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Hyun-Jung Kim

Publications and source records attributed to Hyun-Jung Kim.

At least 19 recordsLinked to original sources

Circular dichroism of emergent chiral stacking orders in quasi-one-dimensional charge density waves

Chirality-driven optical properties in charge density waves are of fundamental and practical importance. Here, we investigate the interaction between circularly polarized light and emergent chiral stacking orders in quasi-one-dimensional (quasi-1D) charge-density waves (CDW) with density-functional theory calculations. In our specific system, self-assembled In nanowires on Si(111) surface, spontaneous mirror symmetry breaking leads to symmetrically distinct four degenerate quasi-1D CDW structures, which exhibit geometrical chirality. Such geometrical chirality may naturally induce optically active phenomena even when the quasi-1D CDW structures are stacked perpendicular to the CDW chain direction. Indeed, we find that left- and right-chiral stacking orders show distinct circular dichroism responses while a nonchiral stacking order does no circular dichroism. Such optical responses are attributed to the existence of glide mirror symmetry of the CDW stacking orders. Our findings suggest that the CDW chiral stacking orders can lead to diverse active optical phenomena such as chirality-dependent circular dichroism, which can be observed in scanning tunneling luminescence measurements with circularly polarized light.

cond-mat.mes-hall

A Feynman-Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise

We consider the (unique) mild solution $u(t,x)$ of a 1-dimensional stochastic heat equation on $[0,T]\times\mathbb R$ driven by time-homogeneous white noise in the Wick-Skorokhod sense. The main result of this paper is the computation of the spatial derivative of $u(t,x)$, denoted by $\partial_x u(t,x)$, and its representation as a Feynman-Kac type closed form. The chaos expansion of $\partial_x u(t,x)$ makes it possible to find its (optimal) Hölder regularity especially in space.

math.PR

Reshaped Weyl fermionic dispersions driven by Coulomb interactions in MoTe2

We report the direct evidence of impacts of the Coulomb interaction in a prototypical Weyl semimetal, MoTe2, that alter its bare bands in a wide range of energy and momentum. Our quasiparticle interference patterns measured using scanning tunneling microscopy are shown to match the joint density of states of quasiparticle energy bands including momentum-dependent self-energy corrections, while electronic energy bands based on the other simpler local approximations of the Coulomb interaction fail to explain neither the correct number of quasiparticle pockets nor shape of their dispersions observed in our spectrum. With this, we predict a transition between type-I and type-II Weyl fermions with doping and resolve its disparate quantum oscillation experiments, thus highlighting the critical roles of Coulomb interactions in layered Weyl semimetals.

cond-mat.mes-hall

$Z_2$ topology of bismuth

While first-principles calculations with different levels of sophistication predict a topologically trivial $Z_2$ state for bulk bismuth, some photoemission experiments show surface states consistent with the interpretation of bismuth being in a topologically non-trivial $Z_2$ state. We resolve this contradiction between theory and experiment by showing, based on quasiparticle self-consistent $GW$ calculations, that the experimental surface states interpreted as supporting a non-trivial phase are actually consistent with a trivial $Z_2$ invariant. We identify this contradiction as the result of a crosstalk effect arising from the extreme penetration depth of the surface states into the bulk of Bi. A film of Bi can be considered bulk-like only for thicknesses of about 1000 bilayers ($\approx$ 400 nm) and more.

cond-mat.mtrl-sci

Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise

We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when the solution is sampled discretely in the physical domain. We consider both the full space and the bounded domain. We establish the exact spatial regularity of the solution, which in turn, using power-variation arguments, allows building the desired estimators. We show that naive approximations of the derivatives appearing in the power-variation based estimators may create nontrivial biases, which we compute explicitly. The proofs are rooted in Malliavin-Stein's method.

math.PR

Statistical analysis of discretely sampled semilinear SPDEs: a power variation approach

Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are proved by using the notion of $Δ$-power variations, introduced herein, along with the Hölder-Zygmund norms. Consequently, we prove a new central limit theorem for $Δ$-power variations of the iterated integrals of a fractional Brownian motion (fBm). These abstract results, besides being of independent interest, in the second part of the paper are applied to estimation of the drift and volatility coefficients of semilinear stochastic partial differential equations in dimension one, driven by an additive Gaussian noise white in time and possibly colored in space. In particular, we solve the earlier conjecture from Cialenco, Kim, Lototsky (2019) about existence of a nontrivial bias in the estimators derived by naive approximations of derivatives by finite differences. We give an explicit formula for the bias and derive the convergence rates of the corresponding estimators. Theoretical results are illustrated by numerical examples.

math.PR

Two-dimensional chiral stacking orders in quasi-one-dimensional charge density waves

Chirality manifests in various forms in nature. However, there is no evidence of the chirality in one-dimensional charge density wave (CDW) systems. Here, we have explored the chirality among quasi-one-dimensional CDW ground states with the aid of scanning tunneling microscopy, symmetry analysis, and density functional theory calculations. We discovered three distinct chiralities emerging in the form of two-dimensional chiral stacking orders composed of degenerate CDW ground states: right-, left-, and nonchiral stacking orders. Such chiral stacking orders correspond to newly introduced chiral winding numbers. Furthermore, we observed that these chiral stacking orders are intertwined with chiral vortices and chiral domain walls, which play a crucial role in engineering the chiral stacking orders. Our findings suggest that the unexpected chiral stacking orders can open a way to investigate the chirality in CDW systems, which can lead to diverse phenomena such as circular dichroism depending on chirality.

cond-mat.mes-hall

Ferromagnetic Weyl Fermions in Two-Dimensional Layered Electride Gd$_2$C

Recently, two-dimensional layered electrides have emerged as a new class of materials which possess anionic electron layers in the interstitial spaces between cationic layers. Here, based on first-principles calculations, we discover a time-reversal-symmetry-breaking Weyl semimetal phase in a unique two-dimensional layered ferromagnetic (FM) electride Gd$_2$C. It is revealed that the crystal field mixes the interstitial electron states and Gd 5$d$ orbitals near the Fermi energy to form band inversions. Meanwhile, the FM order induces two spinful Weyl nodal lines (WNLs), which are converted into multiple pairs of Weyl nodes through spin-orbit coupling. Further, we not only identify Fermi-arc surface states connecting the Weyl nodes but also predict a large intrinsic anomalous Hall conductivity due to the Berry curvature produced by the gapped WNLs. Our findings demonstrate the existence of Weyl fermions in the room-temperature FM electride Gd$_2$C, therefore offering a new platform to investigate the intriguing interplay between electride materials and magnetic Weyl physics.

cond-mat.mtrl-sci

Symmetry dictated grain boundary state in a two-dimensional topological insulator

Structural imperfections such as grain boundaries (GBs) and dislocations are ubiquitous in solids and have been of central importance in understanding nature of polycrystals. In addition to their classical roles, advent of topological insulators (TIs) offers a chance to realize distinct topological states bound to them. Although dislocation inside three-dimensional TIs is one of the prime candidates to look for, its direct detection and characterization are challenging. Instead, in two-dimensional (2D) TIs, their creations and measurements are easier and, moreover, topological states at the GBs or dislocations intimately connect to their lattice symmetry. However, such roles of crystalline symmetries of GBs in 2D TIs have not been clearly measured yet. Here, we present the first direct evidence of a symmetry enforced Dirac type metallic state along a GB in 1T'-MoTe$_2$, a prototypical 2D TI. Using scanning tunneling microscope, we show a metallic state along a grain boundary with non-symmorphic lattice symmetry and its absence along the other boundary with symmorphic one. Our large scale atomistic simulations demonstrate hourglass like nodal-line semimetallic in-gap states for the former while the gap-opening for the latter, explaining our observation very well. The protected metallic state tightly linked to its crystal symmetry demonstrated here can be used to create stable metallic nanowire inside an insulator.

cond-mat.mes-hall

Drift Estimation for Discretely Sampled SPDEs

The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive space-time noise. We consider the traditional for stochastic partial differential equations statistical experiment when the measurements are performed in the spectral domain, and in contrast to the existing literature, we study the asymptotic properties of the maximum likelihood (type) estimators (MLE) when both, the number of Fourier modes and the time go to infinity. In the first part of the paper we consider the usual setup of continuous time observations of the Fourier coefficients of the solutions, and show that the MLE is consistent, asymptotically normal and optimal in the mean-square sense. In the second part of the paper we investigate the natural time discretization of the MLE, by assuming that the first N Fourier modes are measured at M time grid points, uniformly spaced over the time interval [0,T]. We provide a rigorous asymptotic analysis of the proposed estimators when N goes to infinity and/or T, M go to infinity. We establish sufficient conditions on the growth rates of N, M and T, that guarantee consistency and asymptotic normality of these estimators.

math.PR

Statistical Analysis of Some Evolution Equations Driven by Space-only Noise

We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations have been studied, little is known about inverse problems for these equations. We exploit the somewhat unusual structure of the observations coming from these equations that leads to an interesting interplay between classical and non-traditional statistical models. We derive several types of estimators for the drift and/or diffusion coefficients of these equations, and prove their relevant properties.

math.ST

Stochastic parabolic Anderson model with time-homogeneous generalized potential: Mild formulation of solution

A mild formulation for stochastic parabolic Anderson model with time-homogeneous Gaussian potential suggests a way of defining a solution to obtain its optimal regularity. Two different interpretations in the equation or in the mild formulation are possible with usual pathwise product and the Wick product: the usual pathwise interpretation is mainly discussed. We emphasize that a modified version of parabolic Schauder estimates is a key idea for the existence and uniqueness of a mild solution. In particular, the mild formulation is crucial to investigate a relation between the equation with usual pathwise product and the Wick product.

math.AP

An Asymptotic Comparison of Two Time-homogeneous PAM Models

Both Wick-Ito-Skorokhod and Stratonovich interpretations of the parabolic Anderson model (PAM) lead to solutions that are real analytic as functions of the noise intensity e, and, in the limit e->0, the difference between the two solutions is of order e^2 and is non-random.

math.AP

Competing edge structures of Sb and Bi bilayers by trivial and nontrivial band topologies

One-dimensional (1D) edge states formed at the boundaries of 2D normal and topological insulators have shown intriguing quantum phases such as charge density wave and quantum spin Hall effect. Based on first-principles density-functional theory calculations including spin-orbit coupling (SOC), we show that the edge states of zigzag Sb(111) and Bi(111) nanoribbons drastically change the stability of their edge structures. For zigzag Sb(111) nanoribbon, the Peierls-distorted or reconstructed edge structure is stabilized by a band-gap opening. However, for zigzag Bi(111) nanoribbon, such two insulating structures are destabilized due to the presence of topologically protected gapless edge states, resulting in the stabilization of a metallic, shear-distorted edge structure. We also show that the edge states of the Bi(111) nanoribbon exhibit a larger Rashba-type spin splitting at the boundary of Brillouin zone, compared to those of the Sb(111) nanoribbon. Interestingly, the spin textures of edge states in the Peierls-distorted Sb edge structure and the shear-distorted Bi edge structure have all three spin components perpendicular and parallel to the edges, due to their broken mirror-plane symmetry. The present findings demonstrate that the topologically trivial and nontrivial edge states play crucial roles in determining the edge structures of normal and topological insulators.

cond-mat.mtrl-sci

Microscopic mechanism of tunable band gap in potassium doped few-layer black phosphorus

Tuning band gaps in two-dimensional (2D) materials is of great interest in the fundamental and practical aspects of contemporary material sciences. Recently, black phosphorus (BP) consisting of stacked layers of phosphorene was experimentally observed to show a widely tunable band gap by means of the deposition of potassium (K) atoms on the surface, thereby allowing great flexibility in design and optimization of electronic and optoelectronic devices. Here, based on the density-functional theory calculations, we demonstrates that the donated electrons from K dopants are mostly localized at the topmost BP layer and such a surface charging efficiently screens the K ion potential. It is found that, as the K doping increases, the extreme surface charging and its screening of K atoms shift the conduction bands down in energy, i.e., towards higher binding energy, because they have more charge near the surface, while it has little influence on the valence bands having more charge in the deeper layers. This result provides a different explanation for the observed tunable band gap compared to the previously proposed giant Stark effect where a vertical electric field from the positively ionized K overlayer to the negatively charged BP layers shifts the conduction band minimum $Γ_{\rm 1c}$ (valence band minimum $Γ_{\rm 8v}$) downwards (upwards). The present prediction of $Γ_{\rm 1c}$ and $Γ_{\rm 8v}$ as a function of the K doping reproduces well the widely tunable band gap, anisotropic Dirac semimetal state, and band-inverted semimetal state, as observed by angle-resolved photoemission spectroscopy experiment. Our findings shed new light on a route for tunable band gap engineering of 2D materials through the surface doping of alkali metals.

cond-mat.mtrl-sci

Comment on "Quasi-One-Dimensional Metal-Insulator Transitions in Compound Semiconductor Surfaces"

In a recent Letter, Zhao et al. [1] reported the origin of quasi-one-dimensional metal-insulator (MI) transitions in compound semiconductor surfaces. Based on a density-functional theory (DFT) calculation within the generalized gradient approximation (GGA), they claimed that one-atom-wide metallic structures formed by a selective bonding of H or Li atoms to GaN(10-10) and ZnO(10-10) undergo the Peierls-type MI transitions, leading to a charge-density-wave (CDW) formation with periodic lattice distortion. However, we here demonstrate that such a CDW phase is due to the artifact of the GGA, while the antiferromagnetic (AFM) ground state is predicted by the hybrid DFT calculation and the exact-exchange plus correlation in the random-phase approximation (EX + cRPA). [1] J. Z. Zhao, W. Fan, M. J. Verstraete, Z. Zanolli, J. Fan, X. B. Yang, H. Xu, and S. Y. Tong, Phys. Rev. Lett. 117, 116101 (2016).

cond-mat.mes-hall

Origins of the structural phase transitions in MoTe$_2$ and WTe$_2$

Layered transition metal dichalcogenides MoTe$_2$ and WTe$_2$ share almost similar lattice constants as well as topological electronic properties except their structural phase transitions. While the former shows a first-order phase transition between monoclinic and orthorhombic structures, the latter does not. Using a recently proposed van der Waals density functional method, we investigate structural stability of the two materials and uncover that the disparate phase transitions originate from delicate differences between their interlayer bonding states near the Fermi energy. By exploiting the relation between the structural phase transitions and the low energy electronic properties, we show that a charge doping can control the transition substantially, thereby suggesting a way to stabilize or to eliminate their topological electronic energy bands.

cond-mat.mes-hall

Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution

Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the stochastic heat equation with space-only Gaussian white noise on a bounded interval. The main result is that the space-time regularity of the solution is the same for additive noise and for multiplicative noise in the Wick-Itô-Skorokhod interpretation.

math.PR