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

Zoltán Tajkov

Nanostructures Department, Centre for Energy Research,

Department of Biological Physics, Eötvös Loránd University

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

Electrons in solids - Band theory

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

\left[ -\frac{\hbar^2}{2m}\nabla^2 + U\left( \mathbf{r} \right) \right] \psi\left( \mathbf{r} \right) = \varepsilon \psi\left( \mathbf{r} \right)

averaged potential

Electrons in solids - Band theory

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

\left[ -\frac{\hbar^2}{2m}\nabla^2 + U\left( \mathbf{r} \right) \right] \psi\left( \mathbf{r} \right) = \varepsilon \psi\left( \mathbf{r} \right)

Why do we use it?

electrical resistivity
optical absorption
foundation of solid-state electronics

It explains...

Electrons in solids - Beyond band theory

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

Why do we use it?

Because we can.

An example: methane

1 carbon atom + 4 hydrogen atoms = 10 electrons

30 independent coordinates

100 points per coordinate

\( 100^{30}=10^{60} \) complex number

1 complex number in every atom

We can store the wave function in \( 10^{30} m^3 \)

Strongly correlated electron systems

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

Colossal magnetoresistance
High-temperature superconductivity
VO\( _2 \)

Elbio Dagotto, Science 309, 257 (2005)

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

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

SSH chain

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

What does the experiment say? STM results

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

DMRG - Beyond meanfield

Theory

Degenerate ground state!

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

Experiments

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

The team

Oroszlányi László

Koltai János

Hagymási Imre

Nemes-Incze Péter

Péter Vancsó

András Pálinkás

Levente Tapasztó

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

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

LDA+U vs LDA, meanfield

Possible explanations I.

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

External electric field

Possible explanations II.

E-field strength 0.05 V/Å

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

Quantum confinement

Possible explanations III.

Rhombohedral Graphite

\( (d \circ f) \varphi \) - Balatonisclear - 2021. 09. 17.

Experiments - one more thing

Symmetry breaking