Dimitrie Culcer

Two-dimensional surface charge transport in topological insulators

The dominant scattering angles can be inferred by studying the ratio of the transport time to the Bloch lifetime as a function of the Wigner-Seitz radius rs. The current generates a spin polarization that could provide a smoking-gun signature of surface state transport. We also discuss the eect on the surface states of adding metallic contacts.

Interface roughness, valley-orbit coupling, and valley manipulation in quantum dots

We present a systematic study of interface roughness and its effect on coherent dynamical processes in quantum dots. The potential due to a sharp, flat interface lifts the degeneracy of the lowest energy valleys and yields a set of valley eigenstates. Interface roughness is characterized by fluctuations in the location of the interface and in the magnitude of the potential step. Variations in the position of the interface, which are expected to occur on the length scale of the lattice constant, reduce the magnitude of the valley-orbit coupling. Variations in the size of the interface potential step alter the magnitude of the valley-orbit coupling and induce transitions between different valley eigenstates in dynamics involving two (or more) dots. Such transitions can be studied experimentally by manipulating the bias between two dots and can be detected by charge sensing. However, if the random variable characterizing the position of the interface is correlated over distances of the order of a quantum dot, which is unlikely but possible, the phase of the valley-orbit coupling may be different in adjacent dots. In this case tunneling between like and opposite valley eigenstates is in effect a random variable and cannot be controlled. We suggest a resonant tunneling experiment that can identify the matrix elements for tunneling between like and opposite valley eigenstates.

Exchange coupling in silicon quantum dots: Theoretical considerations for quantum computation

We study exchange coupling in Si double quantum dots, which have been proposed as suitable candidates for spin qubits due to their long spin coherence times. We discuss in detail two alternative schemes which have been proposed for implementing spin qubits in quantum dots. One scheme uses spin states in a single dot and the interdot exchange coupling controls interactions between unbiased dots. The other scheme employs the singlet and triplet states of a biased double dot as the two-level system making up the qubit and exchange controls the energy splitting of the levels. Exchange in these two configurations depends differently on system parameters. Our work relies on the Heitler-London approximation and the Hund-Mulliken molecular orbital method. The results we obtain enable us to investigate the sensitivity of the system to background charge fluctuations and determine the conditions under which optimal spots, at which the influence of the charge noise is minimized, may exist in Si double quantum dot structures.

Quantum dot spin qubits in silicon: Multivalley physics

Research on Si quantum dot spin qubits is motivated by the long spin coherence times measured in Si, yet the orbital spectrum of Si dots is increased as a result of the valley degree of freedom. The valley degeneracy may be lifted by the interface potential, which gives rise to a valley-orbit coupling but the latter depends on the detailed structure of the interface and is generally unknown a priori. These facts motivate us to provide an extensive study of spin qubits in Si double quantum dots, accounting fully for the valley degree of freedom and assuming no prior knowledge of the valley-orbit coupling. For single-spin qubits, we analyze the spectrum of a multivalley double quantum dot, discuss the initialization of one qubit, identify the conditions for the lowest energy two-electron states to be a singlet and a triplet well separated from other states, and determine analytical expressions for the exchange splitting. For singlet-triplet qubits, we analyze the single-dot spectrum and initialization process, the double-dot spectrum, singlet-triplet mixing in an inhomogeneous magnetic field, and the peculiarities of spin blockade in multivalley qubits. We review briefly the hyperfine interaction in Si and discuss its role in spin blockade in natural Si, including intravalley and intervalley effects. We study the evolution of the double-dot spectrum as a function of magnetic field. We address briefly the situation in which the valley-orbit coupling is different in each dot due to interface roughness. We propose a new experiment for measuring the valley splitting in a single quantum dot. We discuss the possibility of devising other types of qubits in Si QDs, and the size of the intervaley coupling due to the Coulomb interaction.

Dephasing of Si spin qubits due to charge noise

Spin qubits in silicon quantum dots can have long coherence times, yet their manipulation relies on the exchange interaction, through which charge noise can induce decoherence. Charge traps near the interface of a Si heterostructure lead to fluctuations in the quantum-dot confinement and barrier potentials, which cause gating errors and two-spin dephasing. We quantify these effects in Si double quantum dots using a realistic model of noise. Specifically, we consider both random telegraph noise from a few traps good for dots grown on submicron wafers and 1/f noise from many traps good for larger wafers appropriate for quantum dot arrays. We give estimates of gate errors for single-spin qubit architectures and dephasing in singlet-triplet qubits.

Spin orientation of holes in quantum wells

This paper reviews the spin orientation of spin-3/2 holes in quantum wells. We discuss the Zeeman and Rashba spin splitting in hole systems that are qualitatively different from their counterparts in electron systems. We show how a systematic understanding of the unusual spin-dependent phenomena in hole systems can be gained using a multipole expansion of the spin density matrix. As an example we discuss spin precession in hole systems that can give rise to an alternating spin polarization. Finally, we discuss the qualitatively different regimes of hole spin polarization decay in clean and dirty samples.

Realizing singlet-triplet qubits in multivalley Si quantum dots

There has been significant progress in the implementation and manipulation of singlet-triplet qubits in GaAs quantum dots. Given the considerably longer spin coherence times measured in Si, considerable interest has been generated recently in Si quantum dots. The physics of these systems is considerably more complex than the physics of GaAs quantum dots owing to the presence of the valley degree of freedom, which constitutes the focus of this work. In this paper we investigate the physics of Si quantum dots and focus on the feasibility of quantum coherent singlet-triplet qubit experiments analogous to those performed in GaAs. This additional degree of freedom greatly increases the complexity of the ground state and gives rise to highly nontrivial and interesting physics in the processes of qubit initialization, coherent manipulation and readout. We discuss the operational definition of a qubit in Si-based quantum dots. We find that in the presence of valley degeneracy a singlet-triplet qubit cannot be constructed, whereas for large valley splitting

Generation of spin currents and spin densities in systems with reduced symmetry.

(⪢{k}_{B}T)

Anomalous Hall response of topological insulators

the experiment is similar to GaAs. We show that experiments on singlet-triplet qubits analogous to those in GaAs would provide a method for estimating the valley splitting in Si. A Zeeman field distinguishes between different initialized states for any valley splitting and provides a tool to determine the size of this splitting.

Steady states of spin distributions in the presence of spin-orbit interactions

We show that the spin-current response of a semiconductor crystal to an external electric field is considerably more complex than previously assumed. While in systems of high symmetry only the spin-Hall components are allowed, in systems of lower symmetry other non-spin-Hall components may be present. We argue that, when spin-orbit interactions are present only in the band structure, the distinction between intrinsic and extrinsic contributions to the spin current is not useful. We show that the generation of spin currents and that of spin densities in an electric field are closely related, and that our general theory provides a systematic way to distinguish between them in experiment. We discuss also the meaning of vertex corrections in systems with spin-orbit interactions.