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The Uhlmann phase, which reflects the holonomy as the purified state of a density matrix traverses a loop in the parameter space, has been used to characterize topological properties of several systems at finite temperatures. We test the Uhlmann holonomy against various system-environment couplings in quantum dynamics described by the Lindblad equations of three topological systems, including the Su-Schrieffer-Heeger (SSH) model, Kitaev chain, and Bernevig-Hughes-Zhang (BHZ) model. The Uhlmann phase is shown to remain quantized in all the examples if the initial state is topological and only certain types of the Lindblad jump operators are present. Topological protection at finite temperatures against environmental effects in quantum dynamics is therefore demonstrated albeit only for a restricted class of system-environment couplings., Comment: 10 pages, 4 figures, submitted

The ensemble geometric phase (EGP) has been proposed as a topological indicator for finite-temperatures systems. The ensemble Wilson loop, or the transfer matrix, contains the crucial information in the EGP construction. We propose a proxy index and a proxy EGP directly from the transfer matrix and apply them to time-reversal invariant topological insulators exemplified by the Bernevig-Hughes-Zhang (BHZ) and Kane-Mele (KM) models. The quantized proxy index and proxy EGP smoothly generalize the ground-state topological index to finite temperatures. For the BHZ model, a comparison with another topological indicator, the Uhlmann phase, shows different transition behavior with temperature. For the KM model, the EGP have been generalized to the time-reversal EGP previously, but the proxy EGP does not require any splitting of the contributions. The proxy index and proxy EGP thus offer an efficient means for characterizing finite-temperature topological properties., Comment: 11 pages, 7 figures, submitted

The Hopf insulator is a three-dimensional topological insulator outside the standard classification of topological insulators. Here we consider two types of non-Hermitian Hopf insulators, one without and one with the non-Hermitian skin effect. The isolated gapless points of the Hermitian model are broadened into finite regimes in the non-Hermitian models. However, the modulus of the Hopf index remains quantized in the gapped regions. The model without the non-Hermitian skin effect allows an accurate evaluation of its generalized Hopf index and energy spectrum, showing an agreement between the gapless-regime estimations from the systems with periodic- and open- boundary conditions. Near the zero-energy plane, Fermi rings can be observed whenever the Hopf index is quantized at nonzero values, and there is a bulk-boundary correspondence between the modulus of the Hopf index and the number of Fermi rings. The other model manifests the non-Hermitian skin effect in the generalized Brillouin zone and shows the skewed profiles of the bulk states. The Hopf index and energy spectrum are shown to be sensitive to the boundary condition in the presence of the non-Hermitian skin effect., Comment: 9 pages, 9 figures, submitted

The dynamics of two-dimensional (2D) topological quadrupole insulator (TQI) and Chern insulator (CI) after the real-space configuration is transformed from a cylinder or Mobius strip to open boundary condition (OBC) and vice versa is analyzed. Similar dynamics of both models are observed, but the quadrupole corner states of the TQI makes the signatures more prominent. After the systems transform from a cylinder or Mobius strip to OBC, the occupation of the corner state of the TQI and the edge state of the CI exhibits steady-state behavior. The steady-state values depend on the ramping rate of the configuration transformation, manifesting a type of quantum memory effect. On the other hand, oscillatory density ripples from the merging of edge states persist after the systems transform from OBC to a cylinder or Mobius strip. If the final configuration is a cylinder, the density ripples are along the edges of the cylinder. In contrast, the density ripples can traverse the bulk after the systems transform from OBC to a Mobius strip. The transformation of real-space topology thus can be inferred from the dynamical signatures of the topological edge states.

Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical lattices in the classical regime, i.e., essentially "masses and springs". We show that the thermal conductance factorizes into topological and nontopological components. The former takes on three discrete values and arises due to the appearance of edge modes that prevent good contact between the heat reservoirs and the bulk, giving a length-independent reduction of the conductance. In essence, energy input at the boundary mostly stays there, an effect robust against disorder and nonlinearity. These results bridge two seemingly disconnected disciplines of physics, namely topology and thermal transport, and suggest ways to engineer thermal contacts, opening a direction to explore the ramifications of topological properties on nanoscale technology.

Dynamics induced by a change of boundary conditions reveals rate-dependent signatures associated with topological properties in one-dimensional Kitaev chain and SSH model. While the perturbation from a change of the boundary propagates into the bulk, the density of topological edge modes in the case of transforming to open boundary condition reaches steady states. The steady-state density depends on the transformation rate of the boundary and serves as an illustration of quantum memory effects in topological systems. Moreover, while a link is physically broken as the boundary condition changes, some correlation functions can remain finite across the broken link and keep a record of the initial condition. By testing those phenomena in the nontopological regimes of the two models, none of the interesting signatures of memory effects can be observed. Our results thus contrast the importance of topological properties in boundary-induced dynamics.

Structural stability and hydrogen adsorption capacity are two key quantities in evaluating the potential of metal-adatom decorated graphene for hydrogen storage and related devices. We have carried out extensive density functional theory calculations for the adsorption of hydrogen molecules on 12 different adatom (Ag, Au, Ca, Li, Mg, Pd, Pt, Sc, Sr, Ti, Y, and Zr) decorated graphene surfaces where the adatoms are found to be stabilized on double carbon vacancies, thus overcoming the ``clustering problem'' that occurs for adatoms on pristine graphene. Ca and Sr are predicted to bind the greatest number, namely six, of H${}_{2}$ molecules. We find an interesting correlation between the hydrogen capacity and the change of charge distribution with increasing H${}_{2}$ adsorption, where Ca, Li, Mg, Sc, Ti, Y, Sr, and Zr adatoms are partial electron donors and Ag, Au, Pd, and Pt are partial electron acceptors. The ``18-electron rule'' for predicting maximum hydrogen capacity is found not to be a reliable indicator for these systems.

We calculate the dc conductivity $\ensuremath{\sigma}$ in a pseudogapped high ${T}_{c}$ superconductor within a precursor superconductivity theory which is consistent with gauge invariance. Our results contain physical effects beyond those identified previously. Rather than presuming that lifetime effects dominate the $T$ dependence of transport, here we show (consistent with growing experimental support) that the temperature dependence of the effective carrier number is a natural consequence of the pseudogap, and demonstrate reasonable agreement with dc transport in the underdoped cuprates.

In this paper we explore the behavior of the quasiparticle interference (QPI) pattern of scanning tunneling microscopy as a function of temperature $T$, for moderately underdoped cuprates. After ensuring a minimal consistency with angle-resolved photoemission spectroscopy, we find that the QPI pattern is profoundly sensitive to quasiparticle coherence and that it manifests two energy-gap scales. In particular, we find that the superconducting QPI pattern vanishes at the same temperature as that at which the Fermi arcs appear. Experimental support for this conclusion comes from the observation of a nearly dispersionless QPI pattern which has been observed to appear above ${T}_{c}$ in moderately underdoped cuprates. To illustrate the important two energy scale physics we present predictions of the QPI-inferred energy gaps as a function of $T$ for future experiments on moderately underdoped cuprates. This defines the so-called ``Bogoliubov arcs,'' which we find have an extinction point controlled by the size of the superconducting order parameter. This extinction, thus, seems unrelated to the magnetic zone boundary. Moreover, the calculated Bogoliubov arcs persist across the full nodal region, as might be expected, since that is where the superconductivity is thought to be dominant. A second larger energy scale is implied from extrapolation to the antinodes, presuming a simple $d$-wave shape and that the temperatures are not too close to ${T}_{c}$. This corresponds to the pseudogap energy scale in the literature.

We show how, within a preformed-pair scenario for the cuprate pseudogap, the nodal and antinodal responses in angle-resolved photoemission spectroscopy necessarily have very different temperature $T$ dependences. We examine the behavior and the contrasting $T$ dependences for a range of temperatures both below and above ${T}_{c}$. Previously, the distinct nodal and antinodal responses have provided strong support for the ``two-gap scenario'' of the cuprates in which the pseudogap competes with superconductivity. Instead, our theory supports a picture in which the pseudogap derives from pairing correlations, identifying the two-gap components with noncondensed and condensed pairs. Our calculations are based on a microscopic diagrammatic approach for addressing pairing correlations in a regime where the attraction is stronger than BCS and the coherence length is anomalously short. This many body theory-based scheme takes as a starting point the BCS ansatz for the ground-state wave function and incorporates finite temperature effects through coupled equations for the single particle and pair propagators (or $T$ matrix). It leads to reasonably good agreement with a range of different photoemission measurements in the moderately underdoped regime and we emphasize that here there is no explicit curve fitting. We briefly address the more heavily underdoped regime in which the behavior is more complex.