Quantum Interference Corrections Research Articles

Observation of Anomalous Planar Hall Effect Induced by One-Dimensional Weak Antilocalization.

The confinement of electrons in one-dimensional (1D) space highlights the prominence of the role of electron interactions or correlations, leading to a variety of fascinating physical phenomena. The quasi-1D electron states can exhibit a unique spin texture under spin-orbit interaction (SOI) and thus could generate a robust spin current by forbidden electron backscattering. Direct detection of such 1D spin or SOI information, however, is challenging due to complicated techniques. Here, we identify an anomalous planar Hall effect (APHE) in the magnetotransport of quasi-1D van der Waals (vdW) topological materials as exemplified by Bi4Br4, which arises from the quantum interference correction of 1D weak antilocalization (WAL) to the ordinary planar Hall effect and demonstrates a deviation from the usual sine and cosine curves. The occurrence of 1D WAL is correlated to the line-shape Fermi surface and persistent spin texture of (100) topological surface states of Bi4Br4, as revealed by both our angle-resolved photoemission spectroscopy and first-principles calculations. By generalizing the observation of APHE to other non-vdW bulk materials, this work provides a possible characteristic of magnetotransport for identifying the spin/SOI information and quantum interference behavior of 1D states in 3D topological material.

Thermodynamic uncertainty relations in mesoscopic devices.

We investigate the thermodynamic uncertainty relations (TURs) in mesoscopic devices for all universal symmetry classes of Wigner-Dyson and Dirac (chiral). The observables of interest include the TUR (MS), which is defined in terms of the ratio between the mean noise and mean conductance, as well as a new TUR (R) proposed in this article, which is based on the ensemble mean of the noise-to-conductance ratio. A detailed study is made on the quantum interference corrections associated with the TURs. We also analyze the influence of orbital and sublattice/chiral degrees of freedom for the validity of the observables in these chaotic mesoscopic billiards. Our investigation is based on the concatenation between the Landauer-Büttiker theory, the Mahaux-Wendeinmüller theory, and the TURs. We simulate the universal mesoscopic chaotic quantum dots using the random-matrix theory and compare our numerical results with the pertinent experimental data. The results were obtained for a different number of channels and tunneling rates that vary from the opaque to the ideal regime and, in all cases, demonstrate a clear phenomenological distinction between the TURs. In particular, the opaque regime engenders remarkable differences between the observables, even in the semiclassical regime, which characterizes a clear violation of the central limit theorem. Furthermore, we show that the phenomenology of the quantum interference corrections is strikingly robust, surprisingly exhibiting an order of magnitude greater than the supposedly leading semiclassical term for the TUR (R).

Localization effects and anomalous hall conductivity in a disordered 3D ferromagnet

We have prepared the ferromagnetic Heusler alloy CoFeV0.5Mn0.5Si in bulk form via arc melting. The longitudinal resistivity exhibits a minimum at 150 K, which is attributable to competition between quantum interference corrections at low temperatures and inelastic scattering at higher temperatures. The magnetoresistance (MR) is positive and nearly linear at low temperatures and becomes negative at temperatures close to room temperature. The positive MR in the quantum correction regime is evidence of the presence of the enhanced electron interaction as a contributor to the longitudinal resistivity. Hall effect measurements indicate a carrier concentration of the order of 1022 cm−3, which is nearly 3 orders of magnitude higher than that found in the “parent” material CoFeMnSi. The higher carrier concentration is consistent with the predicted half metallicity of CoFeV0.5Mn0.5Si. The anomalous Hall conductivity of CoFeV0.5Mn0.5Si is temperature independent for temperatures below the resistivity minimum, which is strong evidence of the absence of quantum interference effects on the anomalous Hall conductivity in a 3D ferromagnet.

Facet-dependent Electronic Quantum Diffusion in the High-Order Topological Insulator Bi4Br4

We apply the magnetoconductivity characteristic and angle-resolved photoemission spectroscopy (ARPES) to visualize the evolution of surface-selected electronic features of quasi-one-dimensional material ${\mathrm{Bi}}_{4}{\mathrm{Br}}_{4}$. The transport measurements indicate the quantum-interference correction to conductivity possesses a symbolic spin-rotational characteristic correlated to the value of Berry phase with the effects of weak localization and weak antilocalization for (001) and (100) surfaces, respectively. The ARPES spectra provide the experimental evidence for a quasi-one-dimensional surface state at the side (100) surface and an anisotropic massive Dirac surface state at the top (001) surface, respectively, which is highly coincided with the angle-dependent scaling behavior of magnetoconductivity. Our results reveal the facet-dependent electronic quantum diffusion in quasi-one-dimensional ${\mathrm{Bi}}_{4}{\mathrm{Br}}_{4}$, stimulating further investigations of this topological class and applications of the feasible technologies of topological spintronics.

Reliable modeling of weak antilocalization for accurate spin-lifetime extraction

We examine models for the quantum-interference correction to the magnetoconductivity in two-dimensional electron gases (2DEGs) with both Rashba and Dresselhaus spin-orbit coupling for their applicability to experimental data fitting. In particular, we compare the Landau-quantized Cooperon approach, which is mostly only numerically treatable, and the quasiclassical approximation that was recently employed to obtain an explicit solution for arbitrary Rashba and Dresselhaus spin-orbit couplings [Marinescu et al., Phys. Rev. Lett. 112, 156601 (2019)]. It is found that the quasiclassical approximation yields significantly different results even to the lowest order in the magnetic field and appears unsuitable for reliable parameter fitting. The discrepancy emerges when a sum over Landau levels is replaced by an integral over wave vectors. Substantial improvement is achieved by supplementing the quasiclassical model with the first two corrections given by the Euler-MacLaurin formula for approximating a sum by an integral. Corresponding modifications are, however, only feasible in special spin-orbit parameter configurations where the mixing of Landau bands is negligible and a closed-form solution that accounts for Landau quantization is also available. Such a scenario appears in a parameter regime where a persistent spin helix emerges and a transition between weak localization and weak antilocalization takes place. Combining recent findings, we derive a generalized closed-form expression for the magnetoconductivity correction applicable to generic 2DEGs that are grown along a crystal direction with at least two growth-direction Miller indices equal in modulus. The result is a function of spin lifetimes of the long-lived spin textures and valid close to the persistent-spin-helix regime. The accuracy of the derived formula is validated by comparing with results from numerical diagonalization of the multiband Cooperon as well as a recently established Monte Carlo-based real-space simulation in exemplary (001)-, (113)-, and (110)-2DEGs.

Weak localization and crossover from Lifshitz transition in two dimensions

Dirac point plays a crucial role in regulating electronic properties of topological semimetals. In two dimensions, the manipulation of Dirac points can spur a transition from Dirac semimetal through semi-Dirac phase to a gapped phase. Across such a so-called Lifshitz transition, we find that the quantum interference corrections to the conductivity $\ensuremath{\delta}{\ensuremath{\sigma}}_{xx}$ and $\ensuremath{\delta}{\ensuremath{\sigma}}_{yy}$ are always negative, giving rise to a weak localization behavior. The ratio $\ensuremath{\delta}{\ensuremath{\sigma}}_{xx}/\ensuremath{\delta}{\ensuremath{\sigma}}_{yy}$ undergoes a transition from linear to parabolic dependence on the merging parameter across the Lifshitz transition, which leads to a crossover of the temperature dependence of the inverse inelastic scattering time $1/{\ensuremath{\tau}}_{\ensuremath{\varepsilon}}$ from $\ensuremath{\sim}T$ to $\ensuremath{\sim}Tln({T}_{0}/T)$. This fingerprint behavior can be readily tested experimentally through merging Dirac points in two-dimensional lattices. This work presents an alternative perspective to understand weak localization through Lifshitz transition.

Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards

Van der Waals heterostructures based on two-dimensional materials have recently become a very active topic of research in spintronics, both aiming at a fundamental description of spin dephasing processes in nanostructures and as a potential element in spin-based information processing schemes. Here, we theoretically investigate the magnetoconductance of mesoscopic devices built from graphene proximity-coupled to a high spin-orbit coupling material. Through numerically exact tight-binding simulations, we show that the interfacial breaking of inversion symmetry generates robust weak antilocalization even when the $z\rightarrow -z$ symmetric spin-orbit coupling in the quantum dot dominates over the Bychkov--Rashba interaction. Our findings are in interpreted on the light of random matrix theory, which links the observed behavior of quantum interference corrections to a transition from circular-orthogonal to circular-sympletic ensemble.

Effect of cobalt particle deposition on quantum corrections to Drude conductivity in twisted CVD graphene

Graphene applications in electronics require experimental study of the formation of high-quality Ohmic contacts and deeper understanding of electron transport mechanisms at metal/grapheme contacts. We have studied carrier transport in twisted CVD graphene decorated with electrodeposited Co particles forming Ohmic contacts with graphene layers. We have compared layer resistivity as a function of temperature and magnetic field R�(T, B) for as-synthesized and decorated twisted graphene on silicon oxide substrates. Experiments have proven the existence of negative (induction < 1 Tl) and positive (induction > 1 Tl) contributions to magnetoresistance in both specimen types. The R�(T, B) functions have been analyzed based on the theory of 2D quantum interference corrections to Drude conductivity taking into account competition of hopping conductivity mechanism. We show that for the experimental temperature range (2–300 K) and magnetic field range (up to 8 Tl), carrier transport description in test graphene requires taking into account at least three interference contributions to conductivity, i.e., from weak localization, intervalley scattering and pseudospin chirality, as well as graphene buckling induced by thermal fluctuations.

Electronic Griffiths phase and quantum interference in disordered heavy-fermion systems

We investigated the specific heat and electrical resistivity of disordered heavy-fermion systems ${\mathrm{Ce}}_{2}{\mathrm{Co}}_{0.8}{\mathrm{Si}}_{3.2}$ and ${\mathrm{Ce}}_{2}{\mathrm{Co}}_{0.4}{\mathrm{Rh}}_{0.4}{\mathrm{Si}}_{3.2}$. Results show that pronounced non-Fermi-liquid behavior in these Kondo disordered compounds originates from approaching metal-insulator transition rather than from proximity to magnetic instability. Power-law divergence of the local Kondo temperature distribution, $P({T}_{K})$, in the limit of ${T}_{K}\ensuremath{\rightarrow}0$, and clear signature of the quantum interference corrections in the resistivity detected deep below the onset of Kondo coherent state, point to electronic Griffiths phase formation in the studied compounds.

Quantum diagrammatic theory of the extrinsic spin Hall effect in graphene

We present a rigorous microscopic theory of the extrinsic spin Hall effect in disordered graphene based on a nonperturbative quantum diagrammatic treatment incorporating skew scattering and anomalous---impurity concentration-independent---quantum corrections on equal footing. The leading skew scattering contribution to the spin Hall conductivity is shown to quantitatively agree with Boltzmann transport theory over a wide range of parameters. Our self-consistent approach---where all topologically equivalent noncrossing diagrams are resummed---unveils that the skewness generated by spin--orbit-active impurities deeply influences the anomalous component of the spin Hall conductivity, even in the weak scattering regime. This seemingly counterintuitive result is explained by the rich sublattice structure of scattering potentials in graphene, for which traditional Gaussian disorder approximations fail to capture the intricate correlations between skew scattering and side jumps generated through diffusion. Finally, we assess the role of quantum interference corrections by evaluating an important subclass of crossing diagrams recently considered in the context of the anomalous Hall effect, the $X$ and $\Psi$ diagrams [Ado et al., EPL 111, 37004 (2015)]. We show that $\Psi$ diagrams---encoding quantum coherent skew scattering---display a strong Fermi energy dependence, dominating the anomalous spin Hall component away from the Dirac point. Our findings have direct implications for nonlocal transport experiments in spin--orbit-coupled graphene systems.

Detecting monopole charge in Weyl semimetals via quantum interference transport

Topological Weyl semimetals can host Weyl nodes with monopole charges in momentum space. How to detect the signature of the monopole charges in quantum transport remains a challenging topic. Here, we reveal the connection between the parity of monopole charge in topological semimetals and the quantum interference corrections to the conductivity. We show that the parity of monopole charge determines the sign of the quantum interference correction, with odd and even parity yielding the weak anti-localization and weak localization effects, respectively. This is attributed to the Berry phase difference between time-reversed trajectories circulating the Fermi sphere that encloses the monopole charges. From standard Feynman diagram calculations, we further show that the weak-field magnetoconductivity at low temperatures is proportional to $+\sqrt{B}$ in double-Weyl semimetals and $-\sqrt{B}$ in Weyl semimetals, respectively, which could be verified experimentally.

Robust Topological Interfaces and Charge Transfer in Epitaxial Bi2Se3/II-VI Semiconductor Superlattices.

Access to charge transport through Dirac surface states in topological insulators (TIs) can be challenging due to their intermixing with bulk states or nontopological two-dimensional electron gas (2DEG) quantum well states caused by bending of electronic bands near the surface. The band bending arises via charge transfer from surface adatoms or interfaces and, therefore, the choice of layers abutting topological surfaces is critical. Here we report molecular beam epitaxial growth of Bi2Se3/ZnxCd1-xSe superlattices that hold only one topological surface channel per TI layer. The topological nature of conducting channels is supported by π-Berry phase evident from observed Shubnikov de Haas quantum oscillations and by the associated two-dimensional (2D) weak antilocalization quantum interference correction to magnetoresistance. Both density functional theory (DFT) calculations and transport measurements suggest that a single topological Dirac cone per TI layer can be realized by asymmetric interfaces: Se-terminated ZnxCd1-xSe interface with the TI remains "electronically intact", while charge transfer occurs at the Zn-terminated interface. Our findings indicate that topological transport could be controlled by adjusting charge transfer from nontopological spacers in hybrid structures.

Magnetotransport measurements of the surface states of samarium hexaboride using Corbino structures

The recent conjecture of a topologically-protected surface state in SmB$_6$ and the verification of robust surface conduction below 4 K have prompted a large effort to understand the surface states. Conventional Hall transport measurements allow current to flow on all surfaces of a topological insulator, so such measurements are influenced by contributions from multiple surfaces of varying transport character. Instead, we study magnetotransport of SmB$_6$ using a Corbino geometry, which can directly measure the conductivity of a single, independent surface. Both (011) and (001) crystal surfaces show a strong negative magnetoresistance at all magnetic field angles measured. The (011) surface has a carrier mobility of $122\text{ cm}^2/\text{V}\cdot\text{sec}$ with a carrier density of $2.5\times10^{13} \text{ cm}^{-2}$, which are significantly smaller than indicated by Hall transport studies. This mobility value can explain a failure so far to observe Shubnikov-de Haas oscillations. Analysis of the angle-dependence of conductivity on the (011) surface suggests a combination of a field-dependent enhancement of the carrier density and a suppression of Kondo scattering from native oxide layer magnetic moments as the likely origin of the negative magnetoresistance. Our results also reveal a hysteretic behavior whose magnitude depends on the magnetic field sweep rate and temperature. Although this feature becomes smaller when the field sweep is slower, does not disappear or saturate during our slowest sweep-rate measurements, which is much slower than a typical magnetotransport trace. These observations cannot be explained by quantum interference corrections such as weak anti-localization, but are more likely due to an extrinsic magnetic effect such as the magnetocaloric effect or glassy ordering.

Electronic and magnetic properties of zigzag-edged hexagonal graphene ring nanojunctions

The zigzag-edged hexagonal graphene quantum rings (ZHGQRs) are sandwiched between two Au electrodes to construct nanojunctions, and their electronic and magnetic properties are investigated by the first-principles method. It shows that there are always significant transmission gaps (semiconductor behavior) for all ZHGQRs but changing in an obvious oscillating manner with variations of the edge width. The mechanism for such a feature is analyzed deeply, and it is found that the weak localization for the quantum interference correction to conductance and the parity of wave function play the crucial roles. No intrinsic magnetism is observed in the ZHGQRs, this is because there always exist local armchair-edge-like defects at its corners to weaken the spin polarization strongly. And also shown is that the magnetic field can effectively suppress the weak localization behaviors leading to a negative magnetoresistance for the ZHGQR, which is in good agreement with experimental findings in graphene. These findings are of very important for understanding the electromagnetic properties of graphene quantum ring devices.

Interference-induced magnetoresistance in HgTe quantum wells

We study the quantum interference correction to the conductivity in HgTe quantum wells using the Bernevig-Hughes-Zhang model. This model consists of two independent species (blocks) of massive Dirac fermions. We describe the crossover between the orthogonal and symplectic classes with increasing the carrier concentration and calculate, respectively, weak localization and antilocalization corrections in the absence of the block mixing and assuming the white-noise disorder within each block. We have calculated the interference-induced magnetoresistance in a wide interval of magnetic fields, in particular, beyond the diffusion regime. Remarkably, each Dirac cone taken separately gives a linear contribution to the low-field magnetoresistance, which turns out to be asymmetric in magnetic field $B$. We present an interpretation of this result in terms of the Berry-phase formalism. The contributions of the two blocks are related to each other by replacing $B$ to $\ensuremath{-}B$, so that the total magnetoresistance is symmetric and parabolic in the limit $B\ensuremath{\rightarrow}0$. However, in some range of parameters, field dependence turns out to be strongly nonmonotonous. We also demonstrate that block mixing gives rise to additional singular diffusive modes which do not show up in the absence of mixing.

Quantum interference in HgTe structures

We study quantum transport in HgTe/HgCdTe quantum wells under the condition that the chemical potential is located outside of the band gap. We first analyze symmetry properties of the effective Bernevig–Hughes–Zhang Hamiltonian and the relevant symmetry‐breaking perturbations. Based on this analysis, we overview possible patterns of symmetry breaking that govern the quantum interference (weak localization or weak antilocalization) correction to the conductivity in two‐dimensional HgTe/HgCdTe samples. Further, we perform a microscopic calculation of the quantum correction beyond the diffusion approximation. Finally, the interference correction and the low‐field magnetoresistance in a quasi‐one‐dimensional geometry are analyzed.

Gate-tunable quantum transport in double-layer graphene

We analyze the effect of screening provided by the additional graphene layer in double layer graphene heterostructures (DLGs) on transport characteristics of DLG devices in the metallic regime. The effect of gate-tunable charge density in the additional layer is two-fold: it provides screening of the long-range potential of charged defects in the system, and screens out Coulomb interactions between charge carriers. We find that the efficiency of defect charge screening is strongly dependent on the concentration and location of defects within the DLG. In particular, only a moderate suppression of electron-hole puddles around the Dirac point induced by the high concentration of remote impurities in the silicon oxide substrate could be achieved. A stronger effect is found on the elastic relaxation rate due to charged defects resulting in mobility strongly dependent on the electron denisty in the additional layer of DLG. We find that the quantum interference correction to the resistivity of graphene is also strongly affected by screening in DLG. In particular, the dephasing rate is strongly suppressed by the additional screening that supresses the amplitude of electron-electron interaction and reduces the diffusion time that electrons spend in proximity of each other. The latter effect combined with screening of elastic relaxation rates results in a peculiar gate tunable weak-localization magnetoresistance and quantum correction to resistivity. We propose suitable experiments to test our theory and discuss the possible relevance of our results to exisiting data.

Phase coherent transport in graphene nanoribbons and graphene nanoribbon arrays

We have experimentally investigated quantum interference corrections to the conductivity of graphene nanoribbons at temperatures down to 20 mK studying both weak localization (WL) and universal conductance fluctuations (UCF). Since in individual nanoribbons at millikelvin temperatures the UCFs strongly mask the weak localization feature we employ both gate averaging and ensemble averaging to suppress the UCFs. This allows us to extract the phase coherence length from both WL and UCF at all temperatures. Above 1 K, the phase coherence length is suppressed due to Nyquist scattering whereas at low temperatures we observe a saturation of the phase coherence length at a few hundred nanometers, which exceeds the ribbon width, but stays below values typically found in bulk graphene. To better describe the experiments at elevated temperatures, we extend the formula for 1D weak localization in graphene, which was derived in the limit of strong intervalley scattering, to include all elastic scattering rates.

Interference quantum correction to conductivity of AlxGa1−xAs/GaAs double quantum well heterostructures near the balance

We present the results of experimental investigations of the interference quantum correction to the conductivity of the gated double quantum well AlxGa1−xAs/GaAs/AlxGa1−xAs heterostructures. Analyzing the positive magnetoconductiv-ity we obtain the interwell transition rate and the phase relaxation rate under the conditions when one and two quantum wells are occupied. It has been found that the interwell transition rate resonantly depends on the difference between the electron densities in the wells in accordance with the theoretical estimate. The central point, however, is that the dephasing rate in the lower quantum well is independent of whether the upper quantum well contributes to the conductivity or not. The results obtained are interpreted within framework of the recent theory for the dephasing and electron-electron interaction in the double well structures [Burmistrov I S, Gornyi I V and Tikhonov K S 2011 Phys. Rev. B 84 075338].

Weak antilocalization in HgTe quantum wells with inverted energy spectra

The results of experimental study of the magnetoconductivity of 2D electron gas caused by suppression of the interference quantum correction in HgTe single quantum well heterostructure with the inverted energy spectrum are presented. It is shown that only the antilocalization magnetoconductivity is observed at the relatively high conductivity $\sigma>(20-30)G_0$, where $G_0= e^2/2\pi^2\hbar$. The antilocalization correction demonstrates a crossover from $0.5\ln{(\tau_\phi/\tau)}$ to $1.0\ln{(\tau_\phi/\tau)}$ behavior with the increasing conductivity or decreasing temperature (here $\tau_\phi$ and $\tau$ are the phase relaxation and transport relaxation times, respectively). It is interpreted as a result of crossover to the regime when the two chiral branches of the electron energy spectrum contribute to the weak antilocalization independently. At lower conductivity $\sigma<(20-30)G_0$, the magnetoconductivity behaves itself analogously to that in usual 2D systems with the fast spin relaxation: being negative in low magnetic field it becomes positive in higher one. We have found that the temperature dependences of the fitting parameter $\tau_\phi$ corresponding to the phase relaxation time demonstrate reasonable behavior, close to 1/T, over the whole conductivity range from $5G_0$ up to $130G_0$. However, the $\tau_\phi$ value remains practically independent of the conductivity in distinction to the conventional 2D systems with the simple energy spectrum, in which $\tau_\phi$ is enhanced with the conductivity.