Observation of competing, correlated ground states in the flat band of rhombohedral graphite

Department of Physics of Complex Systems, Eötvös Loránd University

MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and  Economics

László Oroszlány 

https://arxiv.org/abs/2201.10844

accepted in Science Advances

The Team

Theory

  • Imre Hagymási, Dresden 
  • Zoltán Tajkov, CER
  • János Koltai, ELTE
  • Assem Alassaf, ELTE
  • Péter Vancsó, CER

Experiment

  • Mohammad Syahid Mohd Isa, CER
  • Krisztián Márity, CER
  • Péter Kun, Konrád Kandrai, CER
  • András Pálinkás, CER
  • Levente Tapasztó, CER
  • Péter Nemes-Incze, CER

Magnetism at the edge of graphene ribbons

Magda et al. Nature 514, 608 (2014)

Ab initio calculations for edge magnetism

LO, J. Ferrer, A. Deák, L. Udvardi, L. Szunyogh, Phys. Rev. B 99, 224412 (2019)

Flat bands in magic angle graphene

Yuan Cao et al. Nature  556 43 (2018)

E(\mathbf{q}) \propto |\mathbf{q}|^N

SSH chain

Rhombohedral (ABC) graphite

\gamma_0\rightarrow\gamma_0f(\mathbf{k})

Sample preparation

Directed exfoliation:

5% \(\rightarrow\) 12% RG

STM measurements: a broad overview

LDOS

LDA+U

STM measurements: widths and splitts

Rising the temperature

\(T_c\)~15-20K

Splitting at half filling: strong perpendicular field 

E-field strength 0.05 V/Å

TO BIG

Splitting at half filling: confinement effects

SPLITTING PERSISTS BEYOND HALF FILLING!

\( \mu_1 \approx 10^{-2} \mu_\mathrm{Bohr} \)

Splitting at half filling: mean-field physics

- LDA

- LDA+U

SPLITTING IS ALWAYS PRESENT AT HALF FILLING!

DMRG bootcamp

S. R. White, Phys. Rev. Lett. 69, 2863 (1992)

U. Schollwoeck, Annals of Physics 326, 96 (2011)

\left|\Psi\right\rangle =\displaystyle\sum_{p_{1}p_{2}\dots p_{N}}\Psi_{p_{1}p_{2}\dots p_{N}}\left|p_{1}\right\rangle \left|p_{2}\right\rangle \cdots\left|p_{N}\right\rangle
H\left|\Psi\right\rangle =E\left|\Psi\right\rangle

MPS Ansatz!

E_{GS}=\min\frac{\left\langle \Psi\right|H\left|\Psi\right\rangle }{\left\langle \Psi\right.\left|\Psi\right\rangle }

state of the art for 1D systems

higher dimensions are tricky

\Psi_{p_1p_2\dots p_N}=\mathrm{Tr}[A_{p_1}A_{p_2}\dots A_{p_N}]

Results obtained with:

Budapest DMRG & ITensor codes

v=\langle H^2 \rangle-\langle H \rangle^2

Interactions beyond meanfield

Three-fold degenerate groundstate!!

Competition of gaped and gapless states!

GAPED

GAPLESS

Symmetry breaking away from charge neutrality

Thank You for your attention!