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Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two complementary aspects. First, we provide a decomposition form for the space-group factor systems to characterize all quantum space groups. It consists of three factors, the factor system for the translation subgroup $L$, an in-homogeneous factor system for the point group $P$, and a factor connecting $L$ and $P$. The three factors satisfy three consistency equations, which are exactly solvable and can completely exhaust all factor systems for space groups. Second, since factors systems are classified by the second cohomology group, we show the (co)homology groups for space groups can be derived from Borels equivariant (co)homology theory, which leads to an algorithm that can compute all (co)homology groups for space groups. To demonstrate the general theory, we explicitly present quantum wallpaper groups with the $mathbb{Z}_2$ gauge group. Furthermore, as a primitive application, we find the time-reversal invariant quantum space groups with inversion symmetry can lead to a novel clifford band theory, where each band is fourfold degenerate to represent certain real Clifford algebras with topologically nontrivial pinor structures over the Brillouin zone. Our work serves as a foundation for exploring quantum mechanical space groups, and can find applications in spin liquids, unconventional superconductors, and artificial lattice systems, including cold atoms, photonic and phononic crystals, and even LC electric circuit networks.
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We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes beta=1,2,4 of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for beta=1,4, thus proving a number of conjectures of Khoruzhenko et al. (Phys. Rev. B, Vol. 80 (2009), 125301). We derive differential equations that characterize the cumulant generating functions for all beta=1,2,4. Furthermore, we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painleve III transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit n -> infinity. Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders.
Heavy metal-ferromagnet bilayer structures have attracted great research interest for charge-to-spin interconversion. In this work, we have investigated the effect of the permalloy seed layer on the Ta polycrystalline phase and its spin Hall angle. Interestingly, for the same deposition rates the crystalline phase of Ta deposited on Py seed layer strongly depends on the thickness of the seed layer. We have observed a phase transition from $alpha$-Ta to ($alpha$+$beta$)-Ta while increasing the Py seed layer thickness. The observed phase transition is attributed to the strain at interface between Py and Ta layers. Ferromagnetic resonance-based spin pumping studies reveal that the spin-mixing conductance in the to ($alpha$+$beta$)-Ta is relatively higher as compared to the to $alpha$-Ta. Spin Hall angles of to $alpha$-Ta and to ($alpha$+$beta$)-Ta are extracted from inverse spin Hall effect (ISHE) measurements. Spin Hall angle of the to ($alpha$+$beta$)-Ta is estimated to be $theta$_SH=-0.15 which is relatively higher than that of to $alpha$-Ta. Our systematic results connecting the phase of the Ta with seed layer and its effect on the efficiency of spin to charge conversion might resolve ambiguities across various literature and open up new functionalities based on the growth process for the emerging spintronic devices.
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.
We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $langle W rangle le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $langle W rangle=5$ indicates the degree of confidence in the detection of Majorana fermions.
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