Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

Agarwal, Kartiek; Randeria, Mallika T.; Yazdani, Ali; Sondhi, S. L.; Parameswaran, S. A.

doi:10.1103/physrevb.100.165103

Cited by 7 publications

(5 citation statements)

References 34 publications

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“…These domain walls (DWs) are our focus below-note that these are distinct from the helical states that have been observed between AB/BA stacking regions in an electric field [24]. Similar DWs in QHFMs have been studied previously [25][26][27][28][29][30] and have been visualized on the surface of bismuth via scanning tunneling microscopy (STM) [31]. As in QHFMs, DWs in magic-angle TBG generically host a pair of gapless dispersing one-dimensional modes.…”

Section: Introductionmentioning

confidence: 70%

“…However, as we show here, in certain parameter regimes the edge modes of energetically stable DWs in TBG are chiral (copropagating) rather than counter-propagating. Hence universal aspects of chiral Luttinger liquid physics can emerge in this setting, that are absent in QHFM-DWs due to corrections from interactions between counterpropagating modes [29].…”

Section: Introductionmentioning

confidence: 99%

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Domain wall competition in the Chern insulating regime of twisted bilayer graphene

Kwan¹,

Wagner²,

Chakraborty³

et al. 2021

Phys. Rev. B

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We consider magic-angle twisted bilayer graphene (TBG) at filling ν = +3, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley-and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry, and is stabilized by a hexagonal boron nitride (hBN) substrate. We identify three different types of domain wall, and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moiré systems. We comment on the implications of these results for transport and scanning probe experiments.

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Section: Introductionmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Domain wall competition in the Chern insulating regime of twisted bilayer graphene

Kwan¹,

Wagner²,

Chakraborty³

et al. 2021

Phys. Rev. B

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“…We concentrate here on the ferroelectric states where two valleys are described by the tilted massless Dirac cone with the same axis orientation and velocity ratio but opposite tilt. We expect the states at the Landau level n = +3 to essentially carry over to the case of bismuth surfaces [3][4][5][6]. In the Supplemental Material [22], we also present a nematic model of two valleys with anisotropic masses whose principal axes are rotated by π/2, as in AlAs quantum wells [7,8], which gives a simpler picture of what we find.…”

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confidence: 85%

“…Introduction. Recently, we have witnessed an explosion of high-quality two-dimensional electronic systems with strongly anisotropic dispersions that can be driven into the quantum Hall regime in the presence of strong magnetic fields [1,2], such as the (111) surface of bismuth [3][4][5][6], AlAs heterostructures [7,8], PbTe(111) quantum wells [9], and the (001) surface of a topological crystalline insulator (TCI) such as Sn 1−x Pb x (Te, Se) [10]. In these systems, at integer fillings of the Landau levels, the Coulomb interaction tends to spontaneously break symmetry by forming valleypolarized states [1,[11][12][13], which can be generally divided into nematic or ferroelectric states according to whether or not the Fermi surface of an individual valley preserves inversion (or twofold rotation) symmetry [1].…”

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confidence: 99%

Local probes for quantum Hall ferroelectrics and nematics

et al. 2020

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Two-dimensional multivalley electronic systems in which the dispersion of individual pockets has low symmetry give rise to quantum Hall ferroelectric and nematic states in the presence of strong quantizing magnetic fields. We investigate the local signatures of these states arising near impurities that can be probed via scanning tunneling microscopy (STM) spectroscopy. For quantum Hall ferroelectrics, we demonstrate a direct relation between the dipole moment measured at impurity bound states and the ideal bulk dipole moment obtained from the modern theory of polarization. We also study the many-body problem with a single impurity via exact diagonalization and find that near strong impurities a nontrivial excitonic state can form with specific features that can be easily identified via STM spectroscopy.

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“…The authors further show that depending on the fillingν of valley-degenerate Landau levels, the low-energy domain wall modes at the same location on the sample is either gapless within the experimental resolution (forν = 1), or has a small tunneling gap (forν = 2). This difference is attributed to an allowed inter-valley scattering process at the domain wall forν = 2, which breaks the valley symmetry protecting the topological boundary modes [4].…”

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confidence: 99%

A River Through Quantum Hall Valleys

2019

Journal Club for Condensed Matter Physics

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Recommended with a Commentary by Liang Fu, MIT A hallmark of topological phases of matter is the presence of conducting boundary modes with unusual properties. Known examples include chiral edge states of quantum Hall states and unpaired Dirac surface states in topological insulators. Now, the highlighted paper reports the discovery of new one-dimensional topological boundary modes in a multi-valley quantum Hall system, where electron interaction and symmetry breaking play crucial roles and lead to unprecedented many-body topological phenomena. The authors uses high-resolution scanning tunneling microscopy (STM) to study the (111) surface states of bismuth. On this surface there are six hole pockets in the surface Brillouin zone, related to one another by rotation or time-reversal symmetry (see Fig.1). Therefore, in the presence of a magnetic field, single-particle Landau levels of hole states have six-fold valley degeneracy. Thanks to the exceptional cleanness of bismuth crystal, STM spectroscopy maps shows little spatial variation of Landau level energy over several hundreds of nanometers. This makes bismuth (111) surface a fruitful platform for studying multicomponent quantum Hall physics with STM. With a magnetic field between 13T and 14T, a set of N = 3 Landau levels from six valleys are within a few meV from the Fermi level. Two types of Landau level splittings are found in STM tunneling spectra, with different magnitudes and origins. First, regardless of the filling, there is an energy splitting of about 1meV between twofold and four-fold degenerate multiplets. This splitting is likely induced by uniaxial strain which lowers the single-particle energy of a pair of valleys. Moreover, when the four-fold degenerate multiplet is tuned to the Fermi level by varying the magnetic field, it further splits into two sets of Landau levels separated by about 0.65meV. Concomitant with this additional Landau level splitting is suppressed tunneling conductance at the Fermi level. These findings strongly suggest that when these four-fold degenerate Landau levels are partially occupied, electron interaction induces an exchange gap and causes the splitting. Early theory [3] predicted that due to the anisotropic energy dispersion of each valley, Coulomb interaction favors a valley-polarized state at integer filling, where a subset of valleys are fully occupied. Such state spontaneously breaks the point group symmetry. Previous works of the same group [1, 2] indeed observed valley ordering from spatially resolved STM

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Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

Cited by 7 publications

References 34 publications

Domain wall competition in the Chern insulating regime of twisted bilayer graphene

Domain wall competition in the Chern insulating regime of twisted bilayer graphene

Local probes for quantum Hall ferroelectrics and nematics

A River Through Quantum Hall Valleys

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