Topological kink states at a tilt boundary in gated multi-layer graphene

The search for new realization of topologically protected edge states is an active area of research. We show that a tilt boundary in gated multi-layer graphene supports topologically protected gapless kink states, associated with quantum valley Hall insulator (QVH). We investigate such kink states from two perspectives: the microscopic perspective of a tight-binding model and an ab-initio calculation on bilayer, and the perspective of symmetry protected topological (SPT) states for general multi-layer. We show that a AB-BA bilayer tilt boundary supports gapless kink states that are undeterred by strain concentrated at the boundary. Further, we establish the kink states as concrete examples of edge states of {\it time-reversal symmetric} ${\mathbb Z}$-type SPT, protected by no valley mixing, electron number conservation, and time reversal $T$ symmetries. This allows us to discuss possible phase transitions upon symmetry changes from the SPT perspective. Recent experimental observations of a network of such tilt boundaries suggest that transport through these novel topological kink states might explain the long standing puzzle of sub-gap conductance. Further, recent observation of gap closing and re-opening in gated bi-layer might be the first example of a transition between two distinct SPT's: QVH and LAF.Comment: Improved a discussion of the structural aspects of the tilt boundary. Included a discussion of boundary condition dependence. Added new section on connection to experiment

Entanglement entropy of the ν=1/2\nu=1/2 composite fermion non-Fermi liquid state

The so-called ``non-Fermi liquid'' behavior is very common in strongly correlated systems. However, its operational definition in terms of ``what it is not'' is a major obstacle against theoretical understanding of this fascinating correlated state. Recently there has been much interest in entanglement entropy as a theoretical tool to study non-Fermi liquids. So far explicit calculations have been limited to models without direct experimental realizations. Here we focus on a two dimensional electron fluid under magnetic field and filling fraction $\nu=1/2$, which is believed to be a non-Fermi liquid state. Using the composite fermion (CF) wave-function which captures the $\nu=1/2$ state very accurately, we compute the second R\'enyi entropy using variational Monte-Carlo technique and an efficient parallel algorithm. We find the entanglement entropy scales as $L\log L$ with the length of the boundary $L$ as it does for free fermions, albeit with a pre-factor twice that of the free fermion. We contrast the results against theoretical conjectures and discuss the implications of the results.Comment: 4+ page

Signatures of unconventional pairing in near-vortex electronic structure of LiFeAs

A major question in Fe-based superconductors remains the structure of the pairing, in particular whether it is of unconventional nature. The electronic structure near vortices can serve as a platform for phase-sensitive measurements to answer this question. By solving Bogoliubov-de Gennes equations for LiFeAs, we calculate the energy-dependent local electronic structure near a vortex for different nodeless gap-structure possibilities. At low energies, the local density of states (LDOS) around a vortex is determined by the normal-state electronic structure. However, at energies closer to the gap value, the LDOS can distinguish an anisotropic from a conventional isotropic s-wave gap. We show within our self-consistent calculation that in addition, the local gap profile differs between a conventional and an unconventional pairing. We explain this through admixing of a secondary order parameter within Ginzburg-Landau theory. In-field scanning tunneling spectroscopy near vortices can therefore be used as a real-space probe of the gap structure

Spin-Orbit Coupling in LaAlO3_3/SrTiO3_3 interfaces: Magnetism and Orbital Ordering

The combination of Rashba spin-orbit coupling and electron correlations can induce unusual phenomena in the metallic interface between SrTiO$_3$ and LaAlO$_3$. We consider effects of Rashba spin-orbit coupling at this interface in the context of the recent observation of anisotropic magnetism. Firstly, we show how Rashba spin-orbit coupling in a system near a band-edge can account for the observed magnetic anisotropy. Secondly, we investigate the coupling between in-plane magnetic-moment anisotropy and nematicity in the form of an orbital imbalance between d$_{xz}$ / d$_{yz}$ orbitals. We estimate this coupling to be substantial in the low electron density regime. Such an orbital ordering can affect magneto transport

Commensurate 4a04a_0 period Charge Density Modulations throughout the Bi2Sr2CaCu2O8+xBi_2Sr_2CaCu_2O_{8+x} Pseudogap Regime

Theories based upon strong real space (r-space) electron electron interactions have long predicted that unidirectional charge density modulations (CDM) with four unit cell (4$a_0$) periodicity should occur in the hole doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector $Q_A$ of the CDM to evolve continuously as if driven primarily by momentum space (k-space) effects. Here we introduce phase resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this new technique reveals a virtually doping independent locking of the local CDM wavevector at $|Q_0|=2\pi/4a_0$ throughout the underdoped phase diagram of the canonical cuprate $Bi_2Sr_2CaCu_2O_8$. These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi surface) based picture of the cuprate CDM but are consistent with strong coupling r-space based theories. Our findings imply that it is the latter that provide the intrinsic organizational principle for the cuprate CDM state

Topological Defects Coupling Smectic Modulations to Intra-unit-cell Nematicity in Cuprate

We study the coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi2Sr2CaCu2O8+{\delta}. By visualizing their spatial components separately, we identified 2\pi topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra-unit-cell nematicity revealed strong empirical evidence for a coupling between them. From these observations, we propose a Ginzburg-Landau functional describing this coupling and demonstrate how it can explain the coexistence of the smectic and intra-unit-cell broken symmetries and also correctly predict their interplay at the atomic scale. This theoretical perspective can lead to unraveling the complexities of the phase diagram of cuprate high-critical-temperature superconductors