arXiv subjects

T. Hakioglu

Publications and source records attributed to T. Hakioglu.

At least 19 recordsLinked to original sources

arXiv2020

Non-orthogonal Spin-Momentum Locking

Spin-momentum locking is a unique intrinsic feature of strongly spin-orbit coupled materials and a key to their promise of applications in spintronics and quantum computation. Much of the existing work, in topological and non-topological pure materials, has been focused on the orthogonal locking in the vicinity of the $\Gamma$ point where the directions of spin and momentum vectors are locked perpendicularly. With the orthogonal case, enforced by the symmetry in pure systems, mechanisms responsible for non-orthogonal spin-momentum locking (NOSML) have drawn little attention, although it has been reported on the topological surface of $\alpha$-$Sn$. Here, we demonstrate that, the presence of the spin-orbit scattering from dilute spinless impurities can produce the NOSML state in the presence of a strong intrinsic spin-orbit coupling in the pristine material. We also observe an interesting coupling threshold for the NOSML state to occur. The relevant parameter in our analysis is the deflection angle from orthogonality which can be extracted experimentally from the spin-and-angle-resolved photoemission (S-ARPES) spectra. Our formalism is applicable to all strongly spin-orbit coupled systems with impurities and not limited to topological ones. The understanding of NOSML bears on spin-orbit dependent phenomena, including issues of spin-to-charge conversion and the interpretation of quasiparticle interference (QPI) patterns as well as scanning-tunneling spectra (STS) in general spin-orbit coupled materials.

cond-mat.mes-hall↗

arXiv2018

Interaction Approach to Anomalous Spin Texture in Warped Topological Insulators

Interactions between the surface and the bulk in a strong topological insulator (TI) cause a finite lifetime of the topological surface states (TSS) as shown by the recent experiments. On the other hand, interactions also induce unitary processes, which, in the presence of anisotropy and the spin-orbit coupling (SOC), can induce non-trivial effects on the spin texture. Recently, such effects were observed experimentally in the $Bi_2X_3$ family, raising the question that the hexagonal warping (HW) may be linked with new spin-related anomalies. The most remarkable among which is the 6-fold periodic canting of the in-plane spin vector. Here, we show that, this anomaly is the result of a {\it triple cooperation between the interactions, the SOC and the HW}. To demonstrate it, we formulate the spin-off-diagonal self energy. A unitary phase with an even symmetry develops in the latter and modulates the spin-1/2 vortex when the Fermi surface is anisotropic. When the anisotropy is provided by the HW, a 6-fold in-plane spin-canting is observed. Our theory suggests that the spin-canting anomaly in $Bi_2X_3$ is a strong evidence of the interactions. High precision analysis of the spin-texture is a promising support for further understanding of the interactions in TIs.

cond-mat.str-el↗

arXiv2009

Canonical transformations in three-dimensional phase space

Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them is listed. Infinitesimal canonical transformations are also discussed. Finally, we show that decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

math-ph↗

arXiv2009

Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism

A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one attempts to construct the three basic transformations in star-product form, while gauge and point transformations are immediate in star-exponential form, interchange has no correspondent, but it is possible in an ordinary exponential form. As an alternative approach, it is shown that all three basic transformations can be constructed in the ordinary exponential form and that in some cases this approach provides more useful tools than the star-exponential form in finding the generating function for given canonical transformation or vice versa. It is also shown that transforms of c-number phase space functions under linear-nonlinear canonical transformations and intertwining method can be treated within this argument.

math-ph↗

arXiv2007

Local current distribution at large quantum dots (QDs): a self-consistent screening model

We report the implementation of the self-consistent Thomas-Fermi screening theory, together with the local Ohm's law to a quantum dot system in order to obtain local current distribution within the dot and at the leads. We consider a large dot (size $>700$ nm) defined by split gates, and coupled to the leads. Numerical calculations show that the non-dissipative current is confined to the incompressible strips. Due to the non-linear screening properties of the 2DES at low temperatures, this distribution is highly sensitive to external magnetic field. Our findings support the phenomenological models provided by the experimental studies so far, where the formation of the (direct) edge channels dominate the transport.

cond-mat.mes-hall↗

arXiv2007

Theoretical investigation of the electron velocity in quantum Hall bars, in the out of linear response regime

We report on our theoretical investigation of the electron velocity in (narrow) quantum-Hall systems, considering the out-of-linear-response regime. The electrostatic properties of the electron system are obtained by the Thomas-Fermi-Poisson nonlinear screening theory. The electron velocity distribution as a function of the lateral coordinate is obtained from the slope of the screened potential within the incompressible strips (ISs). The asymmetry induced by the imposed current on the ISs is investigated, as a function of the current intensity and impurity concentration. We find that the width of the IS on one side of the sample increases linearly with the intensity of the applied current and decreases with the impurity concentration.

cond-mat.mes-hall↗

arXiv2007

Where are the edge-states near the quantum point contacts? A self-consistent approach

In this work, we calculate the current distribution, in the close vicinity of the quantum point contacts (QPCs), taking into account the Coulomb interaction. In the first step, we calculate the bare confinement potential of a generic QPC and, in the presence of a perpendicular magnetic field, obtain the positions of the incompressible edge states (IES) taking into account electron-electron interaction within the Thomas-Fermi theory of screening. Using a local version of the Ohm's law, together with a relevant conductivity model, we also calculate the current distribution. We observe that, the imposed external current is confined locally into the incompressible strips. Our calculations demonstrate that, the inclusion of the electron-electron interaction, strongly changes the general picture of the transport through the QPCs.

cond-mat.mes-hall↗

arXiv2007

A self-consistent microscopic model of Coulomb interaction in a bilayer system as an origin of Drag Effect Phenomenon

In this work we implement the self-consistent Thomas-Fermi model that also incorporates a local conductivity model to an electron-electron bilayer system, in order to describe novel magneto-transport properties such as the Drag Phenomenon. The model can successfully account for the poor screening of the potential within the incompressible strips and its impact on the interlayer Coulomb interaction. An externally applied current in the active layer results in the tilting of the Landau levels and built-up of a Hall potential across the layer, which, in turn, induces a tilted potential profile in the passive layer as well. We investigate the effect of the current intensity, temperature, magnetic field, and unequal density of layers on the self-consistent density and potential profiles of the bilayer system.

cond-mat.mes-hall↗

arXiv2007

The self-consistent calculation of the edge states at quantum Hall effect (QHE) based Mach-Zehnder interferometers (MZI)

The spatial distribution of the incompressible edge states (IES) is obtained for a geometry which is topologically equivalent to an electronic Mach-Zehnder interferometer, taking into account the electron-electron interactions within a Hartree type self-consistent model. The magnetic field dependence of these IES is investigated and it is found that an interference pattern may be observed if two IES merge or come very close, near the quantum point contacts. Our calculations demonstrate that, being in a quantized Hall plateau does not guarantee observing the interference behavior.

cond-mat.mes-hall↗

arXiv2006

The effect of sample properties on the electron velocity in quantum Hall bars

We report on our theoretical investigation of the effects of the confining potential profile and sample size on the electron velocity distribution in (narrow) quantum-Hall systems. The electrostatic properties of the electron system are obtained by the Thomas-Fermi-Poisson nonlinear screening theory. The electron velocity distribution as a function of the lateral coordinate is obtained from the slope of the screened potential at the Fermi level and within the incompressible strips (ISs). We compare our findings with the recent experiments.

cond-mat.mes-hall↗

arXiv2006

$\hbar$-independent Universality of the Quantum-Classical Canonical Transformations

A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also classical mechanical and vice versa is demonstrated in the phase space. Contrary to some earlier results, it is also shown that the quantum generators and their classical counterparts are identical and $\hbar$-independent. The latter is a powerful result bringing the theory of classical canonical transformations and the $\hbar$-independent quantum ones on an equal footing.

quant-ph↗

arXiv2003

Decoherence and dephasing in multilevel systems interacting with thermal environment

We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto $N\sim 10$. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on $N$ for $4< N<10$ and saturate for $10 <N$. We also examine double degenerate systems with $4 \le N$ and observe a strong suppression (almost by two orders of magnitude) of the low temperature relaxation and dephasing rates. An important observation for $4 \le N$ in doubly degenerate energy configuration is that, we find a strong suppression of the RD rates for such systems relative to the singly degenerate ones. These results are also compared qualitatively with the relaxation rates found from the Fermi Golden Rule.

cond-mat.mes-hall↗

arXiv2002

Quantum Computational Gates with Radiation Free Couplings

We examine a generic three state mechanism which realizes all fundamental single and double qubit quantum logic gates operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. At the instant of time that the gate operations are defined the third level is unoccupied which, in a certain sense, derives analogy with the recently suggested dissipation free qubit subspaces. The physical implementation of the mechanism is tentatively suggested in a form of the Aharonov-Bohm persistent current loop in crossed electric and magnetic fields, with the output of the loop read out by a (quantum) Hall effect aided mechanism.

cond-mat.mes-hall↗

arXiv2002

Quantum Computation with Aharonov-Bohm Qubits

We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum $\hbar c/e$ as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to $F_3$ centers in alkali halides) with one trapped electron in one spin projection state.

cond-mat.mes-hall↗

arXiv2001

Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps

Classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate $\hbar$-independent quantum canonical maps. It is shown that such maps act in the noncommutative phase space as dictated by the classical covariance. A crucial observation made is that under the classical covariance the local quantum mechanical picture can become nonlocal in the Hilbert space. This nonlocal picture is made equivalent by the Weyl map to a noncommutative picture in the phase space formulation of the theory. The connection between the entanglement and nonlocality of the representation is explored and specific examples of the generation of entanglement are provided by using such concepts as the generalized Bell states. That the results have direct application in generating vacuum soliton configurations in the recently popular scalar field theories of noncommutative coordinates is also demonstrated.

hep-th↗

arXiv2001

Single and double qubit gates by manipulating degeneracy

A novel mechanism is proposed for single and double qubit state manipulations in quantum computation with four-fold degenerate energy levels. The principle is based on starting with a four fold degeneracy, lifting it stepwise adiabatically by a set of control parameters and performing the quantum gate operations on non-degenerate states. A particular realization of the proposed mechanism is suggested by using inductively coupled rf-squid loops in the macroscopic quantum tunnelling regime where the energy eigen levels are directly connected with the measurable flux states. The one qubit and two qubit controlled operations are demonstrated explicitly. The appearance of the flux states also allows precise read-in and read-out operations by the measurement of flux.

cond-mat↗

arXiv2001

The Moyal-Lie Theory of Phase Space Quantum Mechanics

A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an efficient tool in the quantum phase space transformation theory.

quant-ph↗

arXiv2001

Extended covariance under nonlinear canonical transformation in Weyl quantization

A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for the three fundamental canonical maps as fractional-linear, gauge and contact (point) transformations. Under the nonlinear maps a phase space representation is mapped to another phase space representation thereby extending the standard concept of covariance. This extended covariance allows Dirac-Jordan transformation theory to naturally emerge from the Hilbert space representations in the Weyl quantization.

quant-ph↗