The Zak phase $\gamma$, the generalization of the Berry phase to Bloch wave functions in solids, is often used to characterize inversion-symmetric one-dimensional (1D) topological insulators. Due to its dependence on the real-space origin and unit cell, however, there is an ambiguity in its use in a bulk-boundary correspondence. Here, we extract an origin-independent part of $\gamma$, the so-called intercellular Zak phase ${\gamma }^{\mathrm{inter}}$, and show that it is a bulk quantity that unambiguously predicts the number of surface modes. Specifically, a neutral finite 1D tight-binding system has $n_s={\gamma }^{\mathrm{inter}}/\pi$ (mod 2) in-gap surface modes below the Fermi level if there exists a commensurate inversion-symmetric bulk unit cell. We demonstrate this in two steps: First, we verify that $\pm e{\gamma }^{\mathrm{inter}}/2\pi$ (mod $e)$ equals the extra charge accumulation in the surface region in a terminated system of a translationally invariant 1D insulator, while the remnant part of $\gamma$, the intracellular Zak phase ${\gamma }^{\mathrm{intra}}$, corresponds to the electronic part of the bulk's unit-cell dipole moment. Second, we show that the extra charge accumulation is related to the number of surface modes when the unit cell is inversion symmetric. We study several tight-binding models to quantitatively check both the relation between the extra charge accumulation and the intercellular Zak phase, and the bulk-boundary correspondence using the intercellular Zak phase.

We investigate spin transport in two-dimensional ferromagnetic (FTI) and antiferromagnetic (AFTI) topological insulators. In the presence of an in-plane magnetization AFTI supports zero energy modes, which enables topologically protected edge conduction at low energy. We address the nature of current-driven spin torque in these structures and study the impact of spin-independent disorder. Interestingly, upon strong disorder the spin torque develops an antidamping component (i.e., even upon magnetization reversal) along the edges, which could enable current-driven manipulation of the antiferromagnetic order parameter. This antidamping torque decreases when increasing the system size and when the system enters the trivial insulator regime.

Employing Nernst-Einstein decomposition $\sigma =e^2{\chi }_{c}D$ of the conductivity $\sigma$ onto charge susceptibility (compressibility) ${\chi }_c$ and diffusion constant $D$, we argue that the bad-metallic behavior of $\sigma$ in the regime of high temperatures and lightly doped insulator is dominated by the strong temperature and doping dependence of ${\chi }_c$. In particular, we show how at small dopings ${\chi }_c$ strongly decreases towards undoped-insulating values with increasing temperature and discuss a simple picture leading to the linear-in-temperature resistivity with the prefactor increasing inversely with decreasing concentration $\left(p\right)$ of doped holes, $\rho \propto T/p$. On the other hand, $D$ shows weak temperature and doping dependence in the corresponding regime. We support our arguments by numerical results on the two-dimensional Hubbard model and discuss the proposed picture from the experimental point of view.

The semiconducting single-layer transition-metal dichalcogenides have been identified as ideal materials for accessing and manipulating spin- and valley-quantum numbers due to a set of favorable optical selection rules in these materials. Here, we apply time- and angle-resolved photoemission spectroscopy to directly probe optically excited free carriers in the electronic band structure of a high quality single layer (SL) of ${\mathrm{WS}}_2$ grown on Ag(111). We present a momentum-resolved analysis of the optically generated free hole density around the valence band maximum of SL ${\mathrm{WS}}_2$ for linearly and circularly polarized optical excitations. We observe that the excited free holes are valley polarized within the upper spin-split branch of the valence band, which implies that the photon energy and polarization of the excitation permit selective excitations of free electron-hole pairs with a given spin and within a single valley.

Flexural thermal fluctuations in crystalline membranes affect the band structure of the carriers, which leads to an exponential density-of-states (DOS) tail beyond the unperturbed band edge. We present a theoretical description of this tail for a particular case of holes in single-layer black phosphorus, a material which exhibits an extremely anisotropic quasi-one-dimensional dispersion $\left(m_y/m_x\gg 1\right)$ and, as a result, an enhanced Van Hove singularity at the valence band top. The material parameters are determined by ab initio calculations and then are used for quantitative estimation of the effect of two-phonon (flexural) processes have on the charge carrier DOS. It is shown that unlike the isotropic case, the physics is determined by the phonons with wave vectors of the order of $q^{*}$, where $q^{*}$ determines the crossover between harmonic and anharmonic behavior of the flexural phonons. The spectral density of the holes in single-layer black phosphorus at finite temperatures is calculated.

We employ density-functional theory (DFT) in the generalized gradient approximation (GGA) and its extensions $\mathrm{GGA}+U$ and GGA+Gutzwiller to calculate the magnetic exchange couplings between pairs of Mn ions substituting Cd in a CdTe crystal at very small doping. DFT(GGA) overestimates the exchange couplings by a factor of 3 because it underestimates the charge-transfer gap in Mn-doped II-VI semiconductors. Fixing the nearest-neighbor coupling $J_1$ to its experimental value in $\mathrm{GGA}+U$, in GGA+Gutzwiller, or by a simple scaling of the DFT(GGA) results provides acceptable values for the exchange couplings at second-, third-, and fourth-neighbor distances in Cd(Mn)Te, Zn(Mn)Te, Zn(Mn)Se, and Zn(Mn)S. In particular, we recover the experimentally observed relation $J_4>J_2,J_3$. The filling of the Mn $3d$ shell is not integer, which puts the underlying Heisenberg description into question. However, using a few-ion toy model the picture of a slightly extended local moment emerges so that an integer $3d$-shell filling is not a prerequisite for equidistant magnetization plateaus, as seen in experiment.

A comprehensive understanding of the physical origins of the phase transition behaviors of transition metal oxides is still complex due to the interplay among competing interactions of comparable strengths tuning their nature. Widespread interest in such phase transitions has motivated explorations of nanocrystalline vanadium dioxide $\left({\mathrm{VO}}_2\right)$ in various forms and a long-running debate persists over the roles played by electron-electron correlation with lattice distortion. External stimuli like pressure and temperature have strong effects on the appearance, stability, and spacial distribution of the high-resistive (HR) and low-resistive (LR) phases accompanying their structural modification. Our comprehensive experiments establish the pressure-induced and thermally driven evolution of phase coexistence in ${\mathrm{VO}}_2\left(\mathrm{A}\right)$ nanorods. Our experimental evidence supports coexisting HR and LR phases, where compression suppressed coexistence at $\sim 7$ GPa, followed by a semiconductor-semiconductor transition at around $\sim 10$ GPa with the absence of pressure-induced metallization. X-ray diffraction revealed lattice distortion with local microscopic strain inhomogeneity in the nanorods, without any discontinuity in the pressure-volume data. We further investigated the vibrational modes and relaxations of the samples related to their thermal expansions. We also found that the pressure-dependent hierarchy of microstructural densification contributed significantly to the resulting transport properties.

By using first-principles calculations and a $k·p$ model analysis, we propose that the three-dimensional topological nodal line semimetal state can be realized in the ${\mathrm{CaP}}_3$ family of materials, which includes ${\mathrm{CaP}}_3,{\mathrm{CaAs}}_3,{\mathrm{SrP}}_3,{\mathrm{SrAs}}_3$, and ${\mathrm{BaAs}}_3$, when spin-orbit coupling (SOC) is ignored. The closed topological nodal line near the Fermi energy is protected by time reversal symmetry and spatial inversion symmetry. Moreover, drumheadlike two-dimensional surface states are also obtained on the $c$-direction surface of these materials. When SOC is included, the gaps open along the nodal line and these materials become strong topological insulators with $Z_2$ indices as $(1;010)$.

We develop a theory of heat conductivity in supported graphene, accounting for coherent phonon scattering on disorder induced by an amorphous substrate. We derive spectra for in-plane and out-of-plane phonons in the framework of Green's function approach. The energy parameters of the theory are obtained using molecular dynamics simulations for graphene on a ${\mathrm{SiO}}_2$ substrate. The heat conductivity is calculated by the Boltzmann transport equation. We find that the interaction with the substrate drastically reduces the phonon lifetime and completely suppresses the contribution of flexural (ZA) phonons to the heat conductivity. As a result, the total heat conductivity is reduced by several times, which matches with the tendency observed in the available experimental data. The considered effect is important for managing the thermal properties of graphene-based electronic devices.

The geometrical and electronic structures of a metastable phase of lead phthalocyanine (PbPc) films on graphite have been studied by combined use of low energy electron diffraction (LEED) and two-photon photoemission (2PPE) spectroscopy. In submonolayer (sub-ML) PbPc films on graphite, islands in a metastable phase are formed just after deposition, as we reported previously by use of photoelectron emission microscopy (PEEM) [I. Yamamoto, N. Matsuura, M. Mikamori, R. Yamamoto, T. Yamada, K. Miyakubo, N. Ueno, and T. Munakata, Surf. Sci. 602, 2232 (2008)]. On single crystalline graphite substrates, the metastable islands produce clearly discernible LEED spots. By comparing the unit cell with that of annealed 1 ML films, molecules in the metastable islands are standing upright with a molecular density 1.8 times higher than that in the well-ordered 1 ML films. The LEED spots for the sub-ML films disappear after annealing. The islands in the metastable phase are surrounded by areas of a two-dimensional (2D) gaslike phase composed of flat-lying molecules. The metastable islands melt into the 2D gas phase, consistent with the PEEM results. In 2PPE spectroscopy, the lowest unoccupied molecular orbital (LUMO) derived level of the metastable phase is clearly distinguishable from that of flat-lying molecules. By tracking the thermal annealing process of the films by 2PPE spectroscopy, we clarify the decay of the LUMO derived peak intensity, the work function shift, and the energy shifts of molecular states associated with the transition from the metastable phase to the 2D gas phase. With this, we demonstrate the complementary capabilities of LEED and 2PPE spectroscopy to probe phase transitions of organic films in a nondestructive manner.

We theoretically investigate the phenomena of adiabatic quantum charge pumping through a normal-insulator-superconductor-insulator-normal (NISIN) setup of silicene within the scattering matrix formalism. Assuming a thin barrier limit, we consider the strength of the two barriers $({\chi }_1$ and ${\chi }_2)$ as the two pumping parameters in the adiabatic regime. Within this geometry, we obtain crossed Andreev reflection (CAR) with probability unity in the ${\chi }_1\text{−}{\chi }_2$ plane without concomitant transmission or elastic co-tunneling. Tunability of the band gap at the Dirac point by applying an external electric field perpendicular to the silicene sheet and variation of the chemical potential at the normal silicene region, open up the possibility of achieving either a perfect CAR or transmission process through our setup. This resonant behavior is periodic with the barrier strengths. We analyze the behavior of the pumped charge through the NISIN structure as a function of the pumping strength and angles of the incident electrons. We show that large $\left(Q\sim 2e\right)$ pumped charge can be obtained through our geometry when the pumping contour encloses either the CAR or transmission resonance in the pumping parameter space. We discuss possible experimental feasibility of our theoretical predictions.

First-principles density functional theory methods are used to investigate the structure, energetics, and vibrational motions of the neutral vacancy defect in diamond. The measured optical absorption spectrum demonstrates that the tetrahedral $T_d$ point group symmetry of pristine diamond is maintained when a vacancy defect is present. This is shown to arise from the presence of a dynamic Jahn-Teller distortion that is stabilized by large vibrational anharmonicity. Our calculations further demonstrate that the dynamic Jahn-Teller-distorted structure of $T_d$ symmetry is lower in energy than the static Jahn-Teller distorted tetragonal $D_{2d}$ vacancy defect, in agreement with experimental observations. The tetrahedral vacancy structure becomes more stable with respect to the tetragonal structure by increasing temperature. The large anharmonicity arises mainly from quartic vibrations, and is associated with a saddle point of the Born-Oppenheimer surface and a minimum in the free energy. This study demonstrates that the behavior of Jahn-Teller distortions of point defects can be calculated accurately using anharmonic vibrational methods. Our work will open the way for first-principles treatments of dynamic Jahn-Teller systems in condensed matter.

The competition between interactions in frustrated magnets allows a wide variety of new ground states, often exhibiting emergent physics and unique excitations. Expanding the suite of lattices available for study enhances our chances of finding exotic physics. ${\mathrm{Mn}}_2{\mathrm{Sb}}_2{\mathrm{O}}_7\mathrm{forms}$ in a chiral, kagome-based structure in which a fourth member is added to the kagome-plane triangles to form an armchair unit and link adjacent kagome planes. This structural motif may be viewed as intermediate between the triangles of the kagome network and the tetrahedra in the pyrochlore lattice. ${\mathrm{Mn}}_2{\mathrm{Sb}}_2{\mathrm{O}}_7\mathrm{exhibits}$ two distinct magnetic phase transitions, at 11.1 and 14.2 K, at least one of which has a weak ferromagnetic component. The magnetic propagation vector does not change through the lower transition, suggesting a metamagnetic transition or a transition involving a multicomponent order parameter. Although previously reported in the $P{3}_{1}21$ space group, ${\mathrm{Mn}}_2{\mathrm{Sb}}_2{\mathrm{O}}_7\mathrm{actually}$ crystallizes in $P2$, which allows ferroelectricity, and we show clear evidence of magnetoelectric coupling indicative of multiferroic order. The quasi-two-dimensional “armchair-kagome” lattice presents a promising platform for probing chiral magnetism and the effect of dimensionality in highly frustrated systems.

Hybrid superconductor-semiconducting nanowire devices provide an ideal platform to investigating interesting intragap bound states, such as the Andreev bound states (ABSs), Yu-Shiba-Rusinov (YSR) states, and the Majorana bound states. The competition between Kondo correlations and superconductivity in Josephson quantum dot (QD) devices results in two different ground states and the occurrence of a $0\text{−}\pi$ quantum phase transition. Here we report on transport measurements on hybrid superconductor–InSb nanowire QD devices with different device geometries. We demonstrate a realization of continuous gate-tunable ABSs with both 0-type levels and $\pi$-type levels. This allow us to manipulate the transition between the 0 and $\pi$ junction and explore charge transport and spectrum in the vicinity of the quantum phase transition regime. Furthermore, we find a coexistence of 0-type ABS and $\pi$-type ABS in the same charge state. By measuring temperature and magnetic field evolution of the ABSs, the different natures of the two sets of ABSs are verified, being consistent with the scenario of phase transition between the singlet and doublet ground state. Our study provides insight into Andreev transport properties of hybrid superconductor-QD devices and sheds light on the crossover behavior of the subgap spectrum in the vicinity of the $0\text{−}\pi$ transition.

Phonon partial densities of states (pDOS) of ${}^{57}\mathrm{Fe}_3\mathrm{C}$ were measured from cryogenic temperatures through the Curie transition at 460 K using nuclear resonant inelastic x-ray scattering. The cementite pDOS reveal that low-energy acoustic phonons shift to higher energies (stiffen) with temperature before the magnetic transition. This unexpected stiffening suggests strongly nonharmonic vibrational behavior that impacts the thermodynamics and elastic properties of cementite. Density functional theory calculations reproduced the anomalous stiffening observed experimentally in cementite by accounting for phonon-phonon interactions at finite temperatures. The calculations show that the low-energy acoustic phonon branches with polarizations along the [010] direction are largely responsible for the anomalous thermal stiffening. The effect was further localized to the motions of the ${\mathrm{Fe}}_{\mathrm{II}}$ site within the orthorhombic structure, which participates disproportionately in the anomalous phonon stiffening.

We study the time evolution of a half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long-time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within the approximations used. Instead, nonequilibrium states, similar to the ones observed in the closed system, can emerge at long times as a consequence of the competition between the intrinsic relaxation mechanism (Landau damping, for example), and the bath-induced dissipation.

Motivated by recent measurements of the lifetime (decay width) of paramagnons in quantum antiferromagnet ${\mathrm{TlCuCl}}_3$, we investigate paramagnon decay in a heat bath and formulate an appropriate quantum theory. Our formulation can be split into two regimes: (i) a nonperturbative, “hot quantum soup” regime where the paramagnon width is comparable to its energy; (ii) a usual perturbative regime where the paramagnon width is significantly lower than its energy. Close to the Neel temperature, the paramagnon width becomes comparable to its energy and falls into the hot quantum soup regime. To describe this regime, we develop a new finite frequency, finite temperature technique for a nonlinear quantum field theory; the “golden rule of quantum kinetics.” The formulation is generic and applicable to any three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point. Specifically, we apply our results to ${\mathrm{TlCuCl}}_3$ and find agreement with experimental data. Additionally, we show that logarithmic running of the coupling constant in the upper critical dimension changes the commonly accepted picture of the quantum disordered and quantum critical regimes.

We study quantum disordered ground states of the two-dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg and Kitaev couplings and sufficiently small spin $S$, we find three different symmetric $Z_2$ spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well-known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops ${120}^{\circ }$ order in the semiclassical limit at large $S$. In the opposite Kitaev limit, we find a different spin liquid ground state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings, we find a spin liquid state with unusual spin correlations. Upon spinon condensation, this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.

Measurements on resistivity and magnetic susceptibility have been carried out for Bi single crystals under pressures up to 10.5 GPa. The temperature dependent resistivity shows a semimetallic behavior at ambient and low pressures (below about 1.6 GPa). This is followed by an upturn of resistivity in the low temperature region when the pressure is increased, which is explained as a semiconductor behavior. This feature gradually gets enhanced up to a pressure of about 2.52 GPa. Then a nonmonotonic temperature dependent resistivity appears upon further increasing pressure, which is accompanied by a strong suppression to the low temperature resistivity upturn. Simultaneously, a superconducting transition occurs at about 3.92 K under a pressure of about 2.63 GPa. With further increasing pressure, a second superconducting transition emerges at about 7 K under about 2.8 GPa. For these two superconducting states, the superconductivity induced magnetic screening volumes are quite large. As the pressure further increases to 8.1 GPa, we observe the third superconducting transition at about 8.2 K. The resistivity measurements under magnetic field allow us to determine the upper critical fields ${\mu }_0{H}_{c2}$ of the superconducting phases. The upper critical field for the phase with $T_c=3.92$ K is extremely low. Based on the Werthamer-Helfand-Hohenberg (WHH) theory, the estimated value of ${\mu }_0{H}_{c2}$ for this phase is about 0.103 T, while the upper critical field for the phase with $T_c=7$ K is very high with a value of about 4.56 T. Finally, we present a pressure dependent phase diagram of Bi single crystals. Our results reveal the interesting and rich physics in bismuth single crystals under high pressure.