**RESEARCH INTEREST AND SELECTED PUBLICATIONS**

Our researches focus on the experimental study of the properties of low dimensional electronic systems. They mainly aim at characterizing two dimensional electron 2 gases (2DEG) in various semi-conducting structures or atomically thin layered materials such as graphene. Among the numerous issues raised by these systems, we fixed a particular attention on the quantum Hall regime, and its associated collective states and spin properties. This includes ferromagnetic quantum Hall states, fractional quantum Hall states (associated with non-trivial “anyonic” and “non-abelian anyonic” quantum statistics), electron (Wigner-like) solids, quantum spin Hall phase, Valley physics, etc…

We additionally pay a great attention to more recently discovered 2D systems, such as “topological insulators” or transition metal dichalcogenides (semiconducting or metallic), as well as bulk semi-metals exhibiting “Weyl physics”.

Our main experimental techniques are transport, capacitance, magnetization, and magnetic resonances measurements involving low temperature, high magnetic fields, and light excitation.

Here are subjects we have been or are focusing on:

**–****2D electron “ferromagnetism”… with a small magnetic field:**** **

We have shown that the appearance of spin splitting at low magnetic field in the quantum Hall effect is essentially of many-body origin (the single particle Zeeman energy plays a negligible role). This manifestation of an itinerant quantum Hall ferromagnet in the highest occupied Landau level can be thought of as a Stoner transition, in which exchange interactions between electron compete against the kinetic energy to set up a ferromagnetic state. The only role of the magnetic field is to modify the density of states at the Fermi level through the Landau level degeneracy, and thus reduce the kinetic energy cost of the transition to a ferromagnetic state.

Selected publication:

B. A. Piot et al, “Quantum Hall ferromagnet at high filling factors: A magnetic-field-induced Stoner transition” Phys. Rev. B **72**, 245325 (2005).

This Stoner like
description can be extend to the dilute (low eletron density) regime, where
electron-electron correlation play an even more substantial role (Phys. Rev. B **85**, 195309 (2012).)

A peculiar case of this transition occurs at “filling factor 1” (one Landau level occupied), where ferromagnetism competes with spin textures (Skyrmions). Using state-of-the-art resistive NMR techniques, we have determined this unique phase diagram ruled by interactions and disorder.

B.
A. Piot *et al*, Phys. Rev. Lett. **116**, 106801 (2016).

**–****New quantum statistics in the quantum Hall regime****: **

We have been working on the physics of the filling factor nu= 5/2 fractional quantum Hall effect. The wave function which is supposed to describe this state theoretically, the so-called Moore-Read state, bears unique “non-abelian anyonic” quantum statistics which would underly a new paradigm for topological (fault tolerant) quantum computation.

However, a verification of another key property of the Moore-Read state, which is the p-wave symmetry of the electron wave function at nu= 5/2, had so far been missing. Using Resistively Detected Nuclear Magnetic Resonance (RDNMR) at very low temperature, we have unravelled the sought-after spin polarization of this state and shown that, in agreement with the Moore-Read theory, electron are fully spin polarized in the nu= 5/2 fractional quantum Hall state. This results is a necessary condition for the validity of the Moore-Read theory, and interferometric experiments will now have to determine the exact nature of quantum statistics in the nu= 5/2 state.

M. Stern, B. A. Piot et al, “NMR Probing of the
Spin Polarization of the *ν *= 5*/*2 Quantum Hall State” Phys. Rev. Lett. **108**,
066810 (2012).

**-2DEG in other semiconductors: Magnetism and valley physics**

GaAs has historically been (and still is today) a model system to study new many-body phases in a 2DEG. The main reasons for this are its high purity, its simple “single valley” configuration and its very weak Zeeman energy (g*= -0.44) (making many-body effects sometimes more apparent). However, other high quality systems have recently emerged, with different physical properties, broadening the possible playgrounds to study low dimensional electron systems.

We have for example observed the fractional quantum Hall effect for the first time in a II-VI semiconductor, CdTe, where the Zeeman energy is about 4 times higher than in GaAs (g*= -1.6). We have shown that this relatively higher Zeeman energy leads to a “spin polarized” FQH effect which can be well understood within the composite fermions theory for the quantum Hall effect.

Another interesting asset of CdTe is the possibility to incorporate magnetic ions (Mn) inside the quantum well to form the so-called “Diluted Magnetic Semiconductor”. Such incorporation allows a “Zeeman energy engineering”, since the exchange interactions between electrons and magnetic ions lead to the possibility of tuning (in sign and magnitude) the Zeeman energy. This has made possible the observation of integer and fractional quantum Hall states in the presence of a vanishing Zeeman energy, which can affect the polarization of the ground state.

C. Betthausen et al, Phys. Rev. B 90, 115302 (2014).

An interesting perspective is the stabilization of peculiar spin textures such as Skyrmions by tuning the Zeeman energy properly with the magnetic ions content.

Another parameter that can affect the quantum Hall effect in a 2DEG is the valley degeneracy.

For example we have shown that in a multivalley system like PbTe, the quantized Hall resistance observed in the quantum Hall regime shows and unusual sequence of plateaus, reflecting the peculiar valley degeneracy of this semiconductor.

Other effects of the valley degeneracy can also be found in 2DEG in silicon. Although silicon has widelybeen studied in its “MOSFET” form, we have studied a 2DEG in a “silicon on insulator” structure in which the valley degeneracy can be electrically tuned from 2 to 1.We have observed spectacular effects of the valley degree of freedom on the properties of an interacting 2DEG. In particular, we have shown that the magnetic field required to spin polarize a 2DEG become smaller as the valley degeneracy is lifted, which is in contradiction with a simple “single-particle” approach, and is attributed to many-body effects.

V. T. Renard, B. A. Piot et al., “Valley polarization
assisted spin polarization in two dimensions” Nature Communication
**6**, 7230– (2015).

**– Carbon allotropes (graphite and graphene):**** **

In 2010-2012, we have used De Haas Van Alphen (dHvA) measurements at mK temperatures, with in-situ rotation of the sample in the magnetic field to map out the Fermi surface of graphite. Our results, giving a complete map of the Fermi surface, unequivocally demonstrate that graphite has a 3 dimensional closed Fermi surface.

J. Schneider, B.A. Piot et al., Phys. Rev. Lett. 108, 117401 (2012).

From 2012, within collaborations led by the group of A.Geim, K. Novoselov, and A. Mishchenko from the university of Manchester, we have observed the manifestation of the sought-after Hofstadter’s butterfly” in graphene superlattices. The Hofstadter butterfly is a self-similar electronic energy spectrum of a two-dimensional lattice in a magnetic field, reminiscent of the fractal pattern of a buttery wing. The structure appears because of a commensurability of the lattice constant of the periodic potential and the magnetic length. For BN-graphene supperlattices, a nearly perfect alignment between the BN layer and the graphene sheet leads to “Moire pattern”, which lattice constant equals the magnetic length at about B = 25T. Clones of the Dirac point subsequently appear away from charge neutrality, and under high magnetic fields. Graphene superlattices such as these illustrate the possibility of controllably modifying the electronic spectra of two-dimensional atomic crystals by varying their crystallographic alignment within van der Waals heterostuctures.

L. A. Ponomarenko et al, “Cloning of Dirac fermions in graphene superlattices” Nature **497**,594–597 (2013).

We have additionally performed high magnetic field (30T) capacitance spectroscopy to establish the hierarchy of new many-body quantum states.

G. L. Yu et al, “Hierarchy of hofstadter states and replica quantum hall ferromagnetism in graphene Superlattices” Nature Physics 10, 525 (2014).

Later on, the electron chirality in graphene was unraveled by applying a large magnetic field in the plane of a Van-der-Walls heterostructures tunnelling device. This experiment also demonstrates the possibility to “prepare” electrons with a given valley polarization in graphene.

J. R. Wallbank *et al*,
Science 353, 575 (2016).

*– Topological insulators*

3D Topological Insulators (TIs) are particular
bulk insulators characterized by the existence of 2D conducting states on their
surface. The charge carriers on the surface behave as massless relativistic
particles (Dirac fermions), as in graphene, but their spin is locked to their
translational momentum, which promise applications in the fields of spintronics
and quantum computation. In an effort to deepen our understanding and control
of the spin properties of TIs, we have focused on the characterization of the
coupling between the charge carriers and the nuclei in the Bi2Se3 matrix, the
so-called hyperfine coupling. Our identification of the bulk spin properties
via NMR, made possible thanks to a surprisingly strong hyperfine in Bi_{2}Se_{3},
constitutes a first step toward NMR-based studies and manipulation of the
surface states in these systems.

S. Mukhopadhyay *et
al*.,“Hyperfine coupling and spin polarization in the bulk of the
topological insulator Bi_{2}Se_{3}” Phys. Rev. B **91**, 081105 (2015) (R) .

See also [B. A. Piot et al, Phys. Rev. B, vol. 93, p. 155206 (2016)]

**– Emerging 2D layered materials:**

Study of the many-body effects and Spin/valley coupling in transition metal dichalcogenides

J. Lin et al, Nano Lett. **19**, 1736 (2019).

**-High magnetic field instrumentation and experimental development**

An important part of the group activity is to design, develop and perform new experiments under high magnetic field in collaboration with external users form around the world.

Technical development in extreme physical conditions are vital to offer the best possible working conditions and open new research perspectives. Contact us directly to discuss what can/could be done.

## Voir aussi dans «2S&LDS : Electronic transport – Grenoble : low dimensional systems and quantum transport»

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