scholarly journals DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Paul Eugenio ◽  
Ceren Dag
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Ground States ◽  
Bilayer Graphene ◽  
Chern Number ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Density Matrix Renormalization ◽  
Topological Quantum ◽  
Twisted Bilayer Graphene

Strong interactions between electrons occupying bands of opposite (or like) topological quantum numbers (Chern=\pm1=±1), and with flat dispersion, are studied by using lowest Landau level (LLL) wavefunctions. More precisely, we determine the ground states for two scenarios at half-filling: (i) LLL’s with opposite sign of magnetic field, and therefore opposite Chern number; and (ii) LLL’s with the same magnetic field. In the first scenario – which we argue to be a toy model inspired by the chirally symmetric continuum model for twisted bilayer graphene – the opposite Chern LLL’s are Kramer pairs, and thus there exists time-reversal symmetry (\mathbb{Z}_2ℤ2). Turning on repulsive interactions drives the system to spontaneously break time-reversal symmetry – a quantum anomalous Hall state described by one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle|++⋯+⟩ or all negative |{--\cdots-}\rangle|−−⋯−⟩. If instead, interactions are taken between electrons of like-Chern number, the ground state is an SU(2)SU(2) ferromagnet, with total spin pointing along an arbitrary direction, as with the \nu=1ν=1 spin-\frac{1}{2}12 quantum Hall ferromagnet. The ground states and some of their excitations for both of these scenarios are argued analytically, and further complimented by density matrix renormalization group (DMRG) and exact diagonalization.

scholarly journals Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene

2021 ◽  
Author(s):  
Dmitri Efetov ◽  
Petr Stepanov ◽  
Ming Xie ◽  
Takashi Taniguchi ◽  
Kenji Watanabe ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Bilayer Graphene ◽  
Chern Number ◽  
Zero Magnetic Field ◽  
Magic Angle ◽  
Zero Field ◽  
Superconducting Phases ◽  
Chern Insulators ◽  
Twisted Bilayer Graphene ◽  
The Creation

Abstract The discovery of magic angle twisted bilayer graphene (MATBG) has unveiled a rich variety of superconducting, magnetic and topologically nontrivial phases. The existence of all these phases in one material, and their tunability, has opened new pathways for the creation of unusual gate tunable junctions. However, the required conditions for their creation – gate induced transitions between phases in zero magnetic field – have so far not been achieved. Here, we report on the first experimental demonstration of a device that is both a zero-field Chern insulator and a superconductor. The Chern insulator occurs near moiré cell filling factor = +1 in a hBN non-aligned MATBG device and manifests itself via an anomalous Hall effect. The insulator has Chern number C= ±1 and a relatively high Curie temperature of Tc ≈ 4.5 K. Gate tuning away from this state exposes strong superconducting phases with critical temperatures of up to Tc ≈ 3.5 K. In a perpendicular magnetic field above B > 0.5 T we observe a transition of the = +1 Chern insulator from Chern number C = ±1 to C = 3, characterized by a quantized Hall plateau with Ryx = h/3e2. These observations show that interaction-induced symmetry breaking in MATBG leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B-field. By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.

scholarly journals Electronic Properties of Twisted Bilayer Graphene in the Presence of a Magnetic Field

2020 ◽  
Vol 233 ◽  
pp. 03004
Author(s):  
M.F.C. Martins Quintela ◽  
J.C.C. Guerra ◽  
S.M. João
Keyword(s):  
Magnetic Field ◽  
Electronic Properties ◽  
Twist Angle ◽  
Bilayer Graphene ◽  
Polynomial Method ◽  
Zero Energy ◽  
Energy Bands ◽  
Optical And Electronic Properties ◽  
Twisted Bilayer Graphene ◽  
Kernel Polynomial Method

In AA-stacked twisted bilayer graphene, the lower energy bands become completely flat when the twist angle passes through certain specific values: the so-called “magic angles”. The Dirac peak appears at zero energy due to the flattening of these bands when the twist angle is sufficiently small [1-3]. When a constant perpendicular magnetic field is applied, Landau levels start appearing as expected [5]. We used the Kernel Polynomial Method (KPM) [6] as implemented in KITE [7] to study the optical and electronic properties of these systems. The aim of this work is to analyze how the features of these quantities change with the twist angle in the presence of an uniform magnetic field.

New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field

1993 ◽  
Vol 71 (17) ◽  
pp. 2777-2780 ◽  
Author(s):  
G. Ortiz ◽  
D. M. Ceperley ◽  
R. M. Martin
Keyword(s):  
Magnetic Field ◽  
Time Reversal ◽  
Stochastic Method ◽  
Time Reversal Symmetry

scholarly journals Superconducting edge states in a topological insulator

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
I. V. Yurkevich ◽  
V. Kagalovsky
Keyword(s):  
Topological Insulator ◽  
Time Reversal ◽  
Collective Motion ◽  
Effective Theory ◽  
Strong Interactions ◽  
Time Reversal Symmetry ◽  
Edge States ◽  
Translation Invariant ◽  
Clean System ◽  
The Stability

AbstractWe study the stability of multiple conducting edge states in a topological insulator against perturbations allowed by the time-reversal symmetry. A system is modeled as a multi-channel Luttinger liquid, with the number of channels equal to the number of Kramers doublets at the edge. Assuming strong interactions and weak disorder, we first formulate a low-energy effective theory for a clean translation invariant system and then include the disorder terms allowed by the time-reversal symmetry. In a clean system with N Kramers doublets, N − 1 edge states are gapped by Josephson couplings and the single remaining gapless mode describes collective motion of Cooper pairs synchronous across the channels. Disorder perturbation in this regime, allowed by the time reversal symmetry is a simultaneous backscattering of particles in all N channels. Its relevance depends strongly on the parity if the number of channel N is not very large. Our main result is that disorder becomes irrelevant with the increase of the number of edge modes leading to the stability of the edge states superconducting regime even for repulsive interactions.

scholarly journals Erratum to: Cooperative Time-Reversal Symmetry Breaking Induced by a Magnetic Field in a Quasi-2D d-Wave Superconductor

2011 ◽  
Vol 24 (5) ◽  
pp. 1821-1821
Author(s):  
S. Char fi-Kaddour ◽  
A. Ben Ali ◽  
M. Héritier ◽  
R. Bennaceur
Keyword(s):  
Magnetic Field ◽  
Symmetry Breaking ◽  
Time Reversal ◽  
Time Reversal Symmetry ◽  
D Wave

scholarly journals Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4

Science ◽  
2020 ◽  
Vol 367 (6480) ◽  
pp. 895-900 ◽  
Author(s):  
Yujun Deng ◽  
Yijun Yu ◽  
Meng Zhu Shi ◽  
Zhongxun Guo ◽  
Zihan Xu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Quantum Transport ◽  
Topological Insulator ◽  
Time Reversal ◽  
Magnetic Order ◽  
Anomalous Hall Effect ◽  
Time Reversal Symmetry ◽  
Zero Field ◽  
Exotic States ◽  
Ferromagnetic Layers

In a magnetic topological insulator, nontrivial band topology combines with magnetic order to produce exotic states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. In this work, we probe quantum transport in MnBi2Te4 thin flakes—a topological insulator with intrinsic magnetic order. In this layered van der Waals crystal, the ferromagnetic layers couple antiparallel to each other; atomically thin MnBi2Te4, however, becomes ferromagnetic when the sample has an odd number of septuple layers. We observe a zero-field QAH effect in a five–septuple-layer specimen at 1.4 kelvin, and an external magnetic field further raises the quantization temperature to 6.5 kelvin by aligning all layers ferromagnetically. The results establish MnBi2Te4 as an ideal arena for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.

Sign in / Sign up

Export Citation Format

Share Document