**UPCOMING EVENTS**

**Mikhail Feigelman:** “Mean-field theory of first-order quantum superconductor-insulator transition”

**Date:** Tuesday, September 10, 2024 at 11:15

**Location:** Seminar room for physics (JSI main building)

Recent experimental studies on strongly disordered indium oxide films have revealed an unusual first-order quantum phase transition between the superconducting and insulating states (SIT). This transition is characterized by a discontinuous jump from non-zero to zero values of superfluid stiffness at the critical point, contradicting the conventional “scaling scenario” typically associated with SIT. In this paper, we present a theoretical framework for understanding this first-order transition. Our approach is based on the concept of competition between two fundamentally distinct ground states that arise from electron pairs initially localized by strong disorder: the superconducting state and the Coulomb glass insulator. These ground states are distinguished by two crucially different order parameters, suggesting a natural expectation of a discontinuous transition between them at T = 0. This transition occurs when the magnitudes of the superconducting gap ∆ and the Coulomb gap EC become comparable. Additionally, we extend our analysis to low non-zero temperatures and provide a mean-field “phase diagram” in the plane of (T/∆, EC/∆). Our results reveal the existence of a natural upper bound for the kinetic inductance of strongly disordered superconductors.

**PAST EVENTS**

**Charles Marcus:** “Experiments in Frustrated Josephson Systems”

**Date:** Tuesday, August 13, 2024 at 15:00

**Location:** Seminar room for physics (JSI main building)

This talk will explore in an experimentally accessible system how complex classical physics with frustration evolves into the quantum realm. We will explore this question in Josephson junction arrays using hybrid 2D semiconductor-superconductor hybrids, which allow gate-voltage control of Josephson coupling. Connections to the superconductor-insulator transition, anomalous metals, and topologically protected qubits will be considered. Note: this talk is about experiments.

**Z. D. Kvon:** “Two-dimensional semimetal with strong disorder: Anderson localization, 2D topological Anderson insulator,

unusual mesoscopic conductance fluctuations”

**Date:** Thursday, August 8, 2024 at 15:00

**Location:** Seminar room for physics (JSI main building)

The talk is devoted to the transport properties of strongly disordered 2D system in HgTe quantum wells with semimetallic energy spectrum. In the beginning, it will be told about experimentally found Anderson localization of in this system. The behavior of this localization is fundamentally different from that observed in widely studied two-dimensional one-component electron or hole systems. It is found that such system exhibits two-stage localization: two -dimensional holes are localized first, as particles with the effective mass almost an order of magnitude larger than that of electrons. Then, electrons become localized. It is also found that the system under study does not exhibit any metal–insulator transition: even at the electrical conductivity, an insulator-like temperature dependence is observed. The results for the first time draw attention to the problem of the nature of Anderson localization in a two-dimensional electron–hole system.

Then it was observed no temperature dependence of the resistance of one-dimensional (1D) edge current states in the system studied, indicating the absence of 1D localization. This implies that in quantum wells with an inverted spectrum, there is no topological protection against localization for electrons and holes in the bulk of the quantum well, while 1D edge current states are topologically protected. Consequently, a fundamentally new type of 2D topological insulator, referred to as the 2D topological Anderson insulator, is realized for the first time. Additionally, we observed two quantum phase transitions induced by a magnetic field of approximately 0.5 T in the studied sys- tem: First, from an ordinary Anderson insulator state to a quantum Hall liquid state, and second, from a 2D topological Anderson insulator state to a quantum Hall liquid state.

Finaly, the behavior of unusual mesoscopic conductance fluctuations in HgTe-based two-dimensional semimetal in weak localization regime will be discussed. These fluctuations exist in macroscopic samples with characteristic sizes higher than 100 μm and have anomalously high value (≈ 10e2/h) and anomalous gate voltage, magnetic field (quasiperiodicity and supression at B > 0.5 T) and temperature (exponentialy strong) dependences. Also their amplitude critically depends on disorder degree. Moreover it was found that at the same conductivity value (about 1 kOhm/square) they completely absent in electron metal state realized in the same sample. On the basis of these experimental results it is suggested that the discovered unusual mesoscopic fluctuations of resistance are the result of the formation of a collective state, which is a square grid of electronic conductors in the field of the fluctuation potential of impurities, screened by heavy holes, the concentration of which significantly exceeds the concentration of significantly more light electrons. Finding the explanation of the formation of such a state is an interesting task for the theory of two-dimensional correlated systems.

**Elizaveta Safonova**: “Intensity statistics inside an open wave-chaotic cavity with broken time-reversal invariance”

**Date**: Friday, June 7, 2024 at 13:00

**Location**: Seminar room 133 ( Jadranska ulica 21)

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density P(I) for the single-point intensity I decays as a powerlaw for large intensities: P(I) ∼ I −(M+2), provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law P(I) ∼ exp(−I/I) which turns out to be valid only in the limit M → ∞. We also find the joint probability density of intensities I1, . . . , IL in L > 1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For L → ∞ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions

**Andrei Levin:** “Effect of superconductivity on non-uniform magnetization in dirty superconductor-ferromagnet junctions”

**Date:** Friday, May 24, 2024 at 13:00

**Location:** Seminar room for physics (JSI main building)

We consider a junction between a bulk superconductor and a thin ferro-magnetic layer on its surface (SF junction) with nonuniform magnetization. In the absence of the superconductor, the most energetically favorable state of the ferromagnet is uniform. On the other hand, Cooper pairs from the superconductor can more efficiently diffuse into the ferromagnet if its magnetization changes in space rapidly enough [1, 2]. We demonstrate that the competition between these two effects leads to the second order phase transition between uniformly magnetized and helical states of the ferromagnet.

We assume the junction is in the dirty limit and the ferromagnetic layer is sufficiently thin. In addition, we also assume a tunnel boundary between the superconductor and the ferromagnet. These assumptions allow us to describe the hybrid system in the framework of the 2D Usadel equation.

We have minimized the free energy of the system allowing for an arbitrary nonuniform magnetic state and constructed a Landau functional expanding the free energy in powers of magnetization gradients. This calculation establishes conditions for the phase transition between uniform and helical magnetic states. In particular, we have observed a quite unexpected “resonance” phenomenon: when the exchange energy of the ferromagnet equals the proximity-induced superconducting order parameter, transition to the helical state occurs irrespective of the value of ferromagnetic stiffness.

Then we explored a general case of arbitrary system parameters. In particular, we determine the magnitude of the helical state wave vector far from the phase transition. The final result was obtained numerically with analytical formulas for different asymptotic regions.

Finally, we described the area of the phase transition in the case of trans-parent boundary between the superconductor and the ferromagnet. Our estimations have shown that the nonuniform magnetic state with a relatively large exchange field in the ferromagnet is possible.

[1] F. S. Bergeret, K. B. Efetov, A. I. Larkin, Phys. Rev. B 62, 11872 (2000).

[2] F. S Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod. Phys. 77, 1321 (2005)

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**Benjamin Sacépé:** ” The fate of the superfluid density near the superconductor-insulator transition”

**Date:** Thursday, April 25, 2024 at 13:00

**Location:** Seminar room for physics (JSI main building)

Superconducting films of amorphous Indium Oxide (a:InO) undergo a transition to insulation with increasing disorder, which is due to the localization of pre-formed Cooper pairs. The continuous decrease in critical temperature as critical disorder is approached suggests an equally continuous suppression of superfluid density. In this talk, I will discuss a systematic study of the superfluid density measured via plasmon dispersion spectroscopy of microwave resonators made of a:InO, combined with DC resistivity measurements, as a function of disorder. We observed that the superfluid stiffness defines the superconducting critical temperature over a wide range of disorder, highlighting the dominant role of phase fluctuations. Furthermore, we found that the superfluid density remains surprisingly finite at the critical disorder, indicating an unexpected first-order nature of the disorder-driven quantum phase transition to an insulator.

**Mikhail Feigel’man: **“Andreev conductance in disordered superconductor – ferromagnet junctions with spin-orbit scattering”

**Date:** Friday, April 19, 2024 at 11:15

**Location:** Seminar room for physics (JSI main building)

We calculate the conductance of a junction between a disordered superconductor and a very strong half-metallic ferromagnet admitting electrons with only one spin projection. A usual mechanism of Andreev reflection is strongly suppressed in this case since Cooper pairs are composed of electrons with opposite spins. However, this obstacle can be overcome if we take into account spin-orbit scattering inside the superconductor. Spin-orbit scattering induces a fluctuational (zero on average) spin-triplet component of the superconducting condensate, which is enough to establish Andreev transport into a strong ferromagnet. This remarkably simple mechanism is quite versatile and can explain long-range triplet proximity effect in a number of experimental setups. One particular application of the suggested effect is to measure the spin-orbit scattering time \tau_{\rm SO} in disordered superconducting materials. The value of Andreev conductance strongly depends on the parameter \Delta\tau_{\rm SO} and can be noticeable even in very disordered but relatively light metals like granular aluminum.

**Kamran Behnia: **“Heat propagation in liquid 3He and metallic Fermi liquids”

**Date:** Thursday, April 11, 2024 at 15:30

**Location:** JSI large lecture hall

The normal liquid 3He conforms to Landau’s Fermi liquid picture but only at very low temperature. We have recently shown that the available experimental data can be accounted for assuming that the thermal conductivity is the sum of two contributions: one by quasi-particles (varying as the inverse of temperature) and another by a hydrodynamic sound mode (following the square root of temperature). The first component has been known for decades. The second is zero sound in the hydrodynamic limit [2]. The importance of a short wavelength sound mode was anticipated by early works on weak crystallization [3] and 2kF rotons [4]. We will discuss its role in the transport properties of metallic Fermi liquids whose resistivity displays a quadratic temperature dependence at low T [5] and consequences for the `strange metal’ [6] problematic.

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**Serafim Babkin:** * “*Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field*”*

**Date:** Friday, February 23, 2024 at 11:15

**Location: **C building, 2nd floor

Two-dimensional semiconductor-superconductor heterostructures form the foundation of numerous nanoscale physical systems. However, measuring the properties of such heterostructures, and characterizing the semiconductor in-situ is challenging. A recent experimental study [arXiv:2107.03695] was able to probe the semiconductor within the heterostructure using microwave measurements of the superfluid density. This work revealed a rapid depletion of superfluid density in semiconductor, caused by the in-plane magnetic field which in presence of spin-orbit coupling creates so-called Bogoliubov Fermi surfaces. The experimental work used a simplified theoretical model that neglected the presence of non-magnetic disorder in the semiconductor, hence describing the data only qualitatively. Motivated by experiments, we introduce a theoretical model describing a disordered semiconductor with strong spin-orbit coupling that is proximitized by a superconductor. Our model provides specific predictions for the density of states and superfluid density. Presence of disorder leads to the emergence of a gapless superconducting phase, that may be viewed as a manifestation of Bogoliubov Fermi surface. When applied to real experimental data, our model showcases excellent quantitative agreement, enabling the extraction of material parameters such as mean free path and mobility, and estimating g-tensor after taking into account the orbital contribution of magnetic field. Our model can be used to probe in-situ parameters of other superconductor-semiconductor heterostructures and can be further extended to give access to transport properties.

**Anton Khvalyuk:** *» Near-power-law temperature dependence of the superfluid stiffness in strongly disordered superconductors «*

**Date:** Thursday, January 23, 2024 at 11:15

**Location:** Seminar room for physics (JSI main building)

Superconductors are characterized by appearance of a finite current density j = – 1/c \; \rho_S A in response to a locally homogeneous time-independent external vector potential A, with \rho_S being the superfluid density. In relatively clean BCS superconductors, \rho_S only weakly depends on temperature due an exponentially low density of thermal quasiparticles. However, strong nonmagnetic disorder is known to drastically modify the situation. Notably, the normal state eventually becomes insulating with a hard gap in the single-particle density of states – a so-called pseudogap. In this talk, we report direct measurement of \rho_S(T) in a strongly disordered pseudo-gaped superconductor, amorphous \rm InO_x, revealing an unusually strong power-law suppression of the superfluid stiffness \delta \rho_S (T) \propto T^b at T \ll T_c, with b \sim 1.6. We then address this issue theoretically within a certain model of a disordered superconductor with a pseudogap, resulting in a similar low-temperature power-law behavior with exponent b \sim 1.6 – 3 being disorder-dependent. This power-law suppression of the superfluid density occurs mainly due to the broad distribution of the superconducting order parameter that is known to exist in such superconductors [arXiv:1012.3630]. Our observations demonstrate the existence of low-energy excitations and imply a new channel of dissipation associated to the latter, while the pseudogap rules out the quaisparticles. Our findings have implications for the use of strongly disordered superconductors as superinductance in quantum circuits. The talk is based on our recent paper [arXiv:2311.15126].

**Anton Khvalyuk:** *»Influence of Trotterization error on single-particle tunneling«*

**Date**: Thursday, January 11, 2024 at 15:00

**Location**: F1, Faculty of Mathematics and Physics

**Zheng Vitto Han**: *»**Exotic electronic phases in graphene tuned by a quantum superlattice**«*

**Date**: Thursday, January 11, 2024 at 11:15

**Location**: Seminar room for physics, JSI main building,

In this talk, we will introduce a model system: synergetic interplay between two layers of 2D interacting interacted electronic system, and the emerging phenomena. Taking the van der Waal hybrid system of graphene/CrOCl for example, our theoretical considerations suggest that, due to e-e interactions, the electrons filled (charge transferred from graphene with the help of vertical electrical field) in the surface state (mainly in the Cr-3d orbital in CrOCl, which is about 0.7 nm below graphene) of CrOCl can spontaneously form a long wavelength order, i.e., it undergoes a Wigner crystallization. Such a long wavelength charge order can act as a quantum superlattice, which exerts a moiré-like super potential to the graphene placed on top of it, and further leads to a series of exotic interaction-driven phenomena, including unusually robust quantum Hall phase [1], and exciton-enhanced correlated insulator [2]. Our findings suggest that the paradigm of charge transfer can play key roles in the engineering of quantum electronic states, when the e-e interactions are taking effects. And, according to theory, such a quantum superlattice may be a universal phenomenon in many layered materials [3], and enriched physical phenomena are yet to be discovered.

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**Aleksey Lunkin**: *»**The butterfly effect in a Sachdev-Ye-Kitaev quantum dot system**«*

**Date**: Thursday, January 4, 2024 at 14:00

**Location**: Kuščerjev seminar, Jadranska 19

**The talk will also be broadcast over Zoom via the following link: **https://uni-lj-si.zoom.us/j/4933857795?pwd=TnkycEJsYnRuemdjR0l6czVnTHRLUT09

**Dmitry E. Kiselov: »**

*Theory of superconductivity due to Ngai’s mechanism in lightly doped SrTiO3«*

**Date**: Tuesday, December 5, 2023 at 11:15

**Location**: Seminar room for physics, JSI main building

We develop a theory of superconducting pairing in low-density Strontium titanate based upon the idea of quadratic coupling of electron density to soft transverse optical phonons [1]. This coupling leads to static attractive potential between electrons which decays in real space exponentially with the length $l_{eff}$ that scales inversely with soft optical gap $\omega_T$ . For low electron densities $n \leq 10^{18} cm^{-3}$ attraction between electrons can be considered local and superconducting transition temperature $T_c$ is calculated using old results [2]. We use independently obtained magnitude g of the quadratic coupling strength and find $T_c(n)$ dependence in agreement with experimental data [3] for low doping. Next, we show that suppression of $T_c$ by hydrostatic pressure [4] and strong increase of $T_c$ due to isotop substitution $^{16}O \to\,^{18}O$ observed in [5] are qualitatively explained within our theory.

[1] K. L. Ngai, Phys. Rev. Lett. 32, 215 (1974)

[2] L. P. Gor’kov and T. K. Melik-Barkhudarov, Sov. Phys. – JETP 40, 1452 (1961)

[3] X. Lin, et al, Phys. Rev. Lett. 112, 207002 (2014).

[4] C. Enderlein, et al, Nature Comm. (2020)

[5] A. Stucky, et al, Scientific Reports, 6:37582 (2016

**Pavel Ostrovsky**: *»**Josephson effect in strongly disordered metallic wires**«*

**Date**: Friday, November 17, 2023 at 14:00

**Location**: Kuščerjev seminar, Jadranska 19

**The talk will also be broadcast over Zoom via the following link: **https://uni-lj-si.zoom.us/j/4933857795?pwd=TnkycEJsYnRuemdjR0l6czVnTHRLUT09

**Anton Potočnik** : *»The path towards superconducting quantum computers: interfacing qubits with classical electronics at 10 mK«*

**Date**: Monday, October 16, 2023 at 16:15

**Location**: F1, Jadranska 19

**Vladimir Kravtsov** : *»A renormalization group analysis of the Anderson localization problem in large and infinite dimensions«*

**Date**: Thursday, October 19, 2023 at 15:00

**Location**: Kuščerjev seminar, Jadranska 19, 4th floor

**Igor Poboiko** : *»Theory of free fermions under random projective measurements«*

**Date**: Thursday, October 12, 2023 at 15:00

**Location**: Kuščerjev seminar, Jadranska 19, 4th floor