner crystals 15,31,32 , and the high-quality graphite films introduced in this work offer an enticing playground (especially, at mK temperatures) to study such transitions with many competing order parameters.…”

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confidence: 99%

Dimensional reduction, quantum Hall effect and layer parity in graphite films

et al. 2019

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The quantum Hall effect (QHE) originates from discrete Landau levels forming in a two-dimensional (2D) electron system in a magnetic field 1 . In three dimensions (3D), the QHE is forbidden because the third dimension spreads Landau levels into multiple overlapping bands, destroying the quantisation. Here we report the QHE in graphite crystals that are up to hundreds of atomic layers thick -thickness at which graphite was believed to behave as a 3D bulk semimetal 2 . We attribute the observation to a dimensional reduction of electron dynamics in high magnetic fields, such that the electron spectrum remains continuous only in the direction of the magnetic field, and only the last two quasi-one-dimensional (1D) Landau bands cross the Fermi level 3,4 . In sufficiently thin graphite films, the formation of standing waves breaks these 1D bands into a discrete spectrum, giving rise to a multitude of quantum Hall plateaux. Despite a large number of layers, we observe a profound difference between films with even and odd numbers of graphene layers. For odd numbers, the absence of inversion symmetry causes valley polarisation of the standing-wave states within 1D Landau bands. This reduces QHE gaps, as compared to films of similar thicknesses but with even layer numbers because the latter retain the inversion symmetry characteristic of bilayer graphene 5,6 . High-quality graphite films present a novel QHE system with a paritycontrolled valley polarisation and intricate interplay between orbital, spin and valley states, and clear signatures of electron-electron interactions including the fractional QHE below 0.5 K.The Lorentz force imposed by a magnetic field, B, changes the straight ballistic motion of electrons into spiral trajectories aligned along B (Fig. 1a). Such spiral motion gives rise to Landau bands that are characterised by plane waves propagating along the B direction but quantised in the directions perpendicular to the magnetic field 7 . The increase in B changes the distance between Landau bands, and the resulting crossings of the Fermi level, EF, with the Landau band edges lead to quantum oscillations. When only the lowest few Landau bands cross EF (ultra-quantum regime), the magnetic field effectively makes the electron motion one-dimensional (with conductivity allowed only in the direction parallel to B). In normal metals such as, e.g., copper, this dimensional reduction would require B > 10,000 T. In semimetals with their small Fermi surfaces (e.g., graphite 2,4,8 ) the dimensional reduction and the ultra-quantum regime (UQR) can be reached in moderate B. Indeed, magnetotransport measurements in bulk crystals 4,9-11 and films of graphite 12,13 revealed quantum oscillations reaching the lowest Landau bands. However, no dissipationless QHE transport could be observed as expected for the 3D systems.

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Dimensional reduction, quantum Hall effect and layer parity in graphite films

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“…Recently, a comprehensive resistivity measurement in graphite under high magnetic field has been carried out up to 90 T 12 . The graphite under the high magnetic field (the field ⊥ the graphene plane) exhibits consecutive metal-insulator transitions as well as insulator-metal re-entrant transition at low temperature in an electric resistivity along the out-of-plane (field) direction [10][11][12][13]15,53 .…”

Section: Summary and Discussion On Experimentsmentioning

confidence: 99%

“…For example, we put e − and h + as well as e + and h − in the basis of the x-gauge eigenstates by using Eqs. (13,14). This leads to…”

Section: Parquet Renormalization Group Equationmentioning

confidence: 99%

“…One of the fundamental challenge in condensed matter physics is a realization of three-dimensional unconventional electronic phases in the quantum limit 1 . Recent experimental discoveries of Dirac, Weyl and nodal Dirac semimetal materials 2 lead to growing research interests on novel quantum transports and quantum phase transitions under high magnetic field in these new compounds [3][4][5]7,25 as well as celebrated semimetal compounds such as bismuth 8,16 and graphite [11][12][13][14] . In fact, these semimetallic compounds under the high field often exhibit low-temperature metal-insulator transitions within wide ranges of the field 3,5,10-17 .…”

Section: Introductionmentioning

confidence: 99%

“…The one-dimensional dispersions along z of the electron and hole bands go across the Fermi level at several Fermi points in the Brillouin zone. The experimental Hall conductivity measurements conclude that the relevant semimetal materials within the relevant field regime [10][11][12][13][14][15][16][17] are in the charge neutrality region, where electron and hole densities compensate with each other completely 12,15,38,[43][44][45] . Thereby, to uncover the identities of the low-temperature insulator phases in the experiments [10][11][12][13][14][15][16][17][18] , it is vital to understand a ground-state phase diagram of a microscopic Hamiltonian for the semimetal materials in the quantum limit at their charge neutrality point.…”

Section: Introductionmentioning

confidence: 99%

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Ground-state atlas of a three-dimensional semimetal in the quantum limit

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Shindou

2019

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An interplay between electron correlation and reduced dimensionality due to the Landau quantization gives rise to exotic electronic phases in three-dimensional semimetals under high magnetic field. Using an unbiased theoretical method, we clarify for the first time comprehensive ground-state phase diagrams of a three-dimensional semimetal with a pair of electron and hole pockets in the quantum limit. For the electron interaction, we consider either screened Coulomb repulsive interaction or an attractive electron-electron interaction mediated by a screened electron-phonon coupling, where a screening length is generally given by a dimensionless constant times magnetic length l. By solving the parquet RG equation numerically and employing a mean-field argument, we construct comprehensive ground-state phase diagrams of the semimetal in the quantum limit for these two cases, as a function of the Fermi wave length and the screening length (both normalized by l). In the repulsive interaction case, the ground state is either excitonic insulator (EI) in strong screening regime or Ising-type spin density wave in weak screening regime. In the attractive interaction case, the ground state is either EI that breaks the translational symmetries (strong screening regime), topological EI, charge Wigner crystal (intermediate screening regime), plain charge density wave or marginal Fermi liquid (weak screening regime). We show that the topological EI supports a single copy of massless Dirac fermion at its side surface, and thereby exhibit a √ H ⊥ -type surface Shubnikov-de Haas (SdH) oscillation in in-plane surface transports as a function of a canted magnetic field H ⊥ . Armed with these theoretical knowledge, we discuss implications of recent transport experiments on graphite under the high field.

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Taming the magnetoresistance anomaly in graphite

Camargo

Escoffier

2018

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At low temperatures, graphite presents a magnetoresistance anomaly which manifests as a transition to a high-resistance state (HRS) above a certain critical magnetic field B c . Such HRS is currently attributed to a c-axis chargedensity-wave taking place only when the lowest Landau level is populated. By controlling the charge carrier concentration of a gated sample through its charge neutrality level (CNL), we were able to experimentally modulate the HRS in graphite for the first time. We demonstrate that the HRS is triggered both when electrons and holes are the majority carriers but is attenuated near the CNL. Taking screening into account, our results indicate that the HRS possess a strong in-plane component and can occur below the quantum limit, being at odds with the current understanding of the phenomenon. We also report the effect of sample thickness on the HRS.

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Charge Density Waves in Graphite: Towards the Magnetic Ultraquantum Limit

Cited by 25 publications

References 57 publications

Dimensional reduction, quantum Hall effect and layer parity in graphite films

Dimensional reduction, quantum Hall effect and layer parity in graphite films

Ground-state atlas of a three-dimensional semimetal in the quantum limit

Taming the magnetoresistance anomaly in graphite

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