The Experts below are selected from a list of 129 Experts worldwide ranked by ideXlab platform
A. C. Cem Say - One of the best experts on this subject based on the ideXlab platform.
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Constant-Space, Constant-Randomness Verifiers with Arbitrarily Small Error.
arXiv: Computational Complexity, 2020Co-Authors: M. Utkan Gezer, A. C. Cem SayAbstract:We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed Nonzero Number of coins regardless of the input size. Say and Yakaryilmaz showed that the class of languages that could be verified by these machines within an error bound strictly less than 1/2 is precisely NL, but their construction yields verifiers with error bounds that are very close to 1/2 for most languages in that class. We characterize a subset of NL for which verification with arbitrarily low error is possible by these extremely weak machines. It turns out that, for any $\varepsilon>0$, one can construct a constant-coin, constant-space verifier operating within error $\varepsilon$ for every language that is recognizable by a linear-time multi-head finite automaton (2nfa($k$)). We discuss why it is difficult to generalize this method to all of NL, and give a reasonably tight way to relate the power of linear-time 2nfa($k$)'s to simultaneous time-space complexity classes defined in terms of Turing machines.
Guang Bian - One of the best experts on this subject based on the ideXlab platform.
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Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points
Nature communications, 2017Co-Authors: Ilya Belopolski, Daniel S. Sanchez, Yukiaki Ishida, Tay Rong Chang, Songtian S. Zhang, Hao Zheng, Guoqing Chang, Guang BianAbstract:Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum Nonzero Number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe4 realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe4. We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe4 is a Weyl semimetal with the minimum Number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals.Weyl semimetals are interesting because they are characterized by topological invariants, but specific examples discovered to date tend to have complicated band structures with many Weyl points. Here, the authors show that TaIrTe4 has only four Weyl points, the minimal Number required by time-reversal symmetry.
M. Utkan Gezer - One of the best experts on this subject based on the ideXlab platform.
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Constant-Space, Constant-Randomness Verifiers with Arbitrarily Small Error.
arXiv: Computational Complexity, 2020Co-Authors: M. Utkan Gezer, A. C. Cem SayAbstract:We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed Nonzero Number of coins regardless of the input size. Say and Yakaryilmaz showed that the class of languages that could be verified by these machines within an error bound strictly less than 1/2 is precisely NL, but their construction yields verifiers with error bounds that are very close to 1/2 for most languages in that class. We characterize a subset of NL for which verification with arbitrarily low error is possible by these extremely weak machines. It turns out that, for any $\varepsilon>0$, one can construct a constant-coin, constant-space verifier operating within error $\varepsilon$ for every language that is recognizable by a linear-time multi-head finite automaton (2nfa($k$)). We discuss why it is difficult to generalize this method to all of NL, and give a reasonably tight way to relate the power of linear-time 2nfa($k$)'s to simultaneous time-space complexity classes defined in terms of Turing machines.
Youguo Shi - One of the best experts on this subject based on the ideXlab platform.
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Observation of Topological Edge States at the Step Edges on the Surface of Type-II Weyl Semimetal TaIrTe4.
ACS nano, 2019Co-Authors: Xu Dong, Maoyuan Wang, Dayu Yan, Xianglin Peng, Wende Xiao, Qinsheng Wang, Junfeng Han, Youguo ShiAbstract:Topological materials harbor topologically protected boundary states. Recently, TaIrTe4, a ternary transition-metal dichalcogenide, was identified as a type-II Weyl semimetal with the minimal Nonzero Number of Weyl points allowed for a time-reversal invariant Weyl semimetal. Monolayer TaIrTe4 was proposed to host topological edge states, which, however, lacks of experimental evidence. Here, we report on the topological edge states localized at the monolayer step edges of the type-II Weyl semimetal TaIrTe4 using scanning tunneling microscopy. One-dimensional electronic states that show substantial robustness against the edge irregularity are observed at the step edges. Theoretical calculations substantiate the topologically nontrivial nature of the edge states and their robustness against the edge termination and layer stacking. The observation of topological edge states at the step edges of TaIrTe4 surfaces suggests that monolayer TaIrTe4 is a two-dimensional topological insulator, providing TaIrTe4 as a promising material for topological physics and devices.
Ilya Belopolski - One of the best experts on this subject based on the ideXlab platform.
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Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points
Nature communications, 2017Co-Authors: Ilya Belopolski, Daniel S. Sanchez, Yukiaki Ishida, Tay Rong Chang, Songtian S. Zhang, Hao Zheng, Guoqing Chang, Guang BianAbstract:Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum Nonzero Number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe4 realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe4. We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe4 is a Weyl semimetal with the minimum Number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals.Weyl semimetals are interesting because they are characterized by topological invariants, but specific examples discovered to date tend to have complicated band structures with many Weyl points. Here, the authors show that TaIrTe4 has only four Weyl points, the minimal Number required by time-reversal symmetry.
