arXiv subjects

Piet W. Brouwer

Publications and source records attributed to Piet W. Brouwer.

At least 91 records · Page 5Linked to original sources

arXiv2013

A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors

We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time reversal symmetry in the presence of interactions. For a closed geometry, Fidkowski and Kitaev have shown that such systems have a $\mathbb{Z}_8$ topological classification. We show that in the weak coupling limit, these systems retain a unitary scattering matrix at zero temperature, with a topological index given by the trace of the Andreev reflection matrix, $\mbox{tr}\, r_{\rm he}$. With interactions, $\mbox{tr}\, r_{\rm he}$ generically takes on the finite set of values $0$, $\pm 1$, $\pm 2$, $\pm 3$, and $\pm 4$. We show that the two topologically equivalent phases with $\mbox{tr}\, r_{\rm he} = \pm 4$ support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.

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arXiv2013

Spin-wave-induced corrections to the electronic density of states in metallic ferromagnets

We calculate the correction to the electronic density of states in a disordered ferromagnetic metal induced by spin-wave mediated interaction between the electrons. Our calculation is valid for the case that the exchange splitting in the ferromagnet is much smaller than the Fermi energy, but we make no assumption on the relative magnitude of the exchange splitting and the elastic electronic scattering time. In the "clean limit", where the exchange splitting is much larger than the electronic scattering rate, we find a correction with a T^{d/2} temperature dependence, where d is the effective dimensionality of the ferromagnet. In the opposite "dirty limit" the density-of-states correction is a non-monotonous function of energy and temperature.

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arXiv2013

Semiclassical theory of speckle correlations

Coherent wave propagation in random media results in a characteristic speckle pattern, with spatial intensity correlations with short-range and long-range behavior. Here, we show how the speckle correlation function can be obtained from a ray picture for two representative geometries: A chaotic cavity and a random waveguide. Our calculation allows us to study the crossover between a "ray limit" and a "wave limit", in which the Ehrenfest time $τ_E$ is larger or smaller than the typical transmission time $τ_D$, respectively. Remarkably, long-range speckle correlations persist in the ray limit $τ_E \gg τ_D$.

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arXiv2013

Topological equivalence of crystal and quasicrystal band structures

A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an explicit construction, we here argue that the end states have precisely the same origin as their counterparts in commensurate models and that incommensurability does not in fact provide a meaningful connection to the topological classification of systems in higher dimensions. In particular, we show that it is possible to smoothly interpolate between states with commensurate and incommensurate modulation parameters without closing the band gap and without states crossing the band gap.

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arXiv2013

Semiclassical theory of the interaction correction to the conductance of antidot arrays

Electron-electron interactions are responsible for a correction to the conductance of a diffusive metal, the "Altshuler-Aronov correction" $δG_{AA}$. Here we study the counterpart of this correction for a ballistic conductor, in which the electron motion is governed by chaotic classical dynamics. In the ballistic conductance, the Ehrenfest time $τ_{E}$ enters as an additional time scale that determines the magnitude of quantum interference effects. The Ehrenfest time effectively poses a short-time threshold for the trajectories contributing to the interaction correction. As a consequence, $δG_{AA}$ becomes exponentially suppressed if the Ehrenfest time is larger than the dwell time or the inverse temperature. We discuss the explicit dependence on Ehrenfest time in quasi-one and two-dimensional antidot arrays. For strong interactions, the sign of $δG_{AA}$ may change as a function of temperature for temperatures in the vicinity of $\hbar/τ_{E}$.

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arXiv2013

Interplay of Aharonov-Bohm and Berry phases in gate-defined graphene quantum dots

We study the influence of a magnetic flux tube on the possibility to electrostatically confine electrons in a graphene quantum dot. Without magnetic flux tube, the graphene pseudospin is responsible for a quantization of the total angular momentum to half-integer values. On the other hand, with a flux tube containing half a flux quantum, the Aharonov-Bohm phase and Berry phase precisely cancel, and we find a state at zero angular momentum that cannot be confined electrostatically. In this case, true bound states only exist in regular geometries for which states without zero-angular-momentum component exist, while non-integrable geometries lack confinement. We support these arguments with a calculation of the two-terminal conductance of a gate-defined graphene quantum dot, which shows resonances for a disc-shaped geometry and for a stadium-shaped geometry without flux tube, but no resonances for a stadium-shaped quantum dot with a $π$-flux tube.

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arXiv2012

Enhanced zero-bias Majorana peak in disordered multi-subband quantum wires

A recent experiment [Mourik et al., Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and the formation of Majorana bound states. Motivated by this experiment, we consider the signature of Majorana bound states in the differential tunneling conductance of multi-subband wires. We show that the weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of subbands, when disorder is added to the end of the quantum wire. We also consider how the topological phase transition is reflected in the gap structure of the current-voltage characteristic.

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arXiv2012

Impurity-assisted Andreev reflection at a spin-active half-metal-superconductor interface

The Andreev reflection amplitude at a clean interface between a half-metallic ferromagnet (H) and a superconductor (S) for which the half metal's magnetization has a gradient perpendicular to the interface is proportional to the excitation energy $\varepsilon$ and vanishes at $\varepsilon=0$ [Béri {\em et al.}, Phys.\ Rev.\ B {\bf 79}, 024517 (2009)]. Here we show that the presence of impurities at or in the immediate vicinity of the HS interface leads to a finite Andreev reflection amplitude at $\varepsilon=0$. This impurity-assisted Andreev reflection dominates the low-bias conductance of a HS junction and the Josephson current of an SHS junction in the long-junction limit.

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arXiv2012

Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling

Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to s-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire.

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arXiv2011

Resonant scattering in graphene with a gate-defined chaotic quantum dot

We investigate the conductance of an undoped graphene sheet with two metallic contacts and an electrostatically gated island (quantum dot) between the contacts. Our analysis is based on the Matrix Green Function formalism, which was recently adapted to graphene by Titov {\em et al.} [Phys.\ Rev.\ Lett.\ {\bf 104}, 076802 (2010)]. We find pronounced differences between the case of a stadium-shaped dot (which has chaotic classical dynamics) and a disc-shaped dot (which has integrable classical dynamics) in the limit that the dot size is small in comparison to the distance between the contacts. In particular, for the stadium-shaped dot the two-terminal conductance shows Fano resonances as a function of the gate voltage, which cross-over to Breit-Wigner resonances only in the limit of completely separated resonances, whereas for a disc-shaped dot sharp Breit-Wigner resonances resulting from higher angular momentum remain present throughout.

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arXiv2011

Dephasing in ferromagnetic nanowires: The role of spin waves

We present a calculation of the dephasing time of electrons in a ferromagnet relevant for the conductance fluctuations. We focus on the contribution from the interaction with spin waves. Explicit results are presented for a quasi-one-dimensional systems. Going beyond previous calculations, we do not restrict ourselves to the limit of a small exchange splitting compared to the electronic elastic scattering time, nor does our calculation rely on the diffusion approximation to describe electronic transport.

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arXiv2011

Topological classification of adiabatic processes

Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter upon rolling the insulator up to a cylinder and threading it with a time dependent flux. In this article we extend the classification of topological pumps to the Wigner Dyson and chiral classes, coupled to multi-channel leads. The topological index distinguishing different topological classes is formulated in terms of the scattering matrix of the system. We argue that similar to topologically non-trivial insulators, topological pumps are characterized by the appearance of protected gapless end states during the course of a pumping cycle. We show that this property allows for the pumping of quantized charge or spin in the weak coupling limit. Our results may also be applied to two dimensional topological insulators, where they give a physically transparent interpretation of the topologically non-trivial phases in terms of scattering matrices.

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arXiv2011

A topological classification of interaction-driven spin pumps

When adiabatically varied in time, certain one-dimensional band insulators allow for the quantized noiseless pumping of spin even in the presence of strong spin orbit scattering. These spin pumps are closely related to the quantum spin Hall system, and their properties are protected by a time-reversal restriction on the pumping cycle. In this paper we study pumps formed of one-dimensional insulators with a time-reversal restriction on the pumping cycle and a bulk energy gap which arises due to interactions. We find that the correlated gapped phase can lead to novel pumping properties. In particular, systems with $d$ different ground states can give rise to $d+1$ different classes of spin pumps, including a trivial class which does not pump quantized spin and $d$ non-trivial classes allowing for the pumping of quantized spin $\hbar/n $ on average per cycle, where $1\leq n\leq d$. We discuss an example of a spin pump that transfers on average spin $ \hbar/2$ without transferring charge.

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arXiv2011

Probability distribution of Majorana end-state energies in disordered wires

One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy $ε_0$ that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of $ε_0$ is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level $ε_1$ has an algebraic tail at small $ε_1$. Our findings have implications for the speed at which a topological quantum computer can be operated.

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arXiv2010

Andreev reflection from non-centrosymmetric superconductors and Majorana bound state generation in half-metallic ferromagnets

We study Andreev reflection at an interface between a half metal and a superconductor with spin-orbit interaction. While the absence of minority carriers in the half metal makes singlet Andreev reflection impossible, the spin-orbit interaction gives rise to triplet Andreev reflection, i.e., the reflection of a majority electron into a majority hole or vice versa. As an application of our calculation, we consider a thin half metal film or wire laterally attached to a superconducting contact. If the half metal is disorder free, an excitation gap is opened that is proportional to the spin-orbit interaction strength in the superconductor. For electrons with energy below this gap a lateral half-metal--superconductor contact becomes a perfect triplet Andreev reflector. We show that the system supports localized Majorana end states in this limit.

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arXiv2010

Andreev reflection at half-metal-superconductor interfaces with non-uniform magnetization

Andreev reflection at the interface between a half-metallic ferromagnet and a spin-singlet superconductor is possible only if it is accompanied by a spin flip. Here we calculate the Andreev reflection amplitudes for the case that the spin flip originates from a spatially non-uniform magnetization direction in the half metal. We calculate both the microscopic Andreev reflection amplitude for a single reflection event and an effective Andreev reflection amplitude describing the effect of multiple Andreev reflections in a ballistic thin film geometry. It is shown that the angle and energy dependence of the Andreev reflection amplitude strongly depends on the orientation of the gradient of the magnetization with respect to the interface. Establishing a connection between the scattering approach employed here and earlier work that employs the quasiclassical formalism, we connect the symmetry properties of the Andreev reflection amplitudes to the symmetry properties of the anomalous Green function in the half metal.

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arXiv2010

Non-Gaussian fluctuations of mesoscopic persistent currents

The persistent current in an ensemble of normal-metal rings shows Gaussian distributed sample-to-sample fluctuations with non-Gaussian corrections, which are precursors of the transition into the Anderson localized regime. We here report a calculation of the leading non-Gaussian correction to the current autocorrelation function, which is of third order in the current. Although the third-order correlation function is small, inversely proportional to the dimensionless conductance $g$ of the ring, the mere fact that it is nonzero is remarkable, since it is an odd moment of the current distribution.

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arXiv2009

Spin torque from tunneling through impurities in a magnetic tunnel junction

We calculate the contribution to the spin transfer torque from sequential tunneling through impurities in a magnetic tunnel junction. For a junction with weakly polarized ferromagnetic contacts, the torque is found to be in the plane spanned by the magnetizations of the ferromagnetic contacts and proportional to $\sin θ$, where $θ$ is the angle between the magnetic moments. If the polarization is larger, the torque acquires a significant out-of-plane component and a different dependence on $θ$.

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