Nonlinear optical (NLO) responses of topological materials are under active research in recent years. Yet by far most studies focused on the bulk properties, whereas the surface effects and the difference between surface and bulk responses have not b
een systematically studied. In this work, we develop a generic Greens function framework to investigate the surface NLO properties of topological materials. The Greens function framework can naturally incorporate many body effects and can be easily extended to high order NLO responses. Using $rm T_d WTe_2$ as an example, we reveal that the surface can behave disparately from the bulk under light illumination. Remarkably, the shift and circular current on the surface can flow in opposite directions to that in the bulk. Moreover, the light induced spin current on the surface can be orders of magnitude stronger than that in the bulk. We also study the responses under inhomogeneous field and higher order NLO effect, which are all distinct on the surface. These anomalous surface NLO responses suggest that light can be a valuable tool for probing the surface states of topological materials, while on the other hand, the surface effects shall be prudently considered when investigating the optical properties of topological materials.
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursi
on will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of quantum while-programs. However, there are as yet no general methods for reasoning about (mutual) recursive procedures and ancilla quantum data structure in quantum computing (with measurement). We fill the gap in this paper by proposing a parameterized quantum assertion logic and, based on which, designing a quantum Hoare logic for verifying parameterized recursive quantum programs with ancilla data and probabilistic control. The quantum Hoare logic can be used to prove partial, total, and even probabilistic correctness (by reducing to total correctness) of those quantum programs. In particular, two counterexamples for illustrating incompleteness of non-parameterized assertions in verifying recursive procedures, and, one counterexample for showing the failure of reasoning with exact probabilities based on partial correctness, are constructed. The effectiveness of our logic is shown by three main examples -- recursive quantum Markov chain (with probabilistic control), fixed-point Grovers search, and recursive quantum Fourier sampling.
Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall conductance without external magnetic field. It requires both nontrivial band topology and time-reversal symmetry (TRS) breaking. In most cases, one could break the TRS of t
ime-reversal invariant topological materials to yield QAH effect, which is essentially a topological phase transition. Conventional topological phase transition induced by external field/stimulus needs a route along which the bandgap closes and re-opens. Hence, the phase transition occurs only when the magnitude of field/stimulus is larger than a critical value. In this work we propose that using gapless surface states, the transition can happen at arbitrarily weak (but finite) external field strength. This can be regarded as an unconventional topological phase transition, where the bandgap closing is guaranteed by bulk-edge correspondence and symmetries, while the bandgap reopening is induced by external fields. We demonstrate this concept on the 2D surface states of 3D topological insulators like $rm Bi_2Se_3$, which become 2D QAH insulators once a circularly polarized light is turned on, according to van Vlecks effective Hamiltonian in Floquet time crystal theory. The sign of quantized Chern number can be controlled via the chirality of the light. This provides a convenient and dynamical approach to trigger topological phase transitions and create QAH insulators.
Nonlinear optical properties, such as bulk photovoltaic effects, possess great potential in energy harvesting, photodetection, rectification, etc. To enable efficient light-current conversion, materials with strong photo-responsivity are highly desir
able. In this work, we predict that monolayer Janus transition metal dichalcogenides (JTMDs) in the 1T phase possess colossal nonlinear photoconductivity owing to their topological band mixing, strong inversion symmetry breaking, and small electronic bandgap. 1T JTMDs have inverted bandgaps on the order of 10 meV and are exceptionally responsive to light in the terahertz (THz) range. By first-principles calculations, we reveal that 1T JTMDs possess shift current (SC) conductivity as large as $2300 ~rm nm cdot mu A / V^2$, equivalent to a photo-responsivity of $2800 ~rm mA/W$. The circular current (CC) conductivity of 1T JTMDs is as large as $10^4~ rm nm cdot mu A / V^2$. These remarkable photo-responsivities indicate that the 1T JTMDs can serve as efficient photodetectors in the THz range. We also find that external stimuli such as the in-plane strain and out-of-plane electric field can induce topological phase transitions in 1T JTMDs and that the SC can abruptly flip their directions. The abrupt change of the nonlinear photocurrent can be used to characterize the topological transition and has potential applications in 2D optomechanics and nonlinear optoelectronics.
We theoretically and computationally demonstrate that static magnetization can be generated under light illumination via nonlinear Edelstein effect (NLEE). NLEE is applicable to semiconductors under both linearly and circularly polarized light, and t
here are no constraints from either spatial inversion or time-reversal symmetry. Remarkably, magnetization can be induced under linearly polarized light in nonmagnetic materials. With ab initio calculations, we reveal several prominent features of NLEE. We find that the orbital contributions can be significantly greater than the spin contributions. And magnetization with various orderings, including anti-ferromagnetic, ferromagnetic, etc., are all realizable with NLEE, which may facilitate many applications, such as unveiling hidden physical effects, creating a spatially varying magnetization, or manipulating the magnetization of anti-ferromagnetic materials. The relationship between NLEE and other magneto-optic effects, including the inverse Faraday effect and inverse Cotton-Mouton effect, is also discussed.
The mid-infrared (MIR), far-infrared (FIR) to terahertz (THz) frequencies are the least developed parts of the electromagnetic spectrum for applications. Traditional semiconductor technologies like laser diodes and photodetectors are successful in th
e visible light range, but are still confronted with great challenges when extended into the MIR/FIR/THz range. In this paper, we demonstrate that topological insulators (TIs), especially those with Mexican-hat band structure (MHBS), provide a route to overcome these challenges. The optical responses of MHBS TIs can be one to two orders of magnitude larger than that of normal semiconductors at the optical-transition edge. We explore the databases of topological materials and discover a number of MHBS TIs whose bandgaps lie between $0.05sim 0.5~rm eV$ and possess giant gains (absorption coefficients) on the order of $10^4 sim 10^5~rm cm^{-1}$ at the transition edge. These findings may significantly boost potential MIR/FIR/THz applications such as photon sources, detectors, ultrafast electro-optical devices, and quantum information technologies.
Spin current generators are critical components for spintronics-based information processing. In this work, we theoretically and computationally investigate the bulk spin photovoltaic (BSPV) effect for creating DC spin current under light illuminatio
n. The only requirement for BPSV is inversion symmetry breaking, thus it applies to a broad range of materials and can be readily integrated with existing semiconductor technologies. The BSPV effect is a cousin of the bulk photovoltaic (BPV) effect, whereby a DC charge current is generated under light. Thanks to the different selection rules on spin and charge currents, a pure spin current can be realized if the system possesses mirror symmetry or inversion-mirror symmetry. The mechanism of BPSV and the role of the electronic relaxation time $tau$ are also elucidated. We apply our theory to several distinct material systems, including transition metal dichalcogenides, anti-ferromagnetic $rm MnBi_2Te_4$, and the surface of topological crystalline insulator cubic $rm SnTe$.
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursi
on will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of non-recursive quantum programs. However, there are as yet no general methods for reasoning about recursive procedures in quantum computing. We fill the gap in this paper by presenting a logic for recursive quantum programs. This logic is an extension of quantum Hoare logic for quantum While-programs. The (relative) completeness of the logic is proved, and its effectiveness is shown by a running example: fixed-point Grovers search.
The effect of Quantum Gravity (QG) may bring a tiny light speed variation as $v(E)=c(1-E/E_{rm LV})$, where $E$ is the photon energy and $E_{rm LV}$ is a Lorentz violation scale. A remarkable regularity was suggested in previous studies to look for t
he light speed variation from high energy photon events of Gamma Ray Bursts (GRBs). We provide a general analysis on the data of 25 bright GRBs observed by the Fermi Gamma-ray Space Telescope (FGST). Such method allows a completed scan over all possibilities in a more clean and impartial way without any bias compared to previous intuitive analysis. The results show that with the increase in the intrinsic energies of photons, such regularity truly emerges and gradually becomes significant. For photons with intrinsic energies higher than 40~GeV, the regularity exists at a significance of 3-5~$sigma$ with $E_{rm LV}=3.6times 10^{17}~rm GeV$ determined by the GRB data.
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The kno
