No abstract

The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates O(N 4 ) independent variables, where N is the number of interacting states (e.g. sites of a real-space discretization). In order to include the flow equation for the two-particle vertex one needs to make further approximations if N becomes too large. We present such an approximation scheme, called the coupled-ladder approximation, for the special case of an onsite interaction. Like the generic third-order-truncated fRG, the coupled-ladder approximation is exact to second order and is closely related to a simultaneous treatment of the random phase approximation in all channels, i.e. summing up parquet-type diagrams. The scheme is applied to a one-dimensional model describing a quantum point contact.

Quantum point contacts (QPCs) and quantum dots (QDs), two elementary building blocks of semiconducting nanodevices, both exhibit famously anomalous conductance features: the 0.7-anomaly in the former case, the Kondo effect in the latter. For both the 0.7-anomaly and the Kondo effect, the conductance shows a remarkably similar low-energy dependence on temperature T , source-drain voltage V sd and magnetic field B. In a recent publication [F. Bauer et al., Nature, 501, 73 (2013)], we argued that the reason for these similarities is that both a QPC and a Kondo QD (KQD) feature spin fluctuations that are induced by the sample geometry, confined in a small spatial regime, and enhanced by interactions. Here we further explore this notion experimentally and theoretically by studying the geometric crossover between a QD and a QPC, focussing on the B-field dependence of the conductance. We introduce a one-dimensional model with local interactions that reproduces the essential features of the experiments, including a smooth transition between a KQD and a QPC with 0.7-anomaly. We find that in both cases the anomalously strong negative magnetoconductance goes hand in hand with strongly enhanced local spin fluctuations. Our experimental observations include, in addition to the Kondo effect in a QD and the 0.7-anomaly in a QPC, Fano interference effects in a regime of coexistence between QD and QPC physics, and Fabry-Perot-type resonances on the conductance plateaus of a clean QPC. We argue that Fabry-Perot-type resonances occur generically if the electrostatic potential of the QPC generates a flatter-than-parabolic barrier top.

We study how the conductance of a quantum point contact is affected by spin-orbit interactions, for systems at zero temperature both with and without electron-electron interactions. In the presence of spin-orbit coupling, tuning the strength and direction of an external magnetic field can change the dispersion relation and hence the local density of states in the point contact region. This modifies the effect of electron-electron interactions, implying striking changes in the shape of the 0.7-anomaly and introducing additional distinctive features in the first conductance step.PACS numbers: 71.70. Ej, Spin-orbit interactions (SOI) play an important role in a variety of fields within mesoscopic physics, such as spintronics and topological quantum systems. In this Letter we study the effects of SOI on the conductance of a quantum point contact (QPC), a one-dimensional constriction between two reservoirs [1,2]. The linear conductance G of a QPC is quantized in multiples of G Q = 2e2 /h, showing the famous staircase as a function of gate voltage. In addition, at the onset of the first plateau, measured curves show a shoulderlike structure near 0.7G Q [3]. In this regime QPCs exhibit anomalous behavior in the electrical and thermal conductance, noise, and thermopower [3][4][5][6][7][8][9][10][11]. The microscopic origin of this 0.7-anomaly has been the subject of a long debate [12][13][14][15][16][17][18]. It has recently been attributed to a strong enhancement of the effects of electron-electron interactions (EEI) by a smeared van Hove singularity in the local density of states (LDOS) at the bottom of the lowest QPC subband [15,18]. While this explains the 0.7-anomaly without evoking SOI, the presence of SOI can change the dispersion relation and hence the LDOS, thus strongly affecting the shape of the 0.7-anomaly. Previous studies of SOI in QPCs exist [19][20][21][22][23], but not with the present emphasis on their interplay with the QPC barrier shape and EEI, which are crucial for understanding the effect of SOI on the 0.7-anomaly.Setup. We consider a heterostructure forming a twodimensional electron system (2DES) in the xy-plane. Gate voltages are used to define a smooth, symmetric potential which splits the 2DES into two leads, connected by a short, one-dimensional channel along the x-axis: the QPC [1,2]. The transition between the leads and the QPC is adiabatic. We also assume the confining potential in the transverse direction to be so steep that the subband spacing is much larger than all other energy scales relevant for transport, in particular those related to the magnetic field and SOI, and consider only transport in the first subband, corresponding to the lowest transverse mode. This can be described by a one-dimensional model with a smooth potential barrier and local EEI [18]. The magnetic field B is assumed to be in the xy-plane, acting as a pure Zeeman field, without orbital effects.A moving electron in an electric field can experience an effective magnetic field B SOI proportional to its momentum k. D...

We present a Keldysh-based derivation of a formula, previously obtained by Oguri using the Matsubara formalisum, for the linear conductance through a central, interacting region coupled to non-interacting fermionic leads. Our starting point is the well-known Meir-Wingreen formula for the current, whose derivative w.r.t. to the source-drain voltage yields the conductance. We perform this derivative analytically, by exploiting an exact flow equation from the functional renormalization group, which expresses the flow w.r.t. voltage of the self-energy in terms of the two-particle vertex. This yields a Keldysh-based formulation of Oguri's formula for the linear conductance, which facilitates applying it in the context of approximation schemes formulated in the Keldysh formalism. (Generalizing our approach to the non-linear conductance is straightforward, but not pursued here.) -We illustrate our linear conductance formula within the context of a model that has previously been shown to capture the essential physics of a quantum point contact in the regime of the 0.7 anomaly. The model involves a tight-binding chain with a one-dimensional potential barrier and onsite interactions, which we treat using second order perturbation theory. We show that numerical costs can be reduced significantly by using a non-uniform lattice spacing, chosen such that the occurence of artificial bound states close to the upper band edge is avoided.

A quantum point contact (QPC) causes a one‐dimensional constriction on the spatial potential landscape of a two‐dimensional electron system. By tuning the voltage applied on the QPC gates which form the constriction at low temperatures the resulting regular step‐like electron conductance quantization can show an additional kink near pinch‐off around 0.7false(2e2/hfalse), called 0.7‐anomaly. In a recent publication, we presented a combination of theoretical calculations and transport measurements that lead to a detailed understanding of the microscopic origin of the 0.7‐anomaly. Functional renormalization group‐based calculations were performed exhibiting the 0.7‐anomaly even when no symmetry‐breaking external magnetic fields are involved. According to the calculations the electron spin susceptibility is enhanced within a QPC that is tuned in the region of the 0.7‐anomaly. Moderate externally applied magnetic fields impose a corresponding enhancement in the spin magnetization. In principle, it should be possible to map out this spin distribution optically by means of the Faraday rotation technique. Here we report the initial steps of an experimental project aimed at realizing such measurements. Simulations were performed for a heterostructure designed to combine transport and optical studies. Based on the simulation results a sample was built and its basic transport and optical properties were investigated.