Second-Order Topological Insulator in van der Waals Heterostructures of CoBr2_2/Pt2_2HgSe3_3/CoBr2_2

Second-order topological insulator, which has (d-2)-dimensional topological hinge or corner states, has been observed in three-dimensional materials, but has yet not been observed in two-dimensional system. In this Letter, we theoretically propose the realization of second-order topological insulator in the van der Waals heterostructure of CoBr$_2$/Pt$_2$HgSe$_3$/CoBr$_2$. Pt$_2$HgSe$_3$ is a large gap $\mathbb{Z}_2$ topological insulator. With in-plane exchange field from neighboring CoBr$_2$, a large band gap above 70 meV opens up at the edge. The corner states, which are robust against edge disorders and irregular shapes, are confirmed in the nanoflake. We further show that the second-order topological states can also be realized in the heterostructure of jacutingaite family $\mathbb{Z}_2$ topological insulators. We believe that our work will be beneficial for the experimental realization of second-order topological insulators in van der Waals layered materials

Topological Corner States in Graphene by Bulk and Edge Engineering

Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner states are difficult to pinpoint. We address this problem in a graphene-based $\mathbb{Z}_2$ topological insulator with spin-orbit coupling and in-plane magnetization both originating from substrates through a Slater-Koster multi-orbital model. The gapless helical edge modes cross inside the bulk, where is also located the magnetization-induced edge gap. After demonstrating its second-order nontriviality in bulk topology by a series of evidence, we show that a difference in bulk-edge onsite energy can adiabatically tune the position of the crossing/anticrossing of the edge modes to be inside the bulk gap. This can help unambiguously identify two pairs of topological corner states with nonvanishing energy degeneracy for a rhombic flake. We further find that the obtuse-angle pair is more stable than the acute-angle one. These results not only suggest an accessible way to "find" topological corner states, but also provide a higher-order topological version of "bulk-boundary correspondence"

Automatic Search for Key-Bridging Technique: Applications to LBlock and TWINE (Full Version)

Key schedules in block ciphers are often highly simplified, which causes weakness that can be exploited in many attacks. At ASIACRYPT 2011, Dunkelman et al. proposed a technique using the weakness in the key schedule of AES, called key-bridging technique, to improve the overall complexity. The advantage of key-bridging technique is that it allows the adversary to deduce some sub-key bits from some other sub-key bits, even though they are separated by many key mixing steps. Although the relations of successive rounds may be easy to see, the relations of two rounds separated by some mixing steps are very hard to find. In this paper, we describe a versatile and powerful algorithm for searching key-bridging technique on word-oriented and bit-oriented block ciphers. To demonstrate the usefulness of our approach, we apply our tool to the impossible differential and multidimensional zero correlation linear attacks on 23-round LBlock, 23-round TWINE-80 and 25-round TWINE-128. To the best of our knowledge, these results are the currently best results on LBlock and TWINE in the single-key setting

The Relationship between the Construction and Solution of the MILP Models and Applications

The automatic search method based on Mix-integer Linear Programming (MILP) is one of the most common tools to search the distinguishers of block ciphers. For differential analysis, the byte-oriented MILP model is usually used to count the number of differential active s-boxes and the bit-oriented MILP model is used to search the optimal differential characteristic. In this paper, we present the influences between the construction and solution of MILP models solved by Gurobi : 1). the number of variables; 2). the number of constraints; 3). the order of the constraints; 4). the order of variables in constraints. We carefully construct the MILP models according to these influences in order to find the desired results in a reasonable time. As applications, we search the differential characteristic of PRESENT,GIFT-64 and GIFT-128 in the single-key setting. We do a dual processing for the constraints of the s-box. It only takes 298 seconds to finish the search of the 8-round optimal differential characteristic based on the new MILP model. We also obtain the optimal differential characteristic of the 9/10/11-round PRESENT. With a special initial constraint, it only takes 4 seconds to obtain a 9-round differential characteristic with probability $2^{-42}$. We also get a 12/13-round differential characteristic with probability $2^{-58}/2^{-62}$. For GIFT-128, we improve the probability of differential characteristic of $9 \sim 21$ rounds and give the first attack on 26-round GIFT-128 based on a 20-round differential characteristic with probability $2^{-121.415}$

Anisotropic shear stress σxy\sigma_{xy} effects in the basal plane of Sr2_2RuO4_4

In this short note, we repeat the calculations the jumps for the specific heat C$_{\sigma_{xy}}$, the elastic compliance S$_{xyxy}^{\sigma_{xy}}$ and the thermal expansion $\alpha_{\sigma_{xy}}$ due to a shear stress $\sigma_{xy}$ in the basal plane of $Sr_2RuO_4$. Henceforth we clarify some issues regarding the elastic theoretical framework suitable to explain the sound speed experiments of Lupien et al. (2001,2002), and partially the strain experiments of Hicks et al. (2014), and Steppke et al. (2016) in strontium ruthenate. We continue to propose that the discontinuity in the elastic constant C$_{xyxy}$ of this tetragonal crystal gives unambiguous experimental evidence that the superconducting order parameter $\Psi$ has two components with a broken time-reversal symmetry state, and that the $\gamma$ band couples the anisotropic electron-phonon interaction to the $[xy]$ in-plane shear stress according to Walker and collaborators [4] and [3]. Some importants words about the roll of the spin equal to one for the transversal phonons are added in the conclusion following Levine [34].Comment: 11 pages, for section 5: added figure 2 and figure 3 replaced. One reference and typos added. figure 4 added. arXiv admin note: text overlap with arXiv:1812.0649